CROSS REFERENCE

[001] This Application claims the benefit of U.S. Provisional Patent Application No.

62/636,758 filed on February 28, 2018, which is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

[002] Mixing of miscible fluids in micro- and millimeter scale channels is difficult to accomplish without agitation of flows with integrated actuators. At least two device architectural mechanisms have been contemplated to achieve mixing without agitation: lamination and chaotic advection. Lamination involves arranging inlet co-flows of differing reagents in alternating lanes across the channel, accomplished either by constructing interdigitated inlets to a single mixing channel or by splitting co-flows and reassembling them repeatedly. This method is relatively straightforward, reducing the characteristic diffusion distance by a predictable amount. Mixing co-flows with chaotic advection involves stretching and folding flow lines through engineered channel geometries or making channels with sufficiently three-dimensional architectures. This is somewhat less straightforward, with performance enhancements to mixing seen at higher Reynolds Numbers than is typical to many applications in biochemical processing.

SUMMARY OF THE INVENTION

[003] Disclosed herein, in some aspects, are systems that comprise 3D-printed modular mixing components and microchannels. In some instances, the systems operate on the basis of splitting and recombining fluid streams to decrease interstream diffusion length. Also disclosed herein, in some aspects, are methods that comprise 3D printing systems of modular mixing components. In general, 3-D printing facilitates straightforward construction of microchannels with complex three-dimensional architectures.

[004] Aspects disclosed herein provide microfluidic devices comprising at least one inlet channel for receiving a fluid stream, an internal microfluidic circuit comprising at least two separate channels that are connected to the inlet such, wherein the at least two separate channels are capable of splitting the fluid stream at least once, and an at least one outlet channel, wherein each element of the internal microfluidic circuit is configured to maintain about the same hydraulic resistance from the at least one inlet channel to the at least one outlet channel. In some embodiments, the microfluidic devices comprises the inlet channel and the outlet channel, wherein the inlet channel supports the fluid stream in a first direction, and the outlet supports the fluid stream in a second direction, wherein the first direction is parallel to the second direction.

In some embodiments, the inlet and outlet channels of the microfluidic device are on different planes. In some embodiments, the inlet channel of the microfluidic device supports a solution flow in a first direction, and the outlet channel supports the solution flow in a second direction, wherein the first direction is not parallel to the second direction. In some embodiments, the microfluidic device comprises a single inlet channel, wherein the fluid stream is split at least once into at least two fluid streams, and wherein the internal microfluidic circuit is configured to merge the at least two fluid streams into the at least one outlet channel. In some embodiments, the microfluidic device comprises at least two inlet channels and a single outlet channel, wherein the internal microfluidic circuit is configured to merge two fluid streams coming from the two inlet channels into the outlet channel. In some embodiments, the microfluidic device divides the diffusion distance of the fluid streams from the inlet(s) to the outlet in half. In some

embodiments, the width or diameter of at least one of the inlet channel, outlet channel, and two separate channels of the microfluidic device is not greater than a 1000 microns. In some embodiments, the microfluidic device is manufactured using a stereolithographic method. In some embodiments, the stereolithographic method of manufacturing the microfluidic device is three-dimensional printing.

[005] Aspects disclosed herein provide microfluidic systems comprises a first microfluidic device comprising a first inlet channel and a second inlet channel, a first internal microfluidic circuit, and a first outlet channel, wherein the first internal microfluidic circuit comprises a first internal channel connected to the first inlet channel, and a second internal channel connected to the second inlet channel, such that a first fluid stream entering the first inlet channel and a second fluid stream entering the second inlet channel are merged into a third fluid stream before exiting the first outlet channel. In some embodiments, the microfluidic system further comprises a second microfluidic device comprising a single inlet channel in communication with the first outlet channel, a second internal microfluidic circuit, and a second outlet channel, wherein the second internal microfluidic circuit comprises at least a third internal channel and a fourth internal channel that split the third fluid stream entering the single inlet channel into at least a fourth and fifth fluid stream, and wherein the second internal microfluidic circuit is configured to merge the fourth and fifth fluid streams into the second outlet channel. In some embodiments, the microfluidic system comprises the first internal channel, wherein the first internal channel turns in a direction that is not parallel to a flow of the first fluid stream as it enters the first inlet channel. In some embodiments, the microfluidic system comprises the third internal channels, wherein the third internal channels turns in a direction that is not parallel to a flow of the third fluid stream as it enters the single inlet channel. In some embodiments, the first inlet channel of the microfluidic system is in a different plane than the first outlet channel. In some embodiments, the single inlet channel of the microfluidic system is in a different plane than the second outlet channel.

