CLAIM OF PRIORITY

[0001] The present application claims priority to U.S. Provisional Patent Application No. 62/886,820, entitled “Hydraulically Amplified Self-Healing Electrostatic (HASEL) Pumps,” filed August 14, 2019.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under grant number 80NSSC18K0962 awarded by NASA. The government has certain rights in the invention.

FIELD OF THE INVENTION

[0003] The present invention relates to soft transducers or actuators and, more particularly, to various pumping systems in which one or more types of hydraulically amplified self-healing electrostatic (HASEL) transducers maybe used.

SUMMARY OF THE INVENTION

[0004] The present disclosure relates to a pumping system including a conduit with an inlet region and an outlet region and a first pump coupled with the conduit between the inlet region and the outlet region. The first pump includes a first actuator chamber configured to house at least a first actuator, a first pump chamber aligned along a longitudinal axis of the conduit, wherein the first pump chamber is in fluid communication with the inlet region and the outlet region, and a first flexible diaphragm separating the first actuator chamber from the first pump chamber.

[0005] Various other aspects and advantages of the invention will be apparent from the following description, figures, and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The present invention is described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the size and relative sizes of layers and regions may be exaggerated for clarity. Like numbers refer to like elements throughout.

[0007] It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention.

[0008] Spatially relative terms, such as “beneath,” “below,” “lower,” “under,” “above,”

“upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” or “under” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary terms “below” and “under” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. In addition, it will also be understood that when a layer is referred to as being “between” two layers, it can be the only layer between the two layers, or one or more intervening layers may also be present.

[0009] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items, and may be abbreviated

[0010] It will be understood that when an element or layer is referred to as being

“on,” “connected to,” “coupled to,” or “adjacent to” another element or layer, it can be directly on, connected, coupled, or adjacent to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to,” “directly coupled to,” or “immediately adjacent to” another element or layer, there are no intervening elements or layers present. Likewise, when light is received or provided “from” one element, it can be received or provided directly from that element or from an intervening element. On the other hand, when light is received or provided “directly from” one element, there are no intervening elements present.

[0011] Embodiments of the invention are described herein with reference to cross- section illustrations that are schematic illustrations of idealized embodiments (and intermediate structures) of the invention. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments of the invention should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. Accordingly, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the actual shape of a region of a device and are not intended to limit the scope of the invention. [0012] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and/or the present specification and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0013] Figures 1A-1C illustrate a cross-sectional view of a pumping system having a flexible electrode which spans a pump chamber, in accordance with an embodiment.

[0014] Figures 1D-1F illustrate a cross-sectional view of a pumping system having a flexible electrode which spans a pump chamber and includes baffled inlet and outlet conduits, in accordance with an embodiment.

[0015] Figures 2A-2C illustrate a cross-sectional view of a pumping system having a flexible electrode extending longitudinally within a pump chamber, in accordance with an embodiment.

[0016] Figures 3A-3C illustrate a cross-sectional view of a pumping system having at least one actuator chamber and at least one expanding actuator therein, in accordance with an embodiment

[0017] Figures 4A, 4B illustrate a cross-sectional view of a pumping system having a plurality of pumps as described with respect to Figures 3A-3C, in accordance with an embodiment [0018] Figures 5A-5C illustrate a cross-sectional view of a pumping system having at least one actuator disposed between an outer conduit and a flexible wall, in accordance with an embodiment.

[0019] Figure 6 illustrates a flow diagram for a method of operating one or more pumps disclosed herein, in accordance with an embodiment.

[0020] Figure 7 illustrates a schematic representation of a pump control system.

[0021] Figures 8A-8E illustrate a “donut” type HASEL actuator, according to one embodiment, in accordance with an embodiment.

[0022] Figure 9 illustrates a pull-in transition of the electrodes of a HASEL actuator upon an increase in the electrostatic force starting to exceed an increase in mechanical restoring force, causing the electrodes to abruptly pull together, in accordance with an embodiment.

[0023] Figures 10A, 10B show additional graphical illustrations of the pull-in instabilities of the donut actuator of Figures 8A-8E, in accordance with an embodiment. [0024] Figures 11A-11C illustrate a stack of the donut-type actuators of Figures 8A- 8E, in accordance with an embodiment.

[0025] Figures 12A, 12B illustrate two different shapes for the donut-type actuators that can exhibit different behaviors because of different electrode layouts, in accordance with an embodiment.

[0026] Figures 13A-13F illustrate an implementation of donut-type HASEL actuators that provides three-dimensional mobility by selectively redistributing a liquid dielectric throughout a ring-shaped deformable shell, in accordance with an embodiment [0027] Figures 14A illustrates an actuation cycle of the donut-type actuator of

Figures 8A-8E, in accordance with an embodiment.

[0028] Figure 14B illustrates an experimental setup for measuring the electromechanical efficiency of the actuator in Figure 14A, in accordance with an embodiment.

[0029] Figures 14C-141 illustrate various electrical measurements for the actuation cycle of Figure 14A, in accordance with an embodiment.

[0030] Figures 15A-15C illustrate an exemplary structure of a zipper-type HASEL actuator, in accordance with an embodiment.

[0031] Figures 16A-16C illustrate toroidal zipper-type HASEL actuators, in accordance with an embodiment.

[0032] Figure 16D illustrates strain recorded per voltage under various loads, in accordance with an embodiment.

[0033] Figures 17A-17C illustrate various geometric and mathematical considerations in actuator calculations, in accordance with an embodiment.

[0034] Figures 18A, 18B illustrate a pumping system using donut-type HASEL actuators, in accordance with an embodiment.

[0035] Figures 19A-19C illustrate a pumping system using linearly contracting HASEL actuators, in accordance with an embodiment.

[0036] Figures 20A-20D illustrate a pouch-type HASEL actuator in off- and on-states under load, in accordance with an embodiment.

[0037] Figure 21 illustrates modeled data and experimental data relating to the performance of the actuator in Figures 20A-20D, in accordance with an embodiment. [0038] Figures 22A-22D illustrate a pumping system using the actuator described in Figures 20A-20D, in accordance with an embodiment.

[0039] Figures 23A, 23B illustrate a perspective exploded view and a cross-sectional view, respectively, of the pumping system described with respect to Figures 22A-22D, in accordance with an embodiment.

[0040] Figure 24A illustrates a top down and cross-sectional view of a passive valve used in the pumping system of Figures 22A-22D, in accordance with an embodiment.

[0041] Figures 24B, 24C illustrate experimental data relating to the passive valve of Figure 24A, in accordance with an embodiment.

[0042] Figures 25A-25H illustrate experimental setups and corresponding experimental data relating to the performance of the pumping system described with respect to Figures 22A-22D when the system is pumping air, in accordance with an embodiment.

[0043] Figures 26A-26D an illustrate experimental setup and corresponding experimental data relating to the performance of the pumping system described with respect to Figures 22A-22D when the system is pumping liquid, in accordance with an embodiment.

[0044] Figure 27 illustrates a comparison chart of several different types of pumping systems, in accordance with an embodiment.

[0045] Figure 28 illustrates a graph showing an actuation signal in accordance with embodiments herein, in accordance with an embodiment. [0046] Figure 29A illustrates a pumping system that includes the pump described with respect to Figures 22A-22D, in accordance with an embodiment.

[0047] Figures 29B, 29C illustrate experimental data related to the pumping system in Figure 29A, in accordance with an embodiment.

[0048] Figures 30A-30D illustrate a pumping system having a plurality of distinct electrodes configured to selectively receive voltage and interact with portions of a flexible electrode to form at least one pocket of dielectric fluid, in accordance with an embodiment.

[0049] Figures 31A-31C illustrate a pumping system having a plurality of distinct electrodes configured to selectively receive voltage and interact with portions of a flexible electrode to form at least one pocket of dielectric fluid, wherein an opening to the pump chamber is selectively opened or closed depending on the location of the pocket, in accordance with an embodiment.

[0050] Figures 31A-31C illustrate a pumping system having a plurality of distinct electrodes configured to selectively receive voltage and interact with portions of a flexible electrode to form at least one pocket of dielectric fluid, wherein an opening to the pump chamber is selectively opened or closed depending on the location of the pocket, in accordance with an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0051] Hydraulically Amplified Self-healing Electrostatic (HASEL) pumps

[0052] Pumps are important mechanical devices for a range of applications, and they are the 2nd most common mechanical device in use behind electric motors. Pumps act to pressurize and move fluids for applications including but not limited to heating and cooling, processing or mixing chemicals, hydraulics, and dispensing fluids. Typical pumps are driven by electric motors and are made from rigid, bulky, and heavy components. As a result, persistent challenges with pumps include reducing noise and vibration, reducing weight, and improving mechanical efficiency.

[0053] Nature also makes extensive use of pumps. Passive pumps such as the sap- lifting mechanism of trees extracts nutrients and moisture from the soil. Active biological pumps, such as the mammalian heart use contracting muscle chambers and valves to circulate blood throughout the body. Other examples include hydraulic structures found in arachnids which pressurize fluid in various regions of their bodies to generate motion. These active pumps are driven by the contraction and relaxation of biological muscle - a soft and compliant material. While human-made pumps continue to be improved, in order to take advantage of the benefits found in nature’s pumps, new types of actuators are needed to develop more life-like pumping systems.

[0054] Research into artificial muscles - soft materials which change shape upon stimulation - has sought to replicate the performance and functionality of biological muscles. This growing field of research has seen dramatic developments over the past 20 years. Recently introduced Hydraulically Amplified Self-healing ELectrostatic (HASEL) actuators (see patent applications “Hydraulically Amplified Self-Healing Electrostatic Actuators” (PCT/US18/023797), and “Hydraulically Amplified Self-Healing Electrostatic Transducers Harnessing Zipping Mechanism” (PCT/US19/020568)) are soft materials capable of performance comparable to natural muscle. HASEL transducers produce mechanical work by applying electrostatic forces to structures consisting of a liquid dielectric and soft or flexible solid dielectric materials. The performance attributes of HASEL transducers make them promising devices for application towards mechanical systems such as pumps.

[0055] Herein, the presented invention describes the use of HASEL actuators in various embodiments of pumping systems. These pumps are separated into 3 distinctly different types: S-shaped HASEL pumps, positive displacement HASEL pumps, and peristaltic HASEL pumps.

[0056] S-shaped HASEL pumps

[0057] Figure 1A shows the cross section of a basic design for an s-shaped HASEL pump.

[0058] The hydraulic structure includes three electrodes, two solid dielectrics, and a liquid dielectric separated by one of the electrodes, in the illustrated embodiment. Electrodes #1 and #2 are planar in geometry and can be constructed from rigid, flexible, or stretchable (or any combination of the three) electrical conductors. Electrode #3 is “S”- shaped (made from a flexible or stretchable electrical conductor) and separated from electrode #1 by a solid dielectric (top dielectric) and separated from electrode #2 by another solid dielectric (bottom dielectric). One end of electrode #3 (in this case the right side) is anchored to the top dielectric with a top support structure, and the other end of electrode #3 (in this case the left side) is anchored to the bottom dielectric with a bottom support structure. The solid dielectrics and the support structures can be made from rigid, flexible, or stretchable (or any combination of the three) material. [0059] On either side of electrode #3 is a liquid. The liquid dielectric is separated by electrode #3 such that the liquid on the left and right side of electrode #3 do not come into direct contact with each other. The liquid dielectric on the left and right side can be the same material, or different materials. In this case the hydraulic structure has an outlet/inlet tube on either side of electrode #3.

[0060] The basic operation of the HASEL S-shaped pump device is shown in Fig. 1B- C. When a potential difference is applied across electrode #1 and #3, there is an electrostatic force between the two electrodes causing them to move toward each other, Fig. IB. Since electrode #3 can move freely (other than its anchor points provided by the support structure), it zips to the left along the top dielectric (HASELs with electrostatic zipping mechanisms covered in US provisional patent application (62/638,170) and PCT application (PCT/US2019/020568)). During this process, the liquid dielectric on the left side of electrode #3 is pushed out of the left tube (positive pressure), while the liquid dielectric on the right side of electrode #3 is sucked into the right tube (negative pressure). Once electrode #3 is fully zipped to the left, the potential difference across electrode #1 and #3 is brought to zero (i.e. the capacitor is discharged) and then there is a potential difference applied across electrode #2 and #3 (Fig. 1C).

