NON-CONTACT MEASUREMENTS OF FLUIDS, PARTICLES AND

BUBBLES

CLAIM OF PRIORITY

This application claims the benefit of U.S. Provisional Patent Application

Serial No. 62/652,738, filed on April 4, 2018, the entire contents of which are hereby incorporated by reference.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Grant Nos.

1DP2EB022358, awarded by the National Institutes of Health; DGE-l 144086, awarded by the National Science Foundation; DP2 HL 137187 awarded by the National Institutes of Health; and R00 HL 117048, awarded by the National Institutes of Health. The Government has certain rights in the invention.

BACKGROUND

Microfluidic devices have long been touted as a powerful analytical tool to characterize a wide range of analytes, including particles, cells, and fluids. These devices, however, have not seen wide-scale adoption outside of the lab [1] because using microfluidic devices can require significant capital. An individual microfluidic device may be cheap, but the vast majority [2] of microfluidic devices operate on optics-based systems which typically include high-speed or sensitive cameras, sophisticated confocal microscopes, vibration isolation tables and laser excitation systems, which often require fluorescent probes [3-5]

SUMMARY

Provided herein are devices and methods for detecting, quantifying, measuring, and/or identifying fluids, fluid flow, and particles in the fluids using electrical signals obtained from a strain sensor on the wall of a channel through which the fluid is flowing based on deformation of the channel wall. In one aspect, a channel is provided, comprising one or more walls having an elastic modulus of 1 MPa or less and defining at least a portion of fluid flow channel; and a strain sensor comprising a graphene layer and a metallic layer wherein the metallic layer comprises a plurality of metallic nanoislands.

In some embodiments, the metallic layer can comprise palladium. In some embodiments, the metallic layer can comprise palladium nanoislands.

In some embodiments, the strain sensor can be embedded in said wall.

In some embodiments, the channel can further comprise one or more electrodes electrically connected to one or more of said metallic nanoislands. In some embodiments, the channel can further comprise one or more leads electrically connected to said electrodes.

In some embodiments, the wall can comprise an inner wall and an outer wall and the strain sensor can be situated between said inner wall and said outer wall.

In some embodiments, the strain sensor can further comprise a polymeric layer.

In some embodiments, the channel can further comprise an inlet and an outlet.

In some embodiments, the strain sensor can be configured to provide an electrical impedance profile associated with the flow of fluid through the fluid flow channel. In some embodiments, the strain sensor can be configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel.

In another aspect, a microfluidic device is provided comprising one or more of the channels described herein.

In some embodiments, the device can further comprise one or more reaction chambers. In some embodiments, the device can further comprise one or more inlet ports. In some embodiments, the device can further comprise one or more microfluidic valves.

In another aspect, a system is provided comprising one or more channels described herein.

In some embodiments, the system can be configured to provide an electrical impedance profile associated with the flow of fluid through the fluid flow channel. In some embodiments, the system can be configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel.

In another aspect, a method is provided for detecting deformation in at least a portion of a channel described herein through which a fluid is flowing, comprising measuring one or more electrical signals from the strain sensor caused by the deformation. In some embodiments, the strain sensor does not directly contact the fluid.

In some embodiments, the one or more electrical signals is a voltage.

In some embodiments, the measuring comprises continuous measuring.

In some embodiments, the method further comprises detecting one or more particles in the fluid. In some embodiments, the one or more particles are rigid or deformable. In some embodiments, the one or more particles is a gas bubble. In some embodiments, the one or more particles is a solid particle. In some embodiments, the one or more particles is a biological cell. In some embodiments, the method can further comprise determining one or more properties of at least one of the particles. In some embodiments, the one or more properties are selected from rigidity, deformability, size, flow rate, and identity. In some embodiments, the method can further comprise quantifying the particles based on the detecting of the particles. In some embodiments, the strain sensor does not directly contact the particle. In some embodiments, the method can further comprise determining the identity of the gas bubble based on the one or more electrical signals. In some embodiments, the method can further comprise determining the identity of the solid particle based on the one or more electrical signals. In some embodiments, the method can further comprise determining the identity of the biological cell based on the one or more electrical signals.

In some embodiments, the method can further comprise calculating a flow rate of the fluid based on the one or more electrical signals.

In another aspect, a method for high throughput particle sorting is provided, comprising passing a fluid containing a plurality of particles through a channel described herein; detecting deformation caused by a particle in at least a portion of the channel by measuring one or more electrical signals from the strain sensor;

identifying one or more properties of the particle based on the one or more electrical signals; sorting the particle based on the one or more properties. In some

embodiments, the particle is a biological cell.