[006] Aspects disclosed herein provide methods of assessing the mixing efficiency of a microfluidic mixing system, said method comprising assembling at least two elements from a library of elements into a contiguous system that supports flow of a fluid stream through the at least two elements, wherein each element has an internal microfluidic circuit connecting an input channel and an output channel; flowing the fluid stream through the at least two elements, wherein the fluid stream comprises a detectable signal; and measuring at least one of the flow rate, hydraulic resistance, and resident volume of the system or an element thereof, wherein measuring comprises detecting the detectable signal. In some embodiments, the method of assessing the mixing efficiency of a microfluidic mixing system comprises controlling the flow rate of the fluid stream into the input channel of at least one element. In some embodiments, the method of assessing the mixing efficiency of a microfluidic mixing system comprises measuring comprises imaging the fluid stream and using an image processing algorithm to quantify flow rate-dependent mixing of the system. In some embodiments, the method of assessing the mixing efficiency of a microfluidic mixing system comprises comparing the mixing efficiency of the microfluidic mixing system to a modified configuration of the microfluidic mixing system, wherein the method further comprises: assembling the at least two elements from the library in a new orientation; flowing the fluid stream through the at least two elements; measuring at least one of a modified flow rate, modified hydraulic resistance, and modified resident volume; and comparing the at least one modified flow rate, modified hydraulic resistance, and modified resident volume to the flow rate, hydraulic resistance, and resident volume. In some

embodiments, the method of assessing the mixing efficiency of a microfluidic mixing system comprises injecting a fluid stream at various flow rates into the microfluidic mixing system in an initial configuration and its modified configuration and determining that either the initial configuration or the modified configuration is more suitable for a chosen flow rate.

BRIEF DESCRIPTION OF THE DRAWINGS

[007] FIG. 1A shows an exemplary computer-aided drafting (CAD) representation of Ll laminator discrete elements disclosed herein. More views of these laminator elements are presented in FIG. 6.

[008] FIG. IB shows an exemplary computer-aided drafting (CAD) representation of L2 laminator discrete elements disclosed herein. More views of these laminator elements are presented in FIG. 6. [009] FIG. 1C shows an exemplary top-view photograph of the second Ll device (with 90 _° rotation with respect to the first Ll), within an Ll + Ll series configuration, showing the doubling of two lamellae to four, and then eight aiming for mixing enhancement. Flow is from the right to left; each block is 1 cm long on each side.

[010] FIG. ID and FIG. IE show CAD representations of the helical 5G and helical 10G devices, respectively.

[011] FIG. 2A shows an exemplary CAD representation of an exemplary experimental setup used to determine mixing efficiency. The systems were placed on a light stage to illuminate the straight pass channel where the microscope was focused to take images (inset).

[012] FIG. 2B shows signal intensity (such as in FIG. 7), which was measured down a line crossing the channel perpendicular to the direction of flow and used to determine mixing efficiency with in-house developed algorithms.

[013] FIG. 3 shows an exemplary flow rate-dependent mixing efficiency for exemplary devices and configurations, panel (a) shows exemplary laminator designs. Panel (b) shows exemplary helical elements. Panel (c) shows planar channel elements. Device nomenclature is given in FIG. 5.

[014] FIG. 4 shows an exemplary trade-off between mixing efficiency, hydraulic resistance, and resident volume for all devices and configurations studied at four flow rates: (a) 1 mL/h, (b) 5 mL/h, (c) 10 mL/h, and (d) 15 mL/h.

[015] FIG. 5 shows an exemplary standard library of components used in these experiments, which include: mixers, straight pass, port, and connectors. Here we include a CAD image of the devices, their respective nomenclature (e.g. Ll, L2, R1G, etc.), their network resistance model, and lastly the devices respective resistance and associated resident volume.