[0061] Now, the electrostatic force generated between electrodes #2 and #3 causes electrode #3 to zip to the right along the bottom dielectric. Thus, the liquid dielectric on the right side of electrode #3 is pushed out of the right tube (positive pressure) and the liquid dielectric on the leftside of electrode #3 is pulled into the left tube (negative pressure). [0062] The outlet/inlet tubes on the left and right side of the hydraulic structure can be modified as seen in Fig. ID, such that each side includes two tubes, one for positive pressure and one for negative pressure. The tubes for negative pressure include a check valve that only lets fluid flow into the pump, while the tubes for positive pressure include a check valve that only lets fluid flow out of the pump. This design can provide a more continuous flow of fluid, much like a mammalian heart.

[0063] This structure illustrated in Figs. 1A - IF was first proposed as a microelectromechanical system (MEMs) in the 90’s (specifically a micro -switch) and known as an S-shaped actuator. More recently the structure was shown as an efficient electrocaloric cooling device. However, none of the previous designs was used to pump fluids as presented here. Additionally, previous versions of the S-shaped actuator do not utilize the presented structure, that is, one of a HASEL actuator.

[0064] An advantage of the support structures in Fig. 1 is to allow electrode #3 to zip along either the top or bottom solid dielectrics enabling a variable control of pressure with application of voltage (see HASELs with electrostatic zipping mechanisms covered in provisional patent application (62/638,170) and PCT application (PCT/US2019/020568)). However, for some applications, it is advantageous to have a pump that is more binary, one which is either off or generates a fixed pressure when on. Figure 2 shows a HASEL pump which utilizes a pull-in instability for a pump with a discrete number of stable states.

[0065] The structure of this device shown in Fig. 2 is similar to that shown in Fig. 1; however, in this case, electrode #3 has a planar geometry and is parallel to both electrodes #1 and #2. A chamber of liquid dielectric separates electrode #3 from the top solid dielectric, and a separate chamber of liquid dielectric separates electrode #3 from the bottom solid dielectric. Each chamber has an inlet and outlet tube. Electrode #3 is constructed from a stretchable or flexible material.

[0066] The rest state shown in Fig. 2A is one of the stable states of the pump. When a potential difference is applied across electrodes #1 and #3 that exceed the mechanical restoring force of the system, electrode #3 is abruptly pulled upwards against the top dielectric. This state is another stable state of the system, and generates a positive pressure in the top chamber, and a negative pressure in the bottom chamber, Fig. 2B.

[0067] When a potential difference is applied across electrodes #2 and #3 that exceed the mechanical restoring force of the system, electrode #3 is abruptly pulled downwards against the bottom dielectric. This state is another stable state of the system, and generates a positive pressure in the bottom chamber, and a negative pressure in the top chamber, Fig. 2C. Thus, this device has three stable states: off [Fig. 2A], electrode #3 pulled upwards [Fig. 2B], or electrode #3 pulled downwards [Fig. 2C]. Systems with an alternate number of stable states are possible (i.e. two or four stable states). Additionally, the inlet/outlet tubes can be designed with check valves to control the flow of fluid (as seen in Fig. ID).

[0068] Positive displacement HASEL pumps

[0069] Figure 3 depicts a HASEL diaphragm pump, in accordance with an embodiment. This design of pump involves stacks of HASEL actuators which act on a stretchable diaphragm. The HASEL actuators and diaphragm are mounted within a housing. The inlet and outlet of the housing connect to a conduit for transporting the pumped fluid (gas or liquid). One-way valves allow for flow only in one direction. When voltage is applied, the HASEL actuators expand to deform the stretchable diaphragm. This forces liquid to flow out of the pumping chamber through the one-way valve. When voltage is turned off, the elastic force of the membrane causes the HASEL actuators to relax to the initial thickness. As this occurs, fluid is drawn into the pumping chamber through the one way valve.

[0070] As shown in Fig. 3, this specific type of positive displacement pump (PDP) includes one or more HASEL actuators or stacks of actuators placed within a housing. A stretchable or flexible diaphragm is mounted to the housing (Fig 3A). The inlet and outlet of the housing connect to a conduit which serves to transport fluid (liquid or gas) through the pump. The inlet of the housing features a one-way valve to allow flow of fluid into the pump chamber. The outlet of the housing features a one-way valve to allow flow out of the pump chamber. When voltage is applied, expansion of the HASEL actuator(s) deform the diaphragm. As a result, pressure within the pump chamber increases and fluid flows through the outlet (Fig 3B). Once voltage is turned off, the elastic diaphragm forces the HASEL actuator(s) to return to their original position. This force creates a negative pressure gradient between the inlet and pump chamber and fluid fills the pump chamber.

[0071] This pump cycle can be controlled by varying input voltage to the HASEL actuator(s). This gives control over volumetric flow rate and pressure of the pump. While one design of HASEL actuators is shown for this pump, a variety of HASEL actuator designs could be applied to create such a diaphragm pump, including actuators that contract on activation (i.e., Peano-HASELs). The pump can be designed for a range of length scales and flow rates. Both the size of the HASEL actuator(s) and number of actuators in a stack can be varied to suit the flowrate and pressure requirements of a specific application.

[0072] Capacitive self-sensing can be employed to provide feedback on actuator position and force in order to achieve closed-loop pumping. Multiple actuation signals can be superimposed together to achieve multifunctional operation. For example, a low frequency signal can be combined with a high frequency signal to achieve a combination of pumping and vibratory mixing.

[0073] Figure 4 shows a multiple stage HASEL Diaphragm pump. Much like the human heart, the HASEL diaphragm pumps can be placed in series with one-way valves separating each pump in order to increase the pressure generated in the pumped fluid. Moving from left to right as shown in Fig. 4, fluid pressure increases at each pump stage so that PI < P2 < P3. With a three stage pump, for example, the system alternates between two states where A) the two outer pumps are activated while the middle is inactive and B) the middle pumps is active while the two outer pumps are inactive.

[0074] As shown in Figure 4, multiple diaphragm pumps can be combined in series to increase the pressure output of the pump.

[0075] An advantage of this pump design of Fig. 4 is that the pumped fluid is isolated from the high voltage of the HASEL actuators. This enables pumping of fluids that are conductive.

[0076] Peristaltic HASEL pumps

[0077] Figure 5 depicts a HASEL pump which uses peristaltic motion to transport and pressurize a fluid. Fluid (liquid, gas, or granular media) is contained within an inner conduit. In the embodiment illustrated in Fig. 5, HASEL transducers are placed between an inner and outer conduit. The outer conduit is stiff enough to minimize deflection from force of the HASEL transducer. The inner conduit, which transports the fluid, is elastic and deforms when the HASEL actuates. HASEL actuators are arranged along the length of the conduit and activated sequentially to pump the fluid within the inner conduit. A peristaltic wave is created by activating every other pair of HASEL actuators in sequence, as shown in A-C. This pumping mechanism is similar to peristaltic pumps found in nature such as the human esophagus or hearts of many invertebrates.

[0078] As shown in Fig. 5, HASEL actuators surround the outer surface of the inner conduit and an outer conduit constrains the HASEL actuators. The outer conduit may be a rigid or flexible structure. HASEL actuators are arranged along the length of the conduit and activated sequentially to pump the fluid within the inner conduit. This pumping mechanism is similar to peristaltic pumps found in nature such as the human esophagus or hearts of many invertebrates. As depicted in Fig 5, when activated, the HASEL actuators compress the inner conduit which pressurizes and displaces the fluid within. If the wall position at rest is an intermediate actuation state for the actuators, then once the actuators are turned off, a distention wave of negative pressure is created that helps to transport fluid in the direction of the peristaltic wave. The depicted sequence shows the peristaltic wave moving from left (Fig 5A) to right (Fig 5B). Fig 5C is the same state as Fig 5A which illustrates that this is a continuous and repeating pumping motion.

[0079] A benefit of this pump design as shown in Fig. 5 is that no valves or additional components are required. Direction of flow depends on motion of the peristaltic wave. Fluid flow rate, direction, and pressure can be altered by changing the order, magnitude, and frequency of the applied voltage signal.

[0080] Multiple actuation signals can be superimposed together to achieve multifunctional operation. For example, a low frequency signal can be combined with a high frequency signal to achieve a combination of pumping and vibratory mixing.

[0081] A further advantage of the pump design in Fig. 5 is that the pumped fluid is isolated from the high voltage of the HASEL actuators. This enables pumping of fluids that are conductive.

[0082] Referring back to Figure 1A, further details of a pumping system 100 is shown having a pump 102. Pump 102 includes a pump chamber 104 having a first wall 106 and a second wall 108. Second wall 108 may be substantially opposite the first wall 106 across the pump chamber 104. First and second walls 106, 108 may each be rigid, flexible, or may have both rigid and flexible sections. A first dielectric 110 is located adjacent the first wall 106. The first dielectric 110 may be a solid or a flexible material and may be formed from materials such as biaxially oriented polyester film, biaxially oriented polypropylene, polyvinylidene fluoride terpolymer, and polyimide film.

[0083] A first electrode 112 is electrically coupled with the first dielectric 110. The first electrode is formed from a conductive material that may be rigid or flexible. In some embodiments, the first electrode 112 is formed from carbon grease, carbon ink, silver ink, conductive fabric, or conductive elastomer.

[0084] The pumping system 100 further includes a second electrode 114. The second electrode may be flexible, stretchable, or otherwise movable over at least a portion of its length. In some embodiments, the second electrode 114 may be formed from a conductive material such as carbon grease, carbon ink, silver ink, conductive fabric, or conductive elastomer. The second electrode 114 includes a first end 116 and a second end 118. First end 116 is coupled with the first wall 106 at a first support structure 120. The support structure 120 may be formed from an insulating material and may be coupled to or integrally formed with the first wall 106. The second end 118 of the second electrode 114 is coupled with the second wall 108 at a second support structure 122. The support structure 122 may be a separate component formed from an insulating material or may be integrally formed with the second wall 108.

[0085] The second electrode 114 divides the pump chamber 104 into at least a first volume 124 and a second volume 126. The first and second volumes 124, 126 are shown to be approximately the same size; however, the volumes can also vary without departing from the scope of the present disclosure. The first a second volumes 124, 126 may be filled with first and second fluids, respectively. The first and second fluids can be the same fluids or different fluids. In some embodiments, the fluids are dielectric fluids including but not limited to vegetable-based transformer oils and silicone-based transformer oils. First and second conduits 128, 130, respectively, may be fluidly connected with the pump 102. More specifically, first conduit 128 may be fluidly connected with first volume 124 and second conduit 130 may be fluidly connected with second volume 130. Figure 1A shows the pump 102 in a resting state or an off-state, which is considered a first stable state.

[0086] A power source (not shown) may be electrically coupled with the first electrode 112 such that the first electrode is configured to transmit a voltage to the first dielectric 110. When voltage is received by the first dielectric 110, a first electric field 132 is generated, as shown in Figure IB. In response to the first electric field 132, at least a portion of the second electrode 114 contacts or otherwise moves toward the first dielectric 110. This position represents a second stable state of the pumping system 100. In the first stable state, the first volume 124 within pump chamber 104 is reduced in size while the second volume 126 is increased. Correspondingly, at least a portion of the first fluid may be pushed out of the pump chamber into the first conduit 128 by positive pump pressure while at least a portion of the second fluid which occupies the second fluid volume 126 and second conduit 130 may be pulled into the pump chamber 104 by negative pump pressure.

[0087] Referring to Figures 1A and 1C, a second dielectric 134 and a third electrode 136 may be included in pumping system 100. Similar to the first dielectric, the second dielectric 134 may be a solid or a flexible material and may be formed from materials such as biaxially oriented polyester film, biaxially oriented polypropylene, polyvinylidene fluoride terpolymer, and polyimide film. The third electrode 136 is formed from a conductive material that may be rigid or flexible and may be formed from materials such as carbon grease, carbon ink, silver ink, conductive fabric, and conductive elastomer. The third electrode 136 is electrically coupled with the second dielectric 134.

[0088] A power source (not shown) may be electrically coupled with the third electrode 136 such that the third electrode is configured to transmit a voltage to the second dielectric 134. When voltage is received by the second dielectric 134, a second electric field 138 is generated, as shown in Figure 1C. In response to the second electric field 138, at least a portion of the second electrode 114 contacts or otherwise moves toward the second dielectric 134. This position represents a third stable state of the pumping system 100. In this third stable state, the first volume 124 within pump chamber 104 is increased while the second volume 126 is reduced in size. Correspondingly, at least a portion of the second fluid occupying the second fluid volume 126 may be pushed out of the pump chamber 104 into the second conduit 130 by positive pump pressure while the first fluid occupying the first fluid volume 124 and first conduit 128 may be pulled into the pump chamber 104 by negative pump pressure.