In one aspect, provided herein is a channel comprising one or more walls having an elastic modulus of 100 MPa or less and defining at least a portion of a fluid flow channel and a first strain sensor comprising a supporting layer and a metallic layer on and in contact with the supporting layer, wherein the metallic layer comprises a plurality of metallic nanoislands.

Implementations can have one or more of the following features. The one or more walls can have an elastic modulus of 50 MPa or less. The one or more walls can have an elastic modulus of 25 MPa or less. The one or more walls can have an elastic modulus of 10 MPa or less. The one or more walls can have an elastic modulus of 5 MPa or less. The one or more walls can have an elastic modulus of 3 MPa or less. The one or more walls can have an elastic modulus of 2 MPa or less. The one or more walls can have an elastic modulus of 1 MPa or less. The one or more walls can have an elastic modulus of between about 50 kPa and 100 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 50 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 25 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 10 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 5 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 3 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 2 MPa. The one or more walls can have an elastic modulus of between about 50 kPa and 1 MPa. The one or more walls can have an elastic modulus of between about 1 MPa and 10 MPa. The one or more walls can have an elastic modulus of between about 1 MPa and 5 MPa. The one or more walls can have an elastic modulus of between about 1

MPa and 3 MPa. The one or more walls can have an elastic modulus of between about 1 MPa and 2 MPa. The supporting layer can include graphene. The supporting layer can include hexagonal boron nitride. The supporting layer can include molybdenum disulfide. The metallic layer can include palladium, gold, or silver. The nanoislands can include palladium, gold, or silver. The nanoislands can be palladium nanoislands. The strain sensor can be embedded in said wall. The strain sensor can be not in contact with the fluid flow channel. The strain sensor can be separated from the fluid flow channel by about 1 to about 10 mih. The strain sensor can be separated from the fluid flow channel by about 1 to about 5 pm. The strain sensor can be separated from the fluid flow channel by about 1 to about 3 pm. The strain sensor can span the fluid flow channel. The sensor can be perpendicular to the long axis of the fluid flow channel, the fluid flow channel having a long axis. The supporting layer can be between the fluid flow channel and the metallic layer. The metallic layer can be between the fluid flow channel and the supporting layer. The channel can further include one or more electrodes electrically connected to one or more of said metallic nanoislands. The channel can further include one or more leads electrically connected to said electrodes. The wall can include an inner wall and an outer wall and the strain sensor can be situated between said inner wall and said outer wall. The strain sensor further can include a polymeric layer. The one or more walls can include a polymer. The polymer can be selected from the group consisting of poly(dimethylsiloxane) (PMDS), poly(ethylene glycol) diacrylate (PEGDA), poly(methyl methacrylate), polyurethane, and combinations thereof. The fluid flow channel can have a cross- section with an area of about 25 pm ² to about 500000 pm ² . The fluid flow channel can have a cross-section with an area of about 2500 pm ² to about 150000 pm ² . The fluid flow channel can have a rectangular cross-section, the cross-section

characterized by a height and a width. The fluid flow channel can have a square cross- section. The height of the cross-section can be about 5 to about 1000 pm. The height of the cross-section can be about 50 to about 300 pm. The width of the cross-section can be about 5 to about 1000 pm. The width of the cross-section can be about 50 to about 750 pm. The channel can further include an inlet and an outlet. The strain sensor can be configured to provide an electrical impedance profile associated with the flow of fluid through the fluid flow channel. The strain sensor can be configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel. The channel can further include one or more additional strain sensors, each independently including a supporting layer and a metallic layer on and in contact with the supporting layer, wherein the metallic layer comprises a plurality of metallic nanoislands.

In another aspect, also provided herein is a microfluidic device comprising one or more channels as described herein. Implementations can have one or more of the following features. The device can further include one or more reaction chambers. The device can further include one or more inlet ports. The device can further include one or more microfluidic valves.

In another aspect, also provided herein is a system comprising one or more channels as described herein.

Implementations can have one or more of the following features. The system can be configured to provide an electrical impedance profile associated with the flow of fluid through the fluid flow channel. The system can be configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel.

In another aspect, also provided herein is a method of detecting deformation in at least a portion of a channel as described herein through which a fluid is flowing, comprising measuring one or more electrical signals from the strain sensor caused by the deformation.

Implementations can include one or more of the following features. The one or more electrical signals can be a voltage. The measuring can include continuous measuring. The method can further include detecting one or more particles in the fluid. The one or more particles can be rigid or deformable. The one or more particles can be a gas bubble. The one or more particles can be a solid particle. The one or more particles can be a biological cell. The method can further include determining one or more properties of at least one of the particles. The one or more properties can be selected from rigidity, deformability, size, flow rate, and identity. The method can further include quantifying the particles based on the detecting of the particles. The strain sensor can not directly contact the particle. The strain sensor can not directly contact the fluid. The method can further include determining the identity of the gas bubble based on the one or more electrical signals. The method can further include determining the identity of the solid particle based on the one or more electrical signals. The method can further include determining the identity of the biological cell based on the one or more electrical signals. The method can further include calculating a flow rate of the fluid based on the one or more electrical signals.