[016] FIG. 6 shows exemplary alternate views of the Ll laminator discrete element showing a side-view (a), top-down view (b) and an interior view (c). Likewise, the bottom row of images shows alternate views of the L2 laminator discrete element showing a rear-view (d), side-view (e), and an interior view (f).

[017] FIG. 7 shows an exemplary process flow diagram for determining mixing efficiency of a device. The process begins by using a stereoscope to take images of the system in question at different flow rates. The pixel intensity for a line perpendicular to the center of the straight pass channel in the system is isolated. This is done for a total of 101 intensity profiles, by taking profiles to the left and right of channel center point, 50 pixels in range, respectively. This data is averaged and put through a flatness correction to adjust for uneven lighting that may occur. Data is then normalized and mixing efficiency is determined. [018] FIG. 8 shows an exemplary linear fit around the measured line intensity of a‘perfectly mixed’ situation run at 0.5 mL/h was used to correct for uneven illumination of other trials at higher flow rates. The fitted line was subtracted from measured intensity of relevant flow rates. An example case is shown here for the measured intensity perpendicular to the center of a channel for the 1L device at three different flow rates: 0.5, 10, and 20 mL/h. Flattened data is later normalized to determine mixing efficiency.

DETAILED DESCRIPTION OF THE INVENTION

[019] Mixing of miscible fluids in micro- and millimeter scale channels may be difficult to accomplish without agitation of flows with integrated actuators. Flows may be strictly laminar at typical flow rates, characterized by Reynolds Numbers several orders of magnitude below the transition region (2000-4000). Consequently, convection may have little influence on co- flowing liquids, leaving diffusion as the dominant mechanism by which streams mix. This may be quite slow in microfluidic systems for biochemical processing, where fluid reagents often contain high-molecular-weight compounds with low diffusion coefficients. These reagents are often rare or costly, and reducing their consumption may be imperative for the success of research programs. This poses a problem for engineers, who must balance the reagent volume resident to their microfluidic system whilst achieving sufficiently high mixing efficiencies. Methods of improving mixing efficiencies may comprise shortening the diffusion distance of mixture components through clever architecting of channel geometries or partitioning of fluids into compartments such as droplets. Furthermore, construction of multi-layer channel devices with three-dimensional features poses a significant challenge for microfabrication technologies.

[020] In order to meet these challenges, additive manufacturing techniques (i.e.,“3D printing”) are disclosed herein that achieve device designs with sophisticated interior architectures and create a system of interconnects based on self-aligned interference fits. The resulting devices are significantly less difficult to manufacture than traditionally micro-machined, multilayer monolithic lab-chips, and enable engineers to construct systems that are suitable for mass manufacturing. Elements of these systems are designed to enable the use of lumped-parameter modeling and network analysis techniques familiar to discrete element-based electronics design. Elements of these systems may be adjusted for the nuances brought on by mass-manufacturing of systems in which multiple fluid reagents may be used. In some instances, the range of channel sizes achievable through additive manufacturing is limited as compared to traditionally micro- machined devices. By way of non-limiting example, a channel disclosed herein may have a width (or diameter) of less than 1000 pm. In some instances a channel disclosed herein may have a width (or diameter) of about 600 pm. Thus, methods comprise developing mixers with a wide coverage of resident volumes and hydraulic resistances to work with channel sizes achievable by additive manufacturing.

[021] In general, systems disclosed herein comprise discrete elements engineered for high- efficiency mixing across a range of flow rates based on the principle of lamination, made possible through additive manufacturing. Typically it is desirable to minimize the addition of resident volume to their microfluidic network design while maximizing mixing efficiency at the flow rate of operation. The resistance of the device may affect this flow rate depending on whether a constant flow rate or constant pressure driven flow is being utilized, but can be managed in conjunction with other resistive components in the network.