[0089] When voltage is removed from the system 100, second electrode 114 returns to the first stable state due to elasticity of the second electrode material and/or due to pressure from the first and second fluids. The pump 102 can be cycled through the different stable states in any order.

[0090] Referring to Figure ID, another embodiment of a pumping system is shown.

Pumping system 140 includes the pump 102 fluidly coupled between the first conduit 128 and the second conduit 130 as described with respect to Figures 1A-1C. A first baffle 142 is included along a portion of the first conduit 128 to divide the first conduit into first and second channels 144, 146, respectively. A second baffle 148 is included along a portion of the second conduit 130 to divide the second conduit into first and second channels 150,

152, respectively. The first and second baffles 142, 148 may be positioned away from the pump 102 such that first and second mixing regions 154, 156 are fluidly coupled with the pump 102. One or more of the channels 144, 146, 154, 156 may include a check valve 158, 160, 162, 164 to control fluid flow into and out of the channels.

[0091] For example, as shown in Figure IE, when pump 102 is in the second stable state and the first fluid is pushed out of pump chamber 104 into the first conduit 128, check valve 160 may allow the displaced first fluid to flow into channel 146 while check valve 158 prevents fluid from entering chamber 144. Correspondingly, as the second fluid is pulled into pump chamber 104, check valve 162 may allow fluid to flow from channel 150 into mixing region 156 and/or pump chamber 104 while check valve 164 prevents fluid occupying channel 152 from flowing into the mixing region 156.

[0092] When pump 102 is in the third stable state, as shown in Figure IF, fluid from chamber 144 flows through check valve 158 in response to negative pump pressure while fluid in chamber 146 is restrained by check valve 160. On the positive pressure side, check valve 164 allows fluid to flow into channel 152 while check valve 162 remains closed to prevent fluid flow into channel 150.

[0093] While two channels per conduit are described, each having a check valve therein, one of skill in the art will appreciate that more or fewer channels and check valves may be implemented within the conduits to achieve different fluid flow patterns without departing from the scope of the present disclosure.

[0094] Moreover, while a single pump 102 is shown between the first and second conduits, additional pumps may be placed in series or in parallel to modify pumping capacity and provide different fluid flow patterns.

[0095] Referring now to Figure 2A, a pumping system 200 is shown. System 200 includes a pump 202 having a pumping chamber 204 defined at least in part by a first wall 206 and a second wall 208. Second wall 208 may be substantially opposite the first wall 206 across the pump chamber 204. First and second walls 206, 208 may each be rigid, flexible, or may have both rigid and flexible sections. A first dielectric 210 is located adjacent the first wall 206. The first dielectric 210 may be a solid or a flexible material and may be formed from materials such as biaxially oriented polyester film, biaxially oriented polypropylene, polyvinylidene fluoride terpolymer, and polyimide film.

[0096] A first electrode 212 is electrically coupled with the first dielectric 210. The first electrode is formed from a conductive material that may be rigid or flexible. In some embodiments, the first electrode 212 is formed from carbon grease, carbon ink, silver ink, conductive fabric, or conductive elastomer.

[0097] The pumping system 200 further includes a second electrode 214. The second electrode may be flexible, stretchable, or otherwise movable over at least a portion of its length. In some embodiments, the second electrode 214 may be formed from a conductive material such as carbon grease, carbon ink, silver ink, conductive fabric, or conductive elastomer. The second electrode 214 includes a first end 216 and a second end 218. First end 216 is coupled with a first support structure 220, which may be formed from an insulating material. The second end 228 of the second electrode 214 is coupled with a second support structure 222, which may also be formed from an insulating material. In the system 200, support structures 220, 222 are part of first and second baffles 242, 248 disposed within first and second conduits 228, 230; however, the support structures may be distinct parts coupled with the baffles. In some embodiments, the support structures 220, 222 may lie on a longitudinal axis 254 of pump chamber 204; however, other locations for the support structures may be selected without departing from the scope of the present disclosure.

[0098] The connections between the second electrode 214 and first and second support structures 220, 222 prevent flow of fluid therethrough and also allow for the second electrode to move. The connections may include pivotable, stretchable, bendable, or otherwise flexible attachments. The resting state shown in Figure 2A is considered a first stable state for pump 202.

[0099] The second electrode 214 divides the pump chamber 204 into at least a first volume 224 and a second volume 226. The first a second volumes 224, 226 may be filled with first and second fluids, respectively. The first and second fluids can be the same fluids or different fluids. In some embodiments, the fluids are dielectric fluids including but not limited to vegetable-based transformer oils and silicone-based transformer oils. While first and second volumes 224, 226 are shown to be approximately the same size, dimensions of the first and second volumes may be the same or different and are selectable based on the fluids to be pumped as well as desired flow rates, pressures, and the like. In some embodiments, the pump 202 may include only a single volume where the second electrode 214 acts as the second wall 208. In other embodiments, the pump 202 may include first and second volumes, where fluid occupying the first volume is a dielectric fluid as discussed above and the fluid occupying the second volume is any fluid, such as a gas or liquid, and may have conductive or poorly insulating properties.

[00100] The first and second conduits 228, 230, respectively, may be fluidly connected with the pump 202. The first baffle 242 divides the first conduit 228 into first and second channels 244, 246. The second baffle 248 divides the second conduit 230 into first and second channels 250, 252. Together with the second electrode 214, the first and second baffles 242, 248 may prevent the first fluid from mixing with the second fluid. Additionally, the configuration shown in system 200 allows for fluid communication between channel 244, second volume 226, and channel 252. Similarly, channel 246, first volume 224, and channel 250 are in fluid communication.

[00101] Operation of the pump 202 is discussed with reference to Figures 2A-C. In

Figure 2B, a voltage is applied to the first dielectric 210 from a power source (not shown) via the first electrode 212. When the voltage is received by the first dielectric 210, a first electric field 232 is generated. In response to the first electric field 232, at least a portion of the second electrode 214 contacts or otherwise moves toward the first dielectric 210. This position represents a second stable state of the pumping system 200. In the second stable state, the first volume 224 within pump chamber 204 is reduced in size while the second volume 226 is increased. Correspondingly, at least a portion of the first fluid is displaced from the pump chamber 204 and into channels 246, 250 of the first and second conduits 228, 230, respectively, by positive pump pressure. At the same time, at least a portion of the second fluid, which occupies the second fluid volume 226 and channels 244, 252 of first and second conduits 228, 230, is pulled into the pump chamber 204 by negative pump pressure.

[00102] Referring to Figures 2A and 2C, a second dielectric 234 and a third electrode 236 may be included in pumping system 200. Similar to the first dielectric, the second dielectric may be a solid or a flexible material and may be formed from materials such as biaxially oriented polyester film, biaxially oriented polypropylene, polyvinylidene fluoride terpolymer, and polyimide film. The third electrode 236 is formed from a conductive material that may be rigid or flexible and may be formed from materials such as carbon grease, carbon ink, silver ink, conductive fabric, and conductive elastomer. The third electrode 236 is electrically coupled with the second dielectric 234. [00103] A power source (not shown) may be electrically coupled with the third electrode 236 such that the third electrode is configured to transmit a voltage to the second dielectric 234. When voltage is received by the second dielectric 234, a second electric field 238 is generated, as shown in Figure 2C. In response to the second electric field 238, at least a portion of the second electrode 214 contacts or otherwise moves toward the second dielectric 234. This position represents a third stable state of the pumping system 200. In this third stable state, the first volume 224 within pump chamber 204 is increased while the second volume 226 is reduced in size. Correspondingly, at least a portion of the second fluid occupying the second fluid volume 226 may be pushed out of the pump chamber 204 into channels 244, 252 within the first and second conduits 228, 230, respectively, by positive pump pressure. The first fluid, which occupies the first fluid volume 224 and channels 246, 250 within the first and second conduits 228, 230, is pulled into the pump chamber 204 by negative pump pressure.

[00104] Pumps 102 and 202 may have different pumping characteristics due to their different configurations. For example, when a voltage is applied to one of the dielectrics included in pump 102, the second electrode 114 may gradually attract to the generated electric field along the length of the second electrode 114 in a “zipping” type response. The zipping mechanism will be discussed in further detail below. In contrast, the second electrode 214 of pump 202 may have a more immediate response when moving between stable states. Thus, the pump 202 may more closely approximate a binary on/off response than pump 102.

[00105] The response of pumps 102 and 202 may also be tuned by adjusting one or more variables of the input signal. For example, frequency, amplitude, polarity, offset and other signal characteristics may be adjusted. In some embodiments, a control module may be coupled with the power source to monitor and/or adjust the actuation signal received by the various pumping systems.

[00106] Referring to Figure 6, a process flow chart is shown outlining a method 600 for operating pumping systems 100 and 200. The method 600 includes providing a first fluid in a first fluid volume of a pump chamber (step 602) and providing a second fluid in a second fluid volume of the pump chamber, the first volume separated from the second volume by a movable electrode (step 604). A first dielectric is provided adjacent a first side of the pump chamber (step 606). At a first time, a first electric field is generated by applying a first voltage to the first dielectric (step 608). At least a portion of the movable electrode is moved toward the first dielectric in response to the first electric field (step 610), thereby applying positive pressure to the first fluid in the first volume (step 612) and applying negative pressure to the second fluid in the second volume (614). The method may further include providing a second dielectric adjacent a second side of the pump chamber (step 616) and, at a second time, generating a second electric field by applying a second voltage to the second dielectric (step 618). At least a portion of the movable electrode is moved toward the second dielectric in response to the second electric field (step 620), thereby applying negative pressure to the first fluid in the first volume (step 622) and applying positive pressure to the second fluid in the second volume (step 624).

[00107] Alternative methods of operating pumping system 100 and 200 are possible. For example, pumps 102 and 202 may be alternated between any of the first, second, and third stable states as desired. Pumps 102, 202 may also by operated by generating only one electric field with a single dielectric rather than generating two electric fields with two dielectrics. In such a configuration, the pumps 102, 202 may alternate between first and second or first and third stable states only. Methods of operating the pumps may also include generating and holding an electric field such that the pumps 102, 202 maintain a single position for an extended duration of time. One or more of frequencies, amplitudes, and signal profiles of the input signal may be adjusted to tune the pump response, fluid flow characteristics, and fluid pressures.

[00108] Figure 7 shows a schematic drawing of a control module 702 operatively coupled with a power source 704. The power source 704 is coupled with pumping system 706. The control module 702 may send a signal 708 instructing power source 704 to provide an actuation signal 710 to the pumping system 706. Variation in the actuation signal 710 may be detected at monitoring signal 712 which may provide information about pressures, flow rates, or other conditions within the pumping system. The monitoring signal may be relayed back to the control module 702 through feedback signal 714. The control module may be configured to calculate a new instruction signal 708 based on the feedback signal 714. Thus, a closed-loop feedback mechanism may be used to monitor and operate pumping systems disclosed herein.

[00109] Referring back to Figures 3A-3C, a pumping system 300 is shown, in accordance with another embodiment. Pumping system 300 includes a pump 302 having a pump chamber 304. Pump chamber 304 is in fluid communication with one or more sections of conduit, for example an inlet conduit 328 and an outlet conduit 330. The pump chamber 304 is defined by a first wall 306 and a second wall 308; the second wall 308 may be substantially opposite the first wall 306 across pump chamber 304. The pump chamber may be aligned along a longitudinal axis 354 of one or more of inlet conduit 328 and outlet conduit 330.

[00110] Pump 302 further includes at least one actuator chamber 310 configured to house at least one actuator 312. The actuator chamber 310 may be separated from pump chamber 304 by the first wall 306. The first wall 306 may be a flexible diaphragm formed from a bendable and/or stretchable material, such as an elastomer, that is impermeable to fluid disposed within the conduits 328, 330 and pump chamber 304. In embodiments having a single actuator chamber 310, wall 308 may be a rigid wall. Alternatively, in configurations where a second actuator chamber 334 is included in pump 302, the wall 308 may be a flexible diaphragm formed from a bendable and/or stretchable material that is impermeable to fluid disposed within the conduits 328, 330 and pump chamber 304. The second actuator chamber 334 may house one or more additional actuators 312.