In another aspect, provided herein a method for high throughput particle sorting including passing a fluid containing a plurality of particles through a channel as described herein, detecting deformation caused by a particle in at least a portion of the channel by measuring one or more electrical signals from the strain sensor, identifying one or more properties of the particle based on the one or more electrical signals, and sorting the particle based on the one or more properties. In some embodiments, the particle can be a biological cell.

The devices, systems, and methods described herein can provide several advantages. First, they can provide low-cost, but ultra-sensitive, metal nanoislands- on-graphene strain sensors to transduce wall deformation events into information about the flow and particles inside the microfluidic channel.

Second, the devices and methods can be used to measure unique properties of fluids and/or rigid or deformable particles in a continuous, high-throughput manner— such as the mechanical properties of analytes at thousands of readings per second.

Third, the devices and methods can evaluate microfluidic devices on a regular benchtop with a simple voltage reading.

Fourth, the measurements provided by the devices and methods herein forgo the need of expensive optics and open the door to a new sterile, non-contact and highly parallel method of measuring analytes in microfluidic devices.

Fifth, the materials and methods described could be used to validate elastohydrodynamic theories, which can be difficult with current experimental techniques. [19, 20]

Sixth, the devices and systems described herein can have high sensitivity at low strains. In some embodiments, this high sensitivity at low strains can allow detection of minute movements of cells for biomechanical analysis or for the analysis of fluid flow, e.g., viscosity or flow rate.

Seventh, the devices and systems described herein can have minimal fabrication steps. Minimal fabrication steps can, in some embodiments, provide reduced costs and/or reduced complexity. In some embodiments, this can lead to improved practical usage of the benefits of microfluidics using the strain sensors described herein.

Eighth, the strain sensors used in the devices, systems, and methods described herein can have low physical profiles. In some embodiments, this allows the application of strain sensors in various kinds of microfluidic channel structures and/or can provide easy incorporation into existing microfluidic or other channel setups.

Ninth, the strain sensors used in the devices, systems, and methods described herein have ultralow stiffness so as to have a negligible effect on the mechanical response of the sidewalls of the channels. In some embodiments, this can provide increased accuracy and/or sensitivity of the devices, systems, and methods described herein, and/or provide compatibility of the strain sensors for use in new or existing microfluidic or other channel devices.

Unless otherwise defined, all 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. Methods and materials are described herein for use in the present invention; other, suitable methods and materials known in the art can also be used. The materials, methods, and examples are illustrative only and not intended to be limiting. All publications, patent applications, patents, sequences, database entries, and other references mentioned herein are incorporated by reference in their entirety. In case of conflict, the present specification, including definitions, will control.

Other features and advantages of the invention will be apparent from the following detailed description and figures, and from the claims.

DESCRIPTION OF DRAWINGS

Figure 1A shows an exemplary schematic overview of elastohydrodynamic sensing.

Figure IB shows that exemplary ultra-sensitive graphene nanoisland sensors can transduce minute elastohydrodynamic deformation into a voltage signal.

Figure 2A shows a cross-sectional view of an exemplary channel 200.

Figure 2B shows a cross-sectional view of an exemplary channel 201.

Figure 2C shows a cross-sectional view of an exemplary channel 202.

Figure 3A shows a top view of an exemplary channel with sensor 300.

Figure 3B shows a cross-sectional view of an exemplary channel with sensor

301

Figure 3C shows an exemplary strain sensor 350. Figure 4A shows an exemplary schematic overview of incorporating exemplary palladium nanoislands-on-graphene sensor and electrodes near the fluidic channel.

Figure 4B shows SEM images of exemplary palladium nanoislands on graphene.

Figure 4C shows a brightfield image of an exemplary device, with fluid the channel (yellow in a color image) and the edge of the sensor visible.

Figure 4D shows an exemplary schematic and mathematical relationship between channel geometry, elastic modulus of the wall, fluid flow rate, viscosity and wall deformation, calculations based on Gervais et al. [13]

Figure 4E shows an exemplary schematic and mathematical relationship between fluid viscosity, particle size, particle velocity and wall deformation, calculations based on Urzay et al.[l6].

Figure 4F shows exemplary viscoelastic relaxation of wall deformation, modeled as a spring-dashpot over a time-scale x, related to the viscous loss modulus, m, and the elastic modulus, E, induced by a passing air bubble.