[022] Discrete microfluidic elements disclosed herein, as well as systems of elements, may be manufactured using stereolithography. Stereolithography enables the facile routing of microfluidic channels in three dimensions, but has much larger manufacturing tolerance than traditional micromachining. For example, in the processes used to construct devices presented herein, tolerances can be as high as 30 pm, whereas micro CNC tolerances are often <5 pm and semiconductor processing tolerances are submicron. In some instances, methods disclosed herein comprise stereolithography. In some instances, stereolithography comprises 3D printing.

[023] Also disclosed herein are methods of experimentally quantifying mixing efficiency and characterizing mixer performance with respect to key engineering design trade-offs between mixing efficiency, resident volume, and hydraulic resistance. Different flow rates into experimental assemblies may be varied using, e.g., a push-pull style syringe pump, to determine suitable experimental assemblies for a given flow rate.

[024] Variation in channel sizes in discrete microfluidic elements directly propagates fluid handling performance errors, implying the need for simple and versatile empirical device characterization methods. For example, in the laminator devices presented herein, manufacturing imprecision may cause the internal inlet-to-outlet distribution of hydraulic resistances to differ from their intended symmetry. In addition, the internal microfluidic network is sufficiently three-dimensional that chaotic advection effects may cause unexpected variation in performance, especially at higher flow rates. Combined with variable interfaces between reagent co-flows and reagents and channel walls, these challenges motivated development of methods of rapidly quantifying the flow rate-dependent mixing efficiency of discrete microfluidic elements.

Assemblies, and flow of fluids therethrough, may be observed using a stereoscope. Images may be recorded over a range of flow rates. By way of non-limiting example, methods may comprise obtaining images maintaining unity gamma such that intensity is linear with concentration of a dye for any sample. EXAMPLES

Example 1. Design of Laminator Discrete Elements

[025] Two variations of a laminator discrete element were designed and manufactured using stereolithography, see FIG. 1. In the first device“Ll” (FIG. 1A), a co-flow of two laminated miscible fluid streams was introduced into the element from a single inlet, split into separate channels such that each fluid stream was isolated, split again individually to duplicate each isolated flow, and merged in the outlet channel in an interdigitated fashion. This resulted in alternating layers of the two fluids. This same basic procedure was performed in the second device,“L2” (FIG. IB), where instead flows of differing fluids were directly introduced into the element from two inlets. In this manner, both components divided the diffusion distance in half from the inlet(s) to the outlet. The internal microfluidic circuit of each element was designed such that the hydraulic resistance from any inlet to the outlet of the element was always the same. This was important to guarantee that each channel segment filled at the same rate, minimizing the risk of gas bubbles being formed in areas of the network where there are closed loops. This was also particularly important for the Ll device, in which the inlet co-flow was assumed to be 50% filled with either fluid. Both devices rotated the relative arrangement of inlet flows by 90° in the plane perpendicular to the direction of flow, as seen in FIG. 1C. Thus, in placing the element in a network, one must consider how inlet fluids are managed both before entering and after exiting a laminator element. For example, in the L2 element, reagents were directly introduced into the component in one plane, but exit the component stacked on top of one another, perpendicular to the plane of their introduction. In the Ll element, reagents must enter the component in a co-flow with the interface between them in one plane, but exit such that this interface is perpendicular to its original orientation. In other words, if the Ll component was not oriented correctly, co-flows would simply be re-arranged into the same configuration they were already in, but in a plane perpendicular to their inlet arrangement.

[026] The Ll and L2 elements were arranged in series with one another to continually shorten the diffusion distance and enable geometric enhancement to the mixing performance of the overall system. This is seen as the Ll + Ll system (FIG. 1C). Note that the second component was rotated 90° with respect to the first component, such that the inlet co-flow was split correctly into two isolating channel segments internally and functioned to enhance mixing. To gauge the mixing efficiency of the Ll and L2 laminator devices within the context of reagent volume and network resistance, the mixing efficiency was compared to helical devices,“H 5G” and“H 10G”, differentiated by their internal path length, number of turns, and consequent hydraulic resistance, (FIG. ID, IE). In order to assess the Ll and L2 laminator devices within the context of these parameters, their mixing efficiencies were compared to those of three more elements. These components were designed with convenient hydraulic resistance (to pure water) values of 1, 2.5, 5, and 10 GPa-s-m3 (“SP 1G”,“S 2.5G”,“H 5G”, and“H 10G” respectively, where“SP” stands for“straight-pass”,“S” for“snake”, and“H” for“helix”). All devices are shown in FIG. 5, along with their network resistance model, respective resistance, and associated resident volume.