[00111] The actuators 312 may be hydraulically amplified self-healing electrostatic (“HASEL”) transducers, which are described in further detail herein with reference to Figures 8A-21. Specifically, the actuators 312 may be similar to the donut-type HASEL actuators 2200 discussed with reference to Figures 8A-14I or zipper-type HASEL actuators discussed with reference to Figures 15A-16D. Multiple actuators 312 may be stacked together in order to adjust and tune the action of the pump.

[00112] Expanding type actuators are shown in Figures 3A-3C. The actuators 312 are considered expanding type actuators because they increase in height (i.e., in the y- direction) when a voltage is applied. The expanding actuator, or stack of expanding actuators, has a first height 314 in an off-state when no voltage is applied to the system. The pump chamber has a corresponding first height 316 associated with the off-state. The first height 316 of the pump chamber may be adjusted by adjusting a location or first height 314 of the actuators. This may be done by varying the size, type, and/or number of actuators 312 in the actuator chamber 310 or by varying one or more dimensions of the actuator chamber 310 itself. For example, an actuator chamber with a smaller height in the y-direction and/or more actuators located therein may push wall 306 toward pump chamber 304 and may reduce the first height 316 and/or first volume of the pump chamber compared to a pump which includes an actuator chamber with a larger height in the y-direction and/or fewer actuators. A system with a larger actuator chamber and/or fewer actuators may pull wall 306 away from pump chamber 304 thereby increasing the first height 316 and/or first volume of the pump chamber. Many design variations relating to dimensions, arrangements, and numbers of actuators are possible without departing from the scope of the present disclosure.

[00113] While Figures 3A-3C show a first stack of four actuators in the first actuator chamber 310 and a second stack of four actuators in the second actuator chamber 334, any number of actuators may be used. The number of actuators in the first chamber can be the same as or different from the number of actuators in the second chamber. For example, the second actuator chamber may include more or fewer actuators than first actuator chamber. The number of actuators used may depend in part upon the first height 316 of pump chamber 304. For example, it may be desirable to include enough actuators within the one or more of the actuator chambers 310, 334 that the actuators are able to expand into and completely close off the pump chamber 304 as shown in Figure 3B. [00114] The pumping system 300 may include one or more valves 318, 320 to control fluid flow. The valves 318, 320 maybe check valves or one-way valves that allow flow in a first direction (e.g., to the right in Figures 3A-3C) while preventing fluid flow in a second direction substantially opposite the first direction (e.g., to the left). One or more of the valves 318, 320 may be disposed within the pump 302 and/or within the inlet and outlet conduits 328, 330.

[00115] Referring now to Figure 3B, pumping system 300 is shown in an on-state. A voltage is applied to the actuators 312 by one or more power sources (not shown). The power source may be modulated by a control unit (not shown) that provides instructions to the power source relating to the actuation signal.

[00116] As discussed above, the actuators 312 are expanding actuators and thus the second height 322 of the actuator stack is larger than the first height 314. The actuators 312 push first wall 306 at least partially into the pump chamber. In the embodiment shown, a second actuator chamber 334 is similarly actuated by the same or a different power source such that the second wall 308 is simultaneously pushed at least partially into the pump chamber. The height of the pump chamber is reduced and, as shown in Figure 3B, can be decreased to zero by bringing the first and second walls 306, 308 into contact.

As the pump chamber height collapses, the fluid occupying the pump chamber is pressurized and displaced from the pump chamber.

[00117] Check valves 318, 320 may control the flow of the displaced fluid. As shown in Figure 3B, the first check valve 318 remains closed to prevent fluid from entering the inlet conduit 328 from the pump chamber. The second check valve 320 opens in response to the fluid pressure and fluid is allowed to flow therethrough into outlet conduit 330.

[00118] Fluid within conduits 328, 330 and pump chamber 304 can be any fluid and can be in liquid of gaseous form. In some embodiments, the fluid can be electrically conductive.

[00119] Referring to Figure 3C, pump 302 returns to an off-state by reducing or removing voltage from the system 300. Expanding actuators 312 relax and decrease in height from second height 322 to the first height 314. Correspondingly, the height of pump chamber 304 increases from zero to the first height 316. As the height and volume of pump chamber 304 increase, a negative pressure is created within the pump chamber 304. The second valve 320 may pull closed in response to the negative pressure, thereby preventing fluid from the outlet conduit 330 from entering the pump chamber 304. The first valve 318 may open in response to the negative pressure, thereby allowing fluid from the inlet conduit 328 to flow through into the pump chamber 304. The pump 302 can be cycled through on- and off-states to continue moving fluid therethrough.

[00120] In some embodiments, the pump 302 can be operated as a variable valve.

For example, the actuators may receive a voltage and expand to such that the height of pump chamber 304 is reduced to a non-zero dimension. The pump may be held in this intermediate state to restrict flow or to control pressure of fluid moving therethrough.

Flow sensors or pressure sensors may be positioned downstream and or upstream of the pump 302 and may provide feedback to a control module. The control module may compare the real-time data to a target flow rate or pressure and calculate a new pump position based on the real-time data.

[00121] In some embodiments, the actuators may expand such that the height of the pump chamber 304 is reduced to zero, thereby closing off fluid communication between the inlet conduit 328 and outlet conduit 330. Many variations on the method of operating pumping system 300 may be used to control various flow and pressure properties of the fluid therein.

[00122] Referring now to Figures 4A and 4B, a pumping system 400 is shown having several pumps 302a, 302b, 302c (Figures 3A-3C) connected, either directly or indirectly, in series between an inlet conduit 428 and an outlet conduit 430. Pump chambers 304a,

304b, and 304c may be in selective fluid communication with each other and with inlet and outlet conduits 428, 430. The pump chambers may be aligned along a longitudinal axis 454 as shown. Each of pumps 302a, 302b, and 302c include at least a first actuator chamber 310a, 310b, 310c which houses an expanding actuator 312 or a stack of expanding actuators. The pumps may further include a second actuator chamber 334a, 334b, 334c which houses at least one expanding actuator 312. First actuator chambers are separated from the pump chambers by a first wall 306a, 306b, 306c. Second actuator chambers are disposed substantially opposite the first actuator chambers and are separated from the pump chamber by second walls 308a, 308b, 308c.

[00123] As discussed with respect to Figures 3A-3C, actuators 312 are expanding actuators having an initial height 314a, 314b, 314c in the y-direction when in an off-state and no voltage is applied to the actuators. When a voltage is applied, the height of the actuators increases to a second height 322a, 322b, 322c, thereby pushing first walls 306a, 306b, 306c and/or second walls 308a, 308b, 308c into pump chambers 304a, 304b, 304c, respectively. One or more check valves 418, 420, 422, 424 can be included within system 400 to control fluid flow. It may be advantageous to include a check valve between each pump with all of the valves oriented to allow fluid flow in the same direction (i.e., toward the right in Figures 4A, 4B).

[00124] When multiple pumps are connected in series, operation of the multiple pumps can be varied over time to control fluid flow and pressure. For example, as shown in Figure 4A, pumping system 400 can be operated such that pumps 302a, 302c are in the same state at the same time (i.e., an on-state in Figure 4A and an off-state in Figure 4E>) while pump 302b is in a different state (i.e., an off-state in Figure 4A and an on-state in Figure 4E>). Such a method of alternating the states of adjacent pumps may assist flow of fluid through the pumping system.

[00125] In some embodiments, fluid enters pump chamber 304a at a first pressure Pi when pump 302a is in an off state (Figure 4E>). When the pump 302a actuates, fluid from pump chamber 304a is pushed through open check valve 420 into pump chamber 304b due to positive pressure from pump 302a and/or negative pressure within pump 302b.

The fluid occupies pump chamber 304b and has a second pressure P2 which may be greater than the first pressure Pi. When pump 302b actuates, the fluid is displaced from pump chamber 304b through open check valve 422 and into pump chamber 304c due to positive pressure from pump 302b and/or negative pressure within pump 302c. The fluid now occupies pump chamber 304c and has a third pressure P3 which may be greater than or equal to P2. Similarly, pump 302c actuates to displace the fluid from pump chamber 304c through open check valve 424 and into the outlet conduit 430 at a pressure P4 which may be greater than or equal to pressure P3. Additional pumps may be added to the pumping system 400 to further modify the pressure of fluid flowing therethrough.

[00126] While the operation of Figures 4A and 4B show adjacent pumps positioned in opposite states (i.e., on, off, on or off, on, off), other operational schemes are possible. For example, one or more of the pumps can be positioned at one or more intermediate state that exists in between fully on- and off-states. For example, at a given time, first pump 302a can be positioned at an intermediate state between on and off such that pump chamber 304a has a height between zero and first height 316a. Simultaneously, second pump 302b can be positioned in an on-state to fully close the pump chamber 304b, and third pump 302c can be positioned in an off -state to fully open pump chamber 304c. By varying the timing of pump actuation, fluid pressure and flow characteristics through the pumping system can be adjusted.

[00127] In some embodiments, actuators 312 are tilting actuators that can be asymmetrically actuated such that a first side of the actuator increases in height more than a second side when voltage is applied. This concept is discussed in detail with respect to Figures 13A-13F. Using a tilting actuator may provide further control of the motion and pressure of fluid moving through pumping system 400 by allowing each pump to exist at more than one state at a given time. For example, the first side of the actuator may be in an intermediate state while the second side is in a fully on- or off-state. In other examples, the first and second sides of the actuator may exist at different intermediate states. Such an actuator may be particularly useful in achieving peristaltic fluid movement as it can gradually push fluid through the pumping system without abrupt changes in pressure. [00128] Using tilt actuation methods may also provide an alternative to using check valve components in the system 400. At a first time, a first side of the actuator nearest a fluid inlet can be actuated to a fully on-state, thereby closing off the fluid channel that leads to the inlet conduit 428, for example, while the second side remains in an off-or intermediate-state to allow fluid flow. At a second time, the second side of the actuator can be actuated to decrease the height of the pump chamber and displace fluid toward the outlet conduit while the first side remains fully on.

[00129] In some embodiments, actuators 312 may be similar to the actuators 2000 shown in Figures 20A-20D. Actuators 2000 are discussed in detail herein below.

[00130] Figures 5A-5C show a pumping system 500. The system 500 includes a plurality of pumps 502a, 502b, 502c, 502b disposed in series and within an outer conduit 510. Outer conduit 510 may be formed from a rigid or semi-rigid material. A first flexible wall 506 and a second flexible wall 508 define a fluid channel within the outer conduit 510. The plurality of pumps includes actuators 512 located in a space between the outer conduit and the first and second flexible walls 506, 508. Specifically, each pump may include a first actuator 512 between the outer conduit 510 and the first flexible wall 506 and/or a second actuator 512 between the outer conduit 510 and the second flexible wall 508. The actuators 512 may be expandable actuators configured to increase in height in the y- direction when a voltage is applied. Specifically, actuators 512 may be donut-type HASEL actuators which can be actuated uniformly for even height change across the actuator or asymmetrically to tilt the actuators. Tilt actuation is further described with respect to Figures 13A-13F below. Alternatively, the actuators 512 may be formed as individual pouches similar to the HASEL actuators discussed with respect to Figures 20A-20D below. [00131] During operation of pumping system 500, voltage may be applied to one or more pumps at a given time. In some embodiments, adjacent pumps may be actuated such that they are in opposite states (e.g., at a given time, pump 502a is on, pump 502b is off, pump 502c is on, pump 502d is off); however, other methods of operating the pumps are possible. For example, pumps can be actuated to intermediate -states between fully on-and off-states to accomplish a smooth peristaltic pumping action. As discussed with respect to Figures 4A-4C, fluid pressure can increase in stages across the pumping system 500. For example, fluid may enter a first pump chamber 504a at a first pressure Pi (Figure 5B). Actuation of pump 502a may push the fluid into second pump chamber 504b at a second pressure P2 which may be greater than Pi (Figure 5C). Actuation of pump 502b may push the fluid into third pump chamber 504c at a third pressure P ₃ which may be greater than second pressure P2 (Figure 5E>). Actuation of pump 502c may push the fluid into fourth pump chamber 504d at a fourth pressure P4 which may be greater than third pressure P ₃ (Figure 5C). Finally, actuation of pump 502d may push the fluid into an outlet conduit or a subsequent pump chamber at a pressure Ps which may be greater than P4 (Figure 5E>). The various pressures achieved through pumping system 500 may depend in part on the size and types of actuators, the size of pump chambers, and the actuation signal used to operate the actuators.