Example 2 Quantifying Mixing Efficiency

[027] FIG. 2 describes an experimental setup used to measure mixing performance of a device having characteristics described herein. A library of discrete microfluidic elements is tabulated in FIG. 5, along with terminal characteristics to flow, internal network representation, and nomenclature used for each element. Elements were assembled so that two inlet reagent flows were merged to form a co-flow, and then passed through the laminator device or combination of devices being characterized. This was followed by a simple straight pass element (“SP 1G”) that was inspected with a stereoscope and high resolution camera such that the interface between differing reagent co-flows was perpendicular to the imaging plane. A water stream containing a dye of known diffusivity and high absorbance was flowed through one inlet, merging with a flow of pure water from the other inlet. A dual-syringe, single driver syringe pump was used to manage inlet flows such that flow rates were well-matched to one another and the dyed stream would be mixed with water in a 1 :1 ratio. The total inlet flow rate was then varied across a range of typical laboratory values and a monochrome image was captured for each flow rate, indicating the extent to which diffusive mixing had occurred.

[028] An image processing algorithm was developed to quantify the flow rate-dependent mixing performance of the devices measured (see FIG. 7). At a given flow rate, the intensity profile of the channel cross-section was measured at the centre of the observed SP 1G component and averaged. The resultant data was then normalized to a scale in which the intensity of the pure water was set to 1 and the intensity of pure dye was set to 0. An edge finding algorithm was used to find the interior of the channel and extract the intensity data interior to the channel. A line was fit to the data corresponding to a perfectly mixed scenario, taken at an extremely low flow rate. This line was subtracted from remaining data corresponding to relevant flow rates to correct for uneven illumination within the channel (more example data from before and after this correction is found in FIG. 8).

[029] Mixing efficiency was determined by measuring the average absolute deviation (AAD) from the mean for each processed intensity frame, or AAD, expressed as:

[030] Here, /„ represents a processed intensity data point along the measurement line and indexed by pixel number n as a function of the flow rate, Q. N represents the total number of pixels in the set, or interior of the channel. (G) represents the mean intensity of that line. The AAD quantifies how poorly or how well reagents were mixed in the channel by assessing how much the intensity distribution in the channel deviates from a mean-valued, flat line. To compute a measure of efficiency, a condition for perfect non-mixing was used to establish the upper theoretical limit of AAD. AAD was assumed to be 0.5, or the AAD of a channel in which exactly one half contains dye and the other half is translucent and in which diffusion is not possible. The mixing efficiency m was therefore calculated as:

[031] Data processing was performed using the R programming language in the RStudio developer environment. As indicated in FIG. 2, the intensity along a line was measured perpendicular to the channel walls in a SP 1G element in series with the mixer element or configuration of elements being measured. An intensity profile was constructed by locating the centre of this line, and then storing values associated within 50 pixels to the right and left of the centre. The edges of the channel walls themselves were found by first measuring the mean intensity value and standard deviation of intensity in 100 pixels at the outer edges of the profile, and then searching for a change in intensity greater than three standard deviations from the left and right edges of the profile to the centre, marking the approximate locations of the edges. The interior of the channel was then determined within a margin of eight pixels of the approximate edges to exclude noise due to the channel-fluid interface. Data for the mixed condition used to baseline illumination inhomogeneity was collected at a flow rate of 0.25 mL/h through the centre of the experimental assembly (see FIG. 2).