[00132] Figures 5A-5C show operation of pumping system 500 using uniform actuation of actuators 512; however, as discussed above, tilting actuation methods may be used instead of or in addition to the uniform actuation. Using tilting actuators may improve efficiency of fluid flow in systems that do not include check valves. At a first time, a first side of the tilting actuator can be actuated to a fully on-state such that fluid flow in a first direction is substantially prevented. While the first side remains fully on to prevent fluid flow, the second side can be actuated to an intermediate or fully on state to gradually push the fluid in a second direction which may be opposite the first direction. Timing of actuation of the plurality of pumps may be selected such that actuators, or sides of actuators, that are adjacent each other achieve a fully on -state in succession to push fluid through pumping system 500 in a peristaltic motion.

[00133] Turning to Figures 8A-8E, a specific type of HASEL actuator in the form of a donut-type HASEL actuator 2200 is shown to illustrate conversion of electrical actuation to mechanical deformation. The donut-type actuator 2200 includes a flexible shell or pouch 2208 (e.g., elastically deformable) that defines an enclosed internal cavity 2209, a liquid dielectric 2212 contained within the enclosed internal cavity 2209, a first electrode 2216 disposed over a first side (not labeled) of the enclosed internal cavity 2209, and a second electrode 2217 disposed over an opposite second side (not labeled) of the enclosed internal cavity 2209. For instance, the first and second electrodes 2216, 2217 may include respective first and second electrical leads 2221, 2223 to which a voltage (e.g., DC voltage) is configured to be applied. While the first and second electrodes 2216, 2217 are illustrated as being disposed on or over an outer surface (not labeled) of the shell 2208 (e.g., the first electrode 2216 being disposed over an upper or a first outer surface and the second electrode 2217 being disposed over a lower or a second outer surface), other embodiments envision that the first and second electrodes 2216, 2217 could be disposed on or over an inner surface (not labeled) of the shell 2208 (e.g., such that the first and second electrodes 2216, 2217 are in direct contact with the liquid dielectric 2212). In a further embodiment, one of the first and second electrodes 2216, 2217 may be disposed over an inner surface of the shell 2208 (e.g., on the inside of the internal cavity 2209) and the other of the first and second electrodes 2216, 2217 may be disposed over an outer surface of the shell 2208 (e.g., outside of the internal cavity 2209). Regardless of whether the first and second electrodes 2216, 2217 are disposed inside or outside of the internal cavity 2209, the first electrode 2216 may be considered disposed over a first side of the internal cavity 2209 and the second electrode 2217 may be considered disposed over a second side of the internal cavity 2209.

[00134] A surface area of the shell 2208 over which the first and second electrodes

2216, 2217 are disposed comprises an active area 2224 of the shell 2208 and a surface area of the shell 208 over which the first and second electrodes 2216, 2217 are not disposed comprises an inactive area 2228 of the deformable shell. While the active area 2224 may be surrounded by the inactive area 2228 as illustrated in the figures, other embodiments envision that the inactive area 2228 may be surrounded by the active area 2224. In any case, application of a voltage to or across the first and second electrodes 2216, 2217 (e.g., via the respective first and second electrical leads 2221, 2223) induces an electric field through the liquid dielectric 2212 (e.g., and shell 2208) to generate electrostatic forces that attract the first and second electrodes 2216, 2217 (where such electrostatic forces generally extend along a first reference axis 2250). The generated electrostatic forces generate an electrostatic Maxwell stress on the active area 2224 of the shell 2204.

Compare Figures 8A-8B. The electrostatic stress displaces the liquid dielectric 2212 in the active area 2224, thus generating hydrostatic pressure that acts on the shell 2208 (e.g., in the inactive area 2228) to urge the shell in one or more different directions so as to move the shell 2208, stretch the shell 2208, etc. [00135] Stated differently, applying a voltage ( e.g., high-voltage signal) across the electrodes 2216, 2217 generates an electrostatic force that causes the electrodes 2216, 2217 to attract or otherwise draw together, where the attraction displaces the liquid dielectric 2212 in between the electrodes 2216, 2217 along a second reference axis 2254 from the active area 2224 into the inactive area 2228, thus coupling electrostatic stress to fluidic pressure. The pressurized liquid dielectric 2212 can deform (e.g., flex) the shell 2208 (e.g., in the inactive area 2228 in this embodiment) to perform mechanical work, such as lifting a load. For instance, the pressurized liquid dielectric 2212 can, upon being forced into the inactive area 2228, urge against the shell 2208 to elastically deform the shell 2208 in the inactive area 2228, such as along a third reference axis 2258 that is parallel to the first reference axis 2250. Compare shape of inactive area 2228 in Figures 8A, 8B, and 8D and also in Figures 8C and 8E. For instance, note how a thickness of the inactive area 2228 increases while a thickness of the active area 2224 decreases thus creating "out-of-plane" deformation of the structure. In one arrangement, the shell 2208 may be inhibited from elastic deformation along at least a portion of the second reference axis 2254 in any appropriate manner. For instance, note how the overall width of the actuator 2200 remains constant in Figures 8A, 8B, and 8D.

[00136] As illustrated, the actuator 2200 can take a toroidal, or any other suitable shape. The ratio of the active area 2224 to inactive area 2228 can be adjusted for scaling force and strain according to hydraulic principles. It can be seen that as the applied voltage increases from Vi to V2, there is a small increase in actuation strains. Compare Figures 8A and 14B. However, when the voltage surpasses a threshold V2 and increases to V3 for instance, the increase in electrostatic force starts to exceed the increase in mechanical restoring force (e.g., owing to the elasticity of the shell 2208 and/ or a load being applied to the shell 2208 ), causing the first and second electrodes 2161, 2162 to abruptly pull together (see Figures 8D and 9); this is a characteristic feature of a so-called pull-in or snap-through transition. Pull-in transitions and other nonlinear behaviors are features of soft active systems that offer opportunities to improve actuation response or functionality and have been used to amplify the response of fluidic and dielectric elastomer (DE) actuators. After the pull-in transition, actuation strain further increases with voltage; this describes the pull-in instability that is shown in Figure 9. Experimental data in Figures 10A and 10B reflects this behavior (e.g., that actuation strain is small until a sudden increase in strain occurs after a certain threshold).

[00137] Figures 10A-10B further illustrate hydraulic behaviors of HASEL actuators such as the donut-type actuators 2200 described in relation to Figures 8A-8E. For the sake of illustration, two donut-type HASEL actuators 2200 are shown in Figures 10A-10B, respectively, as fabricated with identical elastomeric shells and volume of liquid dielectric, but with different electrode areas relative to the diameter of the pouch (the shells, liquid dielectric, and electrodes not labeled in the interest of clarity). As shown, varying the electrode area in this way can tune the strain and force of actuation. Figure 10A shows linear strain as a function of applied voltage under various loads for a first donut-type HASEL actuator with an electrode diameter of 2.5cm. This actuator achieves relatively large strains but generates relatively low force. Figure 10B shows linear strain as a function of applied voltage under various loads for a donut-type HASEL actuator with 1.5cm diameter electrodes. This actuator generates relatively large forces but achieves relatively low strains. In both cases, an electromechanical pull-in instability can be observed, as indicated by a sudden jump in linear strain. This pull-in instability can be harnessed to create unique modes of nonlinear actuation in certain implementations.

[00138] Different performance characteristics of the donut-type HASEL actuators 2200 can be altered by varying the arrangement of the actuators 2200, arrangement of the electrodes 2216, geometry, material, and/or thickness of the shell 2208, volume of liquid dielectric 2212 inside the shell 2208, and/or other parameters. For example, the shell 2208 can be made out of elastomers or flexible plastics to achieve specific actuation responses, and the frequency response of the actuator 2200 can vary depending on the viscosity of the liquid dielectric 2212, the overall size of the actuator 2200, etc. As one example, Figures 11A-11C show that the overall stroke of actuation can be increased by stacking donut-type HASEL actuators 2200 to create a stack 2300. Specifically, Figures 11A-11C show the relaxed state (without an applied voltage in Figure 11A) and an activated state (with an applied voltage in Figures 11B-11C) of a stack 2300 of five donut- type HASEL actuators 2200. As shown, the active areas 2224 of adjacent actuators 2200 in the stack 2300 may overlap and the inactive areas 2228 of adjacent actuators 2200 in the stack 2300 may overlap. In other embodiments, however, active and inactive areas 2224, 2228 of adjacent actuators 2200 in the stack 2300 may overlap or partially overlap.

[00139] In one arrangement, all of the first electrodes 2216 may be electrically interconnected in parallel and all of the second actuators 2217 may be electrically interconnected in parallel. In another arrangement, all of the first electrodes 2216 may be electrically interconnected in series and all of the second actuators 2217 may be electrically interconnected in series. In one arrangement having a stack of five donut-type

HASEL actuators, each with an electrode diameter of 2.5 cm, the stack achieved 37% linear strain, which is comparable to linear strain achieved by biological muscle and corresponds to an actuation stroke of 7 mm (Figure 8B). Hydraulic pressure is generated locally in each donut-type actuators 2200, and liquid dielectrics 2212 (not labeled) are displaced over short distances, allowing for high-speed actuation. The stacked actuators readily showed large actuation response up to a frequency of at least 20 Hz. While not illustrated, one or more objects could be disposed on top of the stack 2300 and moved upwardly and downwardly upon application of a voltage to the stack 2300 and removal of the voltage from the stack 2300.

[00140] As another example of impacting performance of the actuators by altering parameters, Figures 12A-12B illustrate two different shapes for donut-type HASEL actuators 2200 that can exhibit different behaviors because of different electrode layouts. In particular, Figure 12A shows an illustrative donut-type HASEL actuator 2200' with an asterisk-shaped electrode layout both without and with an applied voltage while Figure 12B shows an illustrative donut type HASEL actuator 2200" with an annulus-shaped electrode layout both without and with an applied voltage. In Figure 12B, it can be seen how the active area 2224" may be surrounded by one portion of the inactive area 2228" while another portion of the inactive area 2228" may be surrounded by the active area 2224".

[00141] As another example of impacting performance of the actuators by altering parameters, Figures 13A-13F illustrate an implementation of a donut-type HASEL actuator 2200”’ that can provide three-dimensional mobility. The illustrated donut-type HASEL actuator 2200’” is configured to selectively redistribute a liquid dielectric 2212”’ throughout a ring-shaped deformable shell 2208’”, thereby conferring three-dimensional mobility to the actuator 2200”’. The ring-shaped volume of liquid dielectric 2212 may be surrounded by an insulating skirt 2211’”, with opposing electrode pairs (e.g., 2216i’”/2217i’”, etc.) spaced along the surface of the shell to create a plurality of active areas 2224T", 2224 ₂ ”’, 2224s’” spaced by inactive areas 2228 T”, 2228s 2228s”’. While three active areas 2224”’ and three inactive areas 2228’” are illustrated, it is to be understood that more or fewer such areas may be included.

[00142] By selectively activating electrode pairs, the actuator 2200”’ may redistribute liquid dielectric 2212’” to different regions of the internal cavity 2209’” of the shell 2208”’. For instance, displacing the liquid dielectric 2212’” from one side of the internal cavity 2209”’ to the other may cause the actuator 2200”’ to tilt (e.g., by displacing liquid dielectric from the active areas 2224i’” into the inactive areas 2228 and the active areas 22242”’, 2224 ₃ ”’). This tilting mechanism can be tuned by precise activation of the electrode pairs, for example. For example, Figure 13B shows a rest state for the specific implementation having three electrode pairs. As illustrated in Figure 13D, charging a given pair of electrodes (e.g., electrodes 2216i’”, 2217i”’) causes local compression which results in an overall tilt of the actuator 2200’” from the normal axis 2270’”. A high-voltage connection may be made with electrode 2216i”’ and a ground connection may be made with electrode 2217i’”. In some implementations, all electrode pairs can be activated at once, causing a change in the overall thickness of the actuator 2200’”. As illustrated in Figures 13C, 13E, and 13F, such donut type HASEL actuators 2200’” can be stacked into a stack 2600 to achieve further degrees of three-dimensional mobility. For example, as illustrated by the cross-section of the actuated stack 2600 shown in Figure 13F, electrical connections can be routed through the center of the stack 2600. Again, different modes of actuation can be achieved by varying material selection and geometry, and/or other properties.