Example 3 Device Performance and Engineering Trade-Offs

[032] FIG. 3 shows the flow rate-dependent mixing efficiency for non-limiting, exemplary devices and configurations disclosed herein. A standard T-junction element with no subsequent mixing elements was measured for comparative purposes (data labelled“No Device”). FIG. 1A shows the results for laminator devices and series configurations of laminator devices. The efficiency declined as flow rate increased. The Ll and L2 devices and their series combinations showed significant improvement in efficiency over the T-junction over a large range of flow rates, as well as nearly linear, comparable performance to one another at low flow rates. Like the T-junction, the efficiency for each individual laminator device appeared to plateau at a minimum value with increasing flow rate. This was likely due to faster flow rates resulting in less diffusion and, hence, clear separation of dyed and translucent fluid lamellae. None of the systems approached an asymptotic efficiency of zero at high flow rate; this is due to the fact that some Taylor dispersion-mediated mixing occurs. All laminator systems plateaued at a higher mixing efficiency than the“no device” system. These systems had both a longer path length than the “no device” case and some three-dimensional turns that resulted in some mixing by chaotic advection. The specific value upon which the Ll and L2 devices converged appeared to deviate from one another despite the intended design of both devices resulting in the same number of lamellae. This may be a direct result of imperfect manufacturing. For example, the Ll device may have outperformed the L2 device because of the added channel structure at the inlet which acts to split the flows: imperfect splitting leads to pre-mixing of fluids before lamination was accomplished. This effect may also have caused disparities in the behaviour between Ll + Ll and L2 + Ll series configurations, with the latter resulting in better mixing above 5 mL/h.

However, any of the series combinations of devices led to a significant gain in mixing performance over individual devices. This is consistent with the notion that each device essentially doubles the number.

[033] In designing discrete element microfluidics, two hydraulic terminal characteristics are of importance: resistance to flow and resident volume. The inherently parallel arrangement of the microfluidic network within both Ll and L2 elements implied that their hydraulic resistance is of minimum consequence to most networks of interest. However, the increase in total channel length relative to other elements in the library implied that the resident volume of each component can also significantly impact a reagent volume budget.

[034] In order to assess the Ll and L2 laminator devices within the context of these parameters, their mixing efficiencies were compared to those of three more elements. These components were designed with convenient hydraulic resistance (to pure water) values of 1, 2.5, 5, and 10 GPa-s-m3 (“SP 1G”,“S 2.5G”,“H 5G”, and“H 10G” respectively, where“SP” stands for“straight-pass”,“S” for“snake”, and“H” for“helix”). The helical devices are shown in FIGS. ID and IE; all devices are shown in FIG. 5. Helical devices use the same channel size as others described here, but achieve increased hydraulic resistance by routing a single channel in a snake or helical shape with square walls. The benefit of helical structures to mixing is two-fold: at low flow rates, the longer channel length allows for increased diffusion times and therefore enhanced mixing efficiencies, while at high flow rates mixing is enhanced due to chaotic advection. This is directly evident in FIG. 3 panel (b): the flow rate-dependent efficiency of both devices had a minima around 10 mL/h. By comparison, FIG. 3, panel (c) shows devices with no three-dimensional structure that do not benefit from chaotic advection at higher flow rates.

[035] FIG. 4 represents a map of the design trade-off between resident volume, hydraulic resistance, and mixing efficiency over a broad range of flow rates for the device configurations studied. At low flow rates, roughly <5 mL/h, all devices achieved similar mixing efficiencies, enabling designers with flexible choice of components based on resistance and resident volume characteristics. More specifically, the H 5G device accomplished nearly equivalent mixing efficiencies as the series laminator configurations (Ll + Ll and L2 + L2) with far less cost to resident volume. The H 10G device behaved much like the individual Ll and L2 devices with only slightly worse cost to resident volume. At high flow rates (>15 mL/h), helical devices such as H 5G and H 10G showed similar, advantageous mixing efficiencies relative to others, but the H 5G device outperforms the H 10G with respect to conserving resident volume budget.

[036] Overall, the laminator devices may serve systems requiring high mixing efficiency at low to moderate flow rates (<10 mL/h) where minimal impact on network resistance is desired. However, this may be at the expense of slightly higher volumes relative to helical devices. For microfluidic networks operated typically at low flow rates, there are a variety of resistors in choosing helical devices. However, laminator devices may ensure less sensitivity over a wider range of flow rates, acting to functionally stabilize mixing in the network to unintended operational defects, e.g., opening and closing of downstream valves, which can cause rapid pulses in fluid pressure, and therefore flow rate.