[00143] Figure 14A illustrates a representative process for measuring closed loop electromechanical efficiency of HASEL actuators (e.g., donut-type actuators 2200). Figure 14B illustrates a representative experimental setup for measuring efficiency. As shown, a high-speed camera was used to record displacement, y(t) (e.g., change in thickness of the inactive area 2228). A digital acquisition (DAQ) unit sent a control signal to the HV- amplifier and recorded voltage, V(t), and current l(t). Electrical energy was calculated using voltage and current measurements. Figures 14C-141 graphically represent various electrical measurements for the actuation cycle of Figure 14A. In Figure 14C, voltage was applied as a symmetric triangular pattern with maximum voltage of 21 kV and period of 1.5 s. In Figures 14D-14E, a sudden increase in current and a change in the slope of charge indicates pull-in transition of the donut HASEL actuator. In Figure 14F, total electrical energy consumed was 2.88 mj. In Figures 14G-141, time histories of mechanical variables during actuation were recorded for the same cycle. Total mechanical work or energy output was 0.59 mj. Electromechanical efficiency for the cycle was 21%.

[00144] With reference now to Figures 15A-15C, an exemplary structure of a zipper- HASEL actuator is shown. "Zipper-HASEL actuator" may refer to any actuator described herein which is outfitted with a zipping or zipper-like mechanism as described below. This type of actuator utilizes an electrostatic zipping mechanism to enable lower voltage operation and mitigate pull-in instabilities. [00145] A flexible shell or pouch 3604 (e.g., inextensible and/or elastically deformable) defines an enclosed internal cavity designed with one or more tapered boundaries and that is filled with a liquid dielectric 3606. A first electrode 3602a is disposed over a first side of the enclosed internal cavity and a second electrode 3602b is disposed over a second side of the enclosed internal cavity opposite the first side. The electrodes 3602a, 3602b are placed on opposing sides of a tapered boundary of the shell 3604, extending to or almost to the end of the tapered boundary.

[00146] In some embodiments, an edge of each of the electrodes 3602a, 3602b is flush or nearly flush with an edge of the enclosed internal cavity containing the liquid dielectric 3606. This geometry forms a zipping initiation site 3600 wherein the opposing electrodes 3602a, 3602b are in close proximity to one another, whereas the electrodes 3602a, 3602b are separated by a greater distance toward the opposite end of the electrodes. For example, as shown in Figure 15A, at first reference point 3612 along refence axis 3610, electrodes 3602a and 3602b are separated by a greater distance than at second reference point 3614 which is disposed nearer a peripheral edge of the shell 3604 than the first reference point. However, in some embodiments, such as those shown in Figures 16A-16C, the first reference point (where the distance between electrodes is greater) maybe disposed nearer the peripheral edge.

[00147] Figure 15A illustrates the actuator at rest moments before or simultaneous with application of voltage Vi. In this state, the electric field generated by the relatively low voltage is concentrated at the edge of the tapered boundary where the electrodes 3602a, 3602b are closest together. This causes the tapered region to experience a high electrostatic stress in comparison to the rest of the shell 3604, and in response, the electrodes 3602a, 3602b move closer together.

[00148] As shown in Figure 15B, as voltage is increased to V2, the electrostatic forces 3630 extend further in a direction parallel to reference axis 3620, causing a larger portion of the electrodes 3602a, 3602b to be drawn together as the voltage overcomes the larger distances between the electrodes through the liquid dielectric 3606. This urges the top and bottom layers of the shell to be urged together in opposing directions parallel to reference axis 3620 by the electrodes and forces the liquid dielectric 3606 into the inactive area 3622 of the shell 3604 from the progressive zipping site 3608 which moves progressively to the right in the figure, through the active area 3624 as the voltage is increased further. It should be appreciated that in the case of a strain limiting layer, or when one side of the shell is otherwise fixed in position to another object (e.g., another actuator or a solid surface), that one side may remain stationary and relative movement between the top and bottom layers of the shell may be only with respect to the side which is not fixed.

[00149] Notably, the length of the portion of electrodes 3602a, 3602b which are fully drawn together can be controlled along a continuum from zero to the full length of the electrodes based on how much voltage is supplied. This provides a high degree of control over the extent to which the actuator is actuated as compared to binary or "on/off actuators.

[00150] Upon full actuation caused by voltage V3, shown in Figure 15C, substantially all of the liquid dielectric 3606 is forced into the inactive region of shell 3604. In this state, electrodes 3602a, 3602b are fully drawn together, pinching the active portion of shell 3604. In this fully actuated state, the distance between the electrodes 3602a, 3602b is constant along reference axis 3610 from first reference point 3612 to second reference point 3614.

[00151] In the intermediate state shown in Figure 15B, voltage V2 is sufficient to draw the electrodes 3602a, 3602b together between second reference point 3614 and third reference point 3616. However, voltage V2 may be insufficient to overcome the increased pressure in shell 3604 (as compared to the resting state shown in Figure 36A) and close the gap between third reference point 3616 and fourth reference point 3618. However, increasing the voltage to V3 may overcome the increased pressure and draw the entirety of electrodes 3602a, 3602b together as shown in Figure 15C. It should be noted that embodiments using an inextensible shell 3604 would experience a contraction in a direction along reference axis 3610 in response to the vertical flexing of the shell 3604 caused by the increased pressure. In the embodiment illustrated in Figures 15A-15C, the shell 3604 is elastically deformable.

[00152] Figures 16A-16C illustrate toroidal or donut-shaped HASEL actuators as described above in relation to Figures 8A-8E, for example, but with specific attention to a zipping feature. Figure 16A demonstrates the progressive zipping phenomenon. As a low voltage Vi is first applied, the electrodes are drawn together at zipping initiation site 3900, which is in the center of the active area (i.e., the region sandwiched between the electrodes) of the actuator. As the voltage is increased to V2, and then further to V3, the progressive zipping locations 3902 move outward in a ring-shape, forcing substantially all of the liquid dielectric into the inactive area (i.e., the region outside the electrodes). Figures 16B and 16C show two design variations of toroidal zipper-HASEL actuators. In Figure 16B, the zipping actuation begins from a central point 3903 of active area 3904 where the top layer and bottom layer of the shell material is bonded together and actuation moves outward forcing the liquid dielectric into inactive area 3905 which surrounds active area 3904. Electrostatic forces between the electrodes (covering active area 3904 from top and bottom sides) upon application of voltage draws the electrodes toward each other, displacing liquid dielectric from the active area 3904 into the inactive area 3905. Because the top and bottom layers of the shell are bonded at this central point 3903, that is where the layers are closest together and less electrostatic force is needed to draw the electrodes together. Hence, this is the location at which the zipping initiates. The drawing together of the electrodes forces the liquid dielectric outward in all radial directions.

[00153] In the embodiment of Figure 16C, the zipping initiates along lines where the shell is bonded. Figure 16D shows a representative data set of actuation strain as a function of voltage under various loads for an actuator similar to the embodiment depicted in Figure 16C. Notably, the actuator is capable of operating at 3kV while limiting signs of pull-in instabilities. The progressive zipping of the electrodes inhibits a discontinuous jump in actuation strain, enabling precise control of the deformation state of the actuator with the input voltage.

[00154] It should also be appreciated that, although not illustrated, actuators similar to those shown and described in relation to Figures 16A-16C may be constructed with the inactive are in the center, the inactive area being surrounded by an active area. For example, the first and second electrodes may be annular. [00155] Figures 17A-17C illustrate various geometric considerations of a zipper- HASEL actuator. Figure 17A specifically illustrates a side view of a peano-HASEL actuator shell in three phases: prior to actuation, during actuation, and fully actuated. The shape of the shell is assumed to be two intersecting circle segments beginning with radius r ₀ and transitioning through various smaller radii as the zipping progresses. Figure 17B models the total energy of the system as the sum of the electrical potential energy of electrodes and the gravitational potential energy of a lifted mass. Figure 17C provides an equation of the total energy of the system, parameterized by the angle, a, in the shell.

[00156] HASEL actuators which harness a zipping mechanism are advantageous for several reasons. For example, activation of the actuator begins at much lower voltages than previously reported, since the electric field is initially concentrated in a particular region of the shell. Further, the progressive zipping actuation prevents instabilities within the soft structure, allowing for precise control of the deformation state via input voltage. Further still, zipping mechanisms are easily incorporated into previous designs of HASEL but enable a multitude of new actuator designs facilitating various advantageous functions and motions.

[00157] Figures 18A-18B illustrate a pump 1800 having an expandable shell formed from a first flexible wall 1806 and a second flexible wall 1808. Between the walls is a pump chamber 1804 having a first height 1816 when actuators 1812 disposed therein are in an off-state with no voltage applied to the system. Pump 1800 may be coupled with or integrally formed with an inlet conduit 1828 and an outlet conduit 1830. One or more check valves 1818, 1820 may be disposed between one or more of conduits 1828, 1830 and pump chamber 1804. Actuators 1812 are donut-type HASEL actuators as described above. When voltage is applied to the stack of actuators 1812, fluid inside the HASEL actuators is pushed to a periphery, causing the height of the stack to expand in a y-direction that is substantially perpendicular to a longitudinal axis 1854. Flexible walls 1806, 1808 may stretch to allow the pumps to expand in height, thereby increasing the volume of pump chamber 1804 and drawing fluid through check valve 1818 in response to negative pressure. When the voltage is removed from the system 1800, the actuators 1812 relax to their original height 1816, and the elasticity of flexible walls 1806, 1808 may apply a positive pressure to the fluid within chamber 1804 such that the fluid is displaced through second check valve 1820. In this embodiment, the fluid being pumped flows through the chamber 1804 and around the actuators 1812. As such, the fluid that can be pumped through such a system may be limited to non-conductive fluid.

[00158] Referring now to Figures 19A-19C, a pumping system 1900 is shown. The pumping system includes some components similar to those described with respect to pumping system 300 in Figures 3A-3C. Like reference numbers will be used to identify like structures. System 1900 includes a pump 1902 that may be in fluid communication with an inlet conduit 328 and an outlet conduit 330. Pump 1902 includes at least one actuator housing 310 separated from a pump chamber 304 by a first wall 306. First wall 306 may be flexible, stretchable or otherwise movable by one or more actuators 1912. Actuators 1912 may be linearly contracting HASEL actuators. In contrast to the expanding actuators previously discussed, the linearly contracting actuators 1912 decrease in height in the y- direction when a voltage is applied as shown in Figure 19B. In an on-state, the contracted actuators 1912 pull the first wall 306 away from the pump chamber 304, thereby increasing pump chamber height from a first height 316 to a second height 1916, as shown in Figure 19B. The change in pump chamber dimension creates negative pressure which draws fluid into the pump chamber through a first check valve 318. When voltage is removed from the system, the actuators 1912 return to their elongated, off-state position and allow first wall 306 to apply positive pressure to the fluid within chamber 304. The positive pressure displaces fluid from the pump chamber 304 through second check valve 320 into outlet conduit 330 as shown in Figure 19C.

[00159] Figures 20A-20D show an embodiment of a HASEL actuator 2000. The actuator includes a dielectric film pouch 2002 filled with a fluid dielectric 2004. Two electrodes 2006, 2008 are disposed on the outside of the dielectric film pouch 2002. A first electrode 2006 maybe positioned substantially opposite second electrode 2008 as shown. Figures 20A, 20B show the actuator 2000 in an off-state. In the off-state, no voltage is applied to the actuator and the electrodes 2006, 2008 generally conform to the resting shape of the pouch 2002. The pouch 2002 may be sandwiched between rigid plates 2010 to apply a load F to the actuator 2000. Figures 20C, 20D show the actuator 2000 in an on- state. Voltage is applied to one of electrodes 2006 and 2008 causing the two electrodes to draw together. The electrodes draw together, or zip together, starting at the ends of the electrodes that are nearest each other and draw closer along the length. As the electrodes pull together, dielectric fluid 2004 is displaced toward one side of the pouch 2002 causing the pouch to form a more circular or bulbous pocket at one end. The height of the actuated pouch is shown as y in Figure 20D; on-state height y is greater than the off-state height, or initial height, yo shown in Figure 20C. The on-state height y may be a function of the load F applied to the actuator via the plate 2010 and the applied voltage. These factors may determine a length z of the electrodes that zip together, and correspondingly, how much dielectric fluid is displaced. Force per area for the system illustrated in Figures 20A-20D may be governed by Equation 1 below; height for the system illustrated in Figures 20A- 20D may be governed by Equation 2 below..

Equation 1.

Equation 2.

[00160] Figure 21 shows modeled and experimental data for the expanding HASEL actuator 2000. The top left graph shows actuation pressure as a function of pouch length for a variety of fill volumes. The top right graph shows maximum change in height, also referred to as stroke, as a function of pouch length for a variety of fill volumes. The bottom left graph shows actuation pressure as a function of stroke for a variety of pouch sizes. The bottom right graph shows actuation pressure as a function of stroke for a variety of fill volumes.

[00161] Figures 22A-22D show a diaphragm pump 2012 which uses actuator 2000 to control fluid flow. Pump 2012 includes actuator 2000 having a flexible dielectric film pouch 2002 filled with dielectric fluid 2004. First and second flexible electrodes 2006, 2008 are disposed on the outside of the pouch 2002 as discussed with respect to Figures 20A-20D. The pump 2012 further includes a housing 2022 having a cavity, in which actuator 2000 is disposed, and a chamber 2016 which is separated from the actuator 2000 by a diaphragm 2014. Chamber 2016 is fluidly coupled with an inlet channel 2028 and an outlet channel 2030 which may also be disposed within the pump housing 2022. A first one-way valve 2018 is disposed between inlet channel 2028 and chamber 2016; a second one-way valve 2020 is disposed between chamber 2016 and outlet channel 2030.

[00162] Actuation of pump 2012 is shown in Figures 22C-22D. Referring to Figure 22C, a first step of actuating pump 2012 is shown in the top left figure. Voltage is applied to actuator 2000 via electrode 2006. Electrodes 2006, 2008 zip together along at least a portion of their lengths, thereby pushing dielectric fluid 2004 away from the electrodes to form a more circular or bulbous pocket having an increased height compared with the off- state. The pocket engages diaphragm 2014 and pushes the diaphragm into chamber 2016. Fluid occupying chamber 2016 is pressurized due to the membrane taking up more volume within the chamber 2016 as more voltage is applied to the actuator. Once a first threshold pressure (for example a pressure greater than pressure of fluid in the outlet channel 2030) is reached, as shown in the top right figure, one-way valve 2020 unseats from the pump housing 2022 and allows fluid to pass from the chamber 2016 into the outlet channel 2030. At the bottom right figure, applied voltage is decreased and dielectric fluid 2004 flows back toward the electrodes thereby reducing height of the actuator and reducing pressure in chamber 2016. Once the pressure within chamber 2016 drops below a second threshold pressure (for example, the pressure of fluid in the inlet channel 2028), one-way valve unseats from the pump housing 2022 and allows fluid to flow from inlet channel 2028 into chamber 2016. This final step is shown in the bottom left figure.

[00163] Figure 22D shows pressure in chamber 2016 as a function of volume change of chamber 2016 for each of the steps in the four-step pumping cycle described in Figure 22C. Data is shown for both gas and liquid fluids. For an incompressible fluid, the path from state 1 to state 2 is a vertical line because the incompressibility of the fluid prevents deformation of the diaphragm, until the outlet valve opens (state 2) and the fluid can flow out of the chamber at constant pressure (state 2 to 3). The maximum volume (state 3) is limited by either the volume of the chamber 2016 (i.e., all fluid is pumped out of the chamber) or by the strength of the actuator at the voltage F3, which is the difference of the force exerted by the HASEL actuator and the force required to deform the diaphragms divided by the area of the diaphragm (the curve Pactuator - Pdiaphragm). For an incompressible fluid, the path from state 3 to 4 is again a vertical line. When the inlet valve is open liquid flows into the chamber at constant pressure (state 4 to 1) until the pump reaches state 1.

[00164] For a compressible fluid, the volume of the chamber changes when the fluid is pressurized. In the pressure-volume plane, the process of pressurization is represented by a curved line from state 1 to state 2’, the shape of which is determined by the behavior of the fluid (e.g., ideal gas law). The pumping phase for a compressible fluid follows the horizontal line from state 2’ to state 3. During depressurization, a compressible fluid will expand before pressure in the chamber is low enough to cause the inlet valve to open (state 4’). This transition is again determined by the compressibility of the fluid within the chamber and is represented by the curved line from state 3 to state 4’ in the pressure- volume plane. When the inlet valve is open, fluid flows into the chamber at constant pressure (state 4 to 1) until state 1 is reached.

[00165] The area enclosed by the loops 1-2-3-4 and l-2’-3-4’ represent the mechanical work output during one pumping cycle for an incompressible and a compressible fluid, respectively. More work per cycle is expected when pumping incompressible fluids such as water than when pumping a compressible fluid such as air. When pumping compressible fluids, the shape of paths from 1 to 2’ and 3 to 4’ depends on the ratio of the volumes of states 1 and 2’, and the ratio of the volumes of state 3 and 4’. Reducing the amount of dead space within the pump chamber will increase the slope of the paths from 1 to 2’ and 3 to 4’, which will result in more work per cycle when pumping a compressible fluid. Ultimately the work per cycle for the pump may be limited by the performance of the HASEL actuator (state 3).

[00166] Figures 23A and 23B show an exploded view and a cross-sectional view, respectively, of pump 2012.

[00167] Figure 24A shows a top down and cross-sectional views of an example one way valve that can be used within pump 2012. The one-way valve may be a tethered-plate style valve layer within the pump 2012. Example dimensions are provided; however, other sizes and configurations are possible without departing from the scope of the present disclosure. Figure 24B shows forward flow rate as a function of pressure for the valve shown in Figure 24A. In this particular example, the valve may begin to open and flow rate therethrough increases when pressure reaches 0.1 kPa. Figure 24C measures reverse flow rate as a function of pressure. In this example, flow rate increases until reverse pressure reaches 0.1 kPa, at which point, the valve closes or substantially closes.

[00168] Figures 25A-25H show experimental set-up and results for various testing performance of pump 2012 when pumping air. Figure 25A shows the experimental set-up for measuring blocked pressure by connecting the outlet of the pump directly to a pressure sensor. Data for blocked pressure as a function of applied voltage and blocked pressure as a function of frequency is shown in Figures 25B, 25C, respectively. Figure 25D shows the experimental set-up for measuring flow rate by connecting a flow meter to the pump outlet and opening the pump outlet to atmosphere. Data for average and maximum flow as a function of applied voltage and average and maximum flow as a function of frequency is shown in Figures 25E, 25F, respectively. Figure 25G shows the experimental set-up for measuring flow rate as a function of pressure by attaching the outlet pump to an inflatable membrane. Figure 25H shows a graph of average flow rate and average power as a function of pressure.

[00169] Figures 26A-26D relate to the experimental set-up and results for testing performance of pump 2012 when pumping water. Figure 26A shows blocked pressure as a function of applied voltage. Figure 26B shows blocked pressure as a function of frequency. Figure 26C shows the equipment set-up for testing average flow and average power as a function of pressure. These variables were measured by attaching the pump inlet to a large-diameter reservoir and the outlet to a small-diameter reservoir. Average flow and average power as a function of pressure are shown in Figure 26D.

[00170] Figure 27 illustrates the performance of pump 2012 when pumping air and when pumping liquid in comparison to other types of pumps. Specifically, comparisons of free flow rate and blocked pressure are shown.

[00171] Figure 28 illustrates an example actuation signal used to supply voltage to the pump 2012. The actuation signal can be a reversing polarity sine wave having a peak- to-peak voltage magnitude of F with an offset of F/2. The polarity of the sine wave may switch after every period, T, to reduce effects of charge retention. Other actuation signals are also possible such as square waves, ramped square waves, and triangular waves. [00172] Figures 29A-29C show a system 2900 having a pump 2012 that powers an artificial muscle 2902. Figure 29A shows a photograph of the system at rest and during actuation. The system includes a weight 2904 coupled to the artificial muscle 2902 for use in testing performance of the system under different loading conditions. Figure 29B shows the actuation stroke, or change in length, of the artificial muscle 2902 as a function of time for various loading conditions. Applied voltage to the system for this test was 6kV and frequency was 10 Hz, though other values are possible to obtain different results. Figure 29C shows load as a function of strain for the artificial muscle.

[00173] Referring to Figures 30A-30D, a pumping system 3000 is illustrated. The pumping system 3000 includes a pump chamber 3004 defined by a first wall 3006 and a second wall 3008 and having an inlet region 3028 and an outlet region 3030. The first wall 3006 may comprise a surface of a flexible electrode 3014, as shown or may be a separate flexible wall component. The second wall 3008 may be a rigid or semi-rigid component. The pump chamber 3004 has a first height dimension 3016 in an off -state as shown in Figure 30A. The pump chamber 3004 is configured to receive a volume of fluid 3026, which may be any type of fluid including gases or liquids having conductive, dielectric, or insulative properties.

[00174] Moving the volume of fluid 3026 through the pumping system 3000 may be accomplished by selectively actuating at least two of a plurality of distinct electrodes 3012a-3012h to form one or more dielectric fluid pockets 3058 by selectively moving dielectric fluid volume 3024. For example, referring to Figure 30B, a pocket 3058 of dielectric fluid is formed by applying voltage, V, to spaced apart or non-adjacent electrodes 3012a and 3012d. When the voltage is applied, first and second electric fields 3032a,

3032b are generated by the first dielectric 3010 on which the electrodes are disposed. The electric fields interact with the flexible electrode 3014, causing at least a first and second portion 3018, 3020 of the flexible electrode 3014 to move toward the first dielectric 3010 and displace dielectric fluid to form the pocket 3058. Electrodes 3012b, 3012c between the energized electrodes 3012a, 3012d do not receive voltage in order to facilitate bending of the flexible electrode 3014 away from the electrodes 3012b, 3012c to form the pocket 3058. The first dielectric 3010 may be a rigid or semi-rigid material such as biaxially oriented polyester film, biaxially oriented polypropylene, polyvinylidene fluoride terpolymer, and polyimide film. A second dielectric 3034 formed from a flexible or stretchable material may be included between the dielectric fluid volume 3024 and flexible electrode 3014 as shown, but is not required in all embodiments.

[00175] Formation of the pocket 3058 at least partially decreases the height 3016 of the pump chamber 3004 to moderate flow of the volume of fluid 3026 through the pumping system 3000. In the example shown in Figure 30B, the height of the pocket 3058 is equal to the first height dimension 3016 of pumping chamber 3004 such that the pump chamber 3004 is occluded at the pocket 3058; however, many variations are possible. For example, several smaller pockets may be formed by actuating every other, every third, every fourth, etc. of the plurality of distinct electrodes. In some embodiments, the dielectric fluid volume 3024 may be in fluid communication with a reservoir (not shown) having a reserve volume of dielectric fluid that can be moved into the pumping system 3000 in order to facilitate generating several large pockets of dielectric fluid within the pumping system. Alternatively, a portion of the dielectric fluid volume 3024 may be moved out of pumping system 3000 to increase a height 3016 of pump chamber 3004 and/or decrease the number or size of pockets 358 and/or allow increased fluid flow through the pumping system 3000. Thus, the operation of pumping system 3000 can be adjusted and modified using a variety of design variations including amount of dielectric fluid included in the pumping system, initial height of pump chamber 3004, amount of voltage V, applied to one or more of electrodes 3012a-312h, and sequence of applying voltage Vto the one or more electrodes.

[00176] Referring to Figure 30C, an example of moving the pocket 3058, and thus pumping the fluid volume 3026, is shown. To move the pocket from the location shown in Figure 30B to the location shown in Figure 30C, voltage V is applied to electrode 3012b and 3012c and voltage is withdrawn from electrodes 3012d, 3012e. As the flexible electrode 3014 draws closer to the electrodes 3012b, 3012c, dielectric fluid is displaced toward the electrodes 3012d, 3012e which are not actively generating an electric field. Thus, by selectively applying voltage to spaced apart or non-adjacent distinct electrodes, the pocket 3058 can move along a length of the pumping system 3000 applying positive pressure to a first portion of fluid 3026a (i.e., the portion of fluid to the right of the moving pocket) and applying a negative pressure to a second portion of fluid 3026b (i.e., the portion of fluid to the left of the moving pocket).

[00177] In some embodiments, it may be advantageous to keep the size of pocket 3058 substantially constant during the pumping operation. For example, when operating the pumping system 3000 as a peristaltic pump, it may be advantageous to keep volume 3026a separate from volume 3026b by maintaining the occlusion of pump chamber 3004 with pocket 3058. One way to achieve such operation is to keep constant the number of electrodes that do not receive voltage. For example, in both of the states shown in Figures 30B and 30C, there are two electrodes that do not receive voltage. At a first time, when electrode 3012b receives voltage, voltage is simultaneously withdrawn from electrode 3012d. This transition may include abruptly applying/removing voltage from the respective electrodes or may include tapering or transitioning the voltage application/removal for smoother movement of the pocket. At a second time, when electrode 3012c receives voltage, voltage is simultaneously withdrawn from electrode 3012e. As discussed above, this transition may include abruptly applying/removing voltage from the respective electrodes or may include tapering or transitioning the voltage application/removal. In this way, dimensions of pocket 3058 are substantially constant as the pocket gradually moves along a length of the pumping system 3000 to direct fluid 3026.

[00178] Referring to Figures 31A-31C, a pumping system 3100 is shown having components similar to those described with respect to Figures 30A-30C. Like components are labeled with like reference numbers for simplicity. The function of pumping system 3100 is similar to that of pumping system 3000; however, pumping system 3100 includes an opening 3062 in the second wall 3008 where fluid 3026 may exit pump chamber 3004. As pocket 3058 approaches the opening 3062, positive pressure applied to the first portion of fluid 3026a may cause the first portion of fluid 3026a to exit the pump chamber 3004 through the opening 3062. The amount of fluid displaced through opening 3062 and/or the pressure of that fluid may be adjusted by changing the size of opening 3062, changing the size of the outlet region 3030, and/or changing the speed at which pocket 3058 approaches the opening 3062. Many variations are possible without departing from the scope of the present application.

[00179] Once the pocket 3058 reaches the opening 3062 (Figure 31C), the opening may be occluded by a portion of the pocket such that first and second portions of fluid 3026a, 3026b are prevented from exiting the pump chamber 3004 through opening 3062. While one opening is show in the pumping system 3100, multiple openings may be included which may be selectively occluded by one or more pocket 3058. In some embodiments, a check valve (not shown) may be included within the opening 3062 to further control fluid flowthrough the pumping system 3100.

[00180] While the pumping systems 3000, 3100 are shown in a linear configuration, many shapes are possible. For example, the pumping systems 3000, 3100 may be configured in an arc, s-shape, ring, or other continuous or non-continuous shape. Additionally, while eight electrodes 3012 are shown, more or fewer electrodes may be included along the length of the pumping system. Spacing between the electrodes may be selected such that when an electrode receives an applied voltage, the strength of the resulting electric field does not exceed the dielectric strength of an encapsulation layer 3060 surrounding and separating each electrode. Encapsulation layer 3060 may be a dielectric layer separate from the first dielectric 3010; alternatively, electrodes 3012 may be included in the first dielectric 3010 such that the first dielectric 3010 forms the encapsulation layer.

[00181] In pumping system 3000, 3100, voltage is delivered to the plurality of electrodes 3012 by a power source (not shown). A control module may be operably coupled to the power source to provide switching and voltage application instruction for each of the plurality of electrodes. Feedback mechanisms similar to those described with respect to Figure 7 may be implemented to detect various flow and pressure characteristics of fluid within the pump chamber.

[00182] The foregoing describes embodiments of the present invention and is not to be construed as limiting thereof. Although a few exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. For example, many of the pumping systems may be modified to include different types, numbers, and arrangements of actuators. The actuators may be operated in various ways to achieve different results.

[00183] Many aspects of the invention are described in the present disclosure.

[00184] In a first aspect, a method of pumping fluid is disclosed. The method includes providing a first pump comprising a first actuator chamber that includes at least a first actuator. The pump further includes a first pump chamber and a first flexible diaphragm coupled with the first actuator and separating the first actuator chamber from the first pump chamber. The method further includes electrically actuating the first actuator to move the first flexible diaphragm and applying pressure to a fluid disposed in the first pump chamber.

[00185] In a second aspect, the first actuator comprises an expanding actuator configured to expand the first flexible diaphragm into the first pump chamber. [00186] In a third aspect, applying pressure to the fluid comprises applying a positive pressure.

[00187] In a fourth aspect, the first actuator comprises a contracting actuator configured to contract the first flexible diaphragm into the first actuator chamber.

[00188] In a fifth aspect, applying pressure to the fluid comprises applying a negative pressure.

[00189] In a sixth aspect, electrically actuating the first actuator comprises modulating an amount of voltage applied to the first actuator to selectively adjust an amount of movement of the first actuator.

[00190] In a seventh aspect, electrically actuating the first actuator comprises applying a voltage to at least one of a first electrode on a first side of a flexible membrane pouch and a second electrode on a second side of the flexible membrane pouch, wherein the flexible membrane pouch encloses a dielectric fluid. The method further comprises in an on state, generating an electric field to cause the first electrode and the second electrode to move toward each other; displacing a portion of the dielectric fluid between the first electrode and the second electrode; and changing at least a height dimension of the first actuator by a selected amount.

[00191] In an eight aspect, the height dimension of the first actuator increases in the on state.

[00192] In a ninth aspect, the method further comprises providing a second pump in series with the first pump. The second pump comprises a second actuator chamber comprising at least a second actuator, a second pump chamber, and a second flexible diaphragm coupled with the second actuator and separating the first actuator chamber from the second pump chamber, wherein the second pump chamber is fluidly coupled with the first pump chamber. The method further comprises electrically actuating the second actuator to move the second flexible diaphragm and applying pressure to a fluid disposed in the second pump chamber.

[00193] In a tenth aspect, the first pump is electrically actuated at a first time and the second pump is electrically actuated at a second time different from the first time.

[00194] In an eleventh aspect, the first flexible diaphragm is coupled with the second flexible diaphragm.

[00195] In a twelfth aspect, a pump includes a pump chamber comprising a first wall, a first dielectric adjacent the first wall, a first electrode electrically coupled with the first dielectric, and a second electrode comprising a first end coupled with the first wall of the pump chamber and a second end coupled with a second wall of the pump chamber, wherein the second electrode is flexible between the first and second ends, and wherein the second electrode separates a first volume of fluid from a second volume of fluid.

[00196] In a thirteenth aspect, the first dielectric is configured to generate a first electric field in response to receiving voltage from the first electrode.

[00197] In a fourteenth aspect, at least a portion of the second electrode is configured to move toward the first dielectric in response to the first electric field.

[00198] In a fifteenth aspect, movement of the second electrode toward the first dielectric is configured to apply positive pressure to the first volume of fluid and negative pressure to the second volume of fluid. [00199] In a sixteenth aspect, the first wall is substantially rigid.

[00200] In a seventeenth aspect, the first wall comprises a flexible membrane.

[00201] In an eighteenth aspect, the first wall comprises at least one insulating connector configured to couple with the first end of the second electrode.

[00202] In a nineteenth aspect, the pumping system further comprises a second wall opposite the first wall; a second dielectric adjacent the second wall of the pump chamber; and a third electrode electrically coupled with the second dielectric.

[00203] In a twentieth aspect, the second dielectric is configured to generate a second electric field in response to receiving voltage from the third electrode.

[00204] In a twenty first aspect, at least a portion of the second electrode is configured to move toward the second dielectric in response the second electric field.

[00205] In a twenty second aspect, movement of the second electrode toward the second dielectric is configured to apply negative pressure to the first volume of fluid and positive pressure to the second volume of fluid.

[00206] In a twenty third aspect, the second wall is substantially rigid.

[00207] In a twenty fourth aspect, the system comprises at least two stable states.

[00208] In a twenty fifth aspect, the first dielectric is selected from a group consisting of biaxially oriented polyester film, biaxially oriented polypropylene, polyvinylidene fluoride terpolymer, and polyimide film. [00209] In a twenty sixth aspect, the first electrode is selected from a group consisting of carbon grease, carbon ink, silver ink, conductive fabric, and conductive elastomer.

[00210] In a twenty seventh aspect, the first fluid and the second fluid are liquid dielectrics.

[00211] In a twenty eighth aspect, the liquid dielectrics are selected from a group consisting of vegetable-based transformer oils and silicone-based transformer oils.

[00212] In a twenty nineth aspect, a pump includes a pump chamber comprising a first wall and a second wall opposite the first wall; a first dielectric adjacent the first wall; a first electrode electrically coupled with the first dielectric; and a second electrode comprising a first end and a second end, wherein the first and second ends are supported between the first wall and the second wall, wherein the second electrode is movable between the first and second ends, and wherein the second electrode separates a first volume of fluid from a second volume of fluid.

[00213] In a thirtieth aspect, the first dielectric is configured to generate a first electric field in response to receiving a voltage from the first electrode.

[00214] In a thirty first aspect, a portion of the second electrode between the first and second ends is configured to move toward the first dielectric in response to the first electric field.

[00215] In a thirty second aspect, the first and second ends are supported on a longitudinal axis of the pump chamber. [00216] In a thirty third aspect, the pump further includes a second dielectric adjacent the second wall; and a third electrode electrically coupled with the second dielectric.

[00217] In a thirty fourth aspect, the second dielectric is configured to generate a second electric field in response to receiving a voltage from the third electrode.

[00218] In a thirty fifth aspect, the portion of the second electrode between the first and second ends is configured to move toward the second dielectric in response to the second electric field.

[00219] In a thirty sixth aspect, the second electric field is configured to be generated at a different time than the first electric field.

[00220] In a thirty seventh aspect, the pump comprises at least three stable states.

[00221] In a thirty eighth aspect, a method of pumping fluid includes providing a first fluid in a first volume of a pump chamber; providing a second fluid in a second volume of the pump chamber, wherein the first volume is separated from the second volume by a movable electrode; providing a first dielectric adjacent a first side of the pump chamber; generating a first electric field by applying a first voltage to the first dielectric; and moving at least a portion of the movable electrode toward the first dielectric in response to the first electric field, wherein moving the movable electrode toward the first dielectric applies a positive pressure to the first fluid in the first volume and a negative pressure to the second fluid in the second volume.

[00222] In a thirty nineth aspect, the movable electrode comprises a flexible material. [00223] In a fortieth aspect, the flexible material is selected from a group consisting of carbon grease, carbon ink, silver ink, conductive fabric, or conductive elastomer.

[00224] In a forty first aspect, the first and second fluids comprise the same fluid.

[00225] In a forty second aspect, the first and second fluids are selected from a group consisting of vegetable-based transformer oils and silicone-based transformer oils.

[00226] In a forty third aspect, the method further includes providing a second dielectric adjacent a second side of the pump chamber; generating a second electric field by applying a second voltage to the second dielectric; and moving at least a portion of the movable electrode toward the second dielectric in response to the second electric field, wherein moving the movable electrode toward the second dielectric applies a negative pressure to the first fluid in the first volume and a positive pressure to the second fluid in the second volume.

[00227] In a forty fourth aspect, the first electric field is generated at a first time and the second electric field is generated at a second time different from the first time.

[00228] In a forty fifth aspect, the first and second electric fields are generated at alternating times at a selected frequency.

[00229] In a forty sixth aspect, a pumping system includes a pump chamber defined by a first wall comprising a flexible electrode and a second wall. A first fluid occupies the pump chamber. A dielectric fluid is disposed within a compartment defined by the flexible electrode and a first dielectric. A plurality of separate electrodes are disposed on the first dielectric and each electrode is configured to selectively receive voltage and generate an electric field in response to the applied voltage. [00230] In a forty seventh aspect, a method of operating the pumping system described in the forty sixth aspect includes selectively applying voltage to at least two of the plurality of electrodes, wherein the two of the plurality of electrodes are not adjacent. At least two electric fields are generated in response to applying voltage to at least two of the plurality of electrodes. At least a first and second portion of the flexible electrode are drawn toward the first dielectric in response to the generated electric field, thereby displacing dielectric fluid into a pocket and adjusting at least one of pressure and flow of the fluid occupying the pump chamber.

[00231] Accordingly, many different embodiments stem from the above description and the drawings. It will be understood that it would be unduly repetitious and obfuscating to literally describe and illustrate every combination and subcombination of these embodiments. As such, the present specification, including the drawings, shall be construed to constitute a complete written description of all combinations and subcombinations of the embodiments described herein, and of the manner and process of making and using them, and shall support claims to any such combination or subcombination.

[00232] In the specification, there have been disclosed embodiments of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation. Although a few exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the claims. Therefore, it is to be understood that the foregoing is illustrative of the present invention and is not to be construed as limited to the specific embodiments disclosed, and that modifications to the disclosed embodiments, as well as other embodiments, are intended to be included within the scope of the appended claims. The invention is defined by the following claims, with equivalents of the claims to be included therein