Figure 5A shows an exemplary testing procedure where resistance of the sensor was monitored while fluid was flown different rates into the device.

Figure 5B shows an exemplary data where changes in resistance quickly followed changes in the flow rate.

Figure 5C shows an exemplary theoretical relationship between fluid flow rate and channel deformation for different exemplary devices tested.

Figure 5D shows exemplary percent change in flow rate plotted against the theoretical deformation of the wall for a first exemplary device.

Figure 5E shows exemplary percent change in flow rate plotted against the theoretical deformation of the wall for a second exemplary device.

Figure 5F shows exemplary percent change in flow rate plotted against the theoretical deformation of the wall for a third exemplary device.

Figure 5G shows exemplary percent change in flow rate plotted against the theoretical deformation of the wall for a fourth exemplary device.

Figure 6 shows an exemplary master curve of flow rate versus changes in resistance of the sensor for multiple exemplary devices. Figure 7 A shows that exemplary flowing of 30-50 pL air bubbles in water induces large changes in resistance in an exemplary 300 ^c 300 pm at 2 MPa device. Instances where air bubbles transit through the channel are notated with arrows.

Figure 7B shows that an exemplary“infinitely -long” bubble by clearing the channel with air creates several identifiable regions, from 0-III. The arrow refers to a small induced pressure increase as a calibration peak.

Figure 7C shows an exemplary Region I where an exemplary air bubble just transits across the sensor, shown in schematic, with micrograph still from video and wall deformation. Note the 1 ms and 100 pm deformation, calculated by calibrating fluid deformation.

Figure 7D shows an exemplary Region II where the air bubble drains the channel after the sensor. Note the 10 ms time bar and deformation spanning 10 pm.

Figure 7E shows an exemplary Region III where the channel is void of fluid but the wall deformation occurs over some finite domain due to viscoelastic relaxation. Note the 1 ms time bar and deformation spanning 30 pm.

Figure 7F shows an exemplary Kelvin- Voigt model of viscoelastic relaxation in channel walls (dashed lines) as compared to data. Exemplary model fitted to a square wave with a length that spans region I-II in data as the stress applied from the fluid. Scale bar = 1 mm in all pictures (P1-P3).

Figure 8A shows exemplary data from 80 pm particles being flown through a

300 x 300 pm channel, causing resistance changes. These resistance changes were converted to channel deformation, per calibration from Figure 5. Bar near the x-axis refers to time the particle passed exemplary metal nanoislands-on-graphene sensor from images in Figure 8B.

Figure 8B shows portions of images taken as the exemplary particle passed through fluidic channel and over the metal nanoislands-on-graphene sensor, shown in between dashed lines.

Figure 9 shows an exemplary schematic overview of elastohydrodynamic sensing.

Figure 10 shows an exemplary master curve relating channel deformation to changes in resistance for exemplary devices. Naming convention are the channel’s width (W) by the channel’s height (//) in microns, followed by the elastic modulus of the device. Error of slope calculated on confidence intervals of 95%.

Figure 11A shows that flowing 30-50 pL air bubbles in water causes large changes in resistance in the device made of E = 1 MPa PDMS with channel dimensions of 300 pm ^c 300 pm. Air bubbles are indicated with arrows.

Figure 11B shows an exemplary graph of clearing the channel with air, which creates several identifiable regions from 0— III. The green arrow indicates a calibration peak.

Figure 12 shows an exemplary Kelvin-Voigt model of viscoelastic relaxation of several trials in channel walls (dashed lines) as compared with the data (solid lines).

Figure 13A shows 80 pm silica particles were flown through a 300 pm ^c 300 pm, E = 1 MPa channel, causing resistance changes.

Figure 13B shows portions of images taken as an exemplary particle passed through fluidic channel and over the sensor, delineated in orange.

Figure 13C shows exemplary human mesenchymal stem cells (25-40 pm in diameter) that were flown in an exemplary channel, and the channel deformation was monitored.

Figure 13D shows portions of image as cells passed through an exemplary fluidic channel. The background image was subtracted to highlight cell motion with the line to guide the eye. Metal nano-island-on-graphene sensor interface is shown with a dashed line.

Figure 14A exemplary brightfield microscopy of fabricated device with focus on the channel.

Figure 14B exemplary brightfield microscopy of fabricated device with focus on the graphene sensor layer.

Figure 15 shows exemplary deformation at W= 0 at different flow rates along the length, /. _, of the channel for an exemplary W= 750 pm, h ₀ = 200 pm device.

Figure 16 shows exemplary voltage signal from a device as multiple bubbles transit inside the channel. Figure 17 shows exemplary expansion of the time window from -1.75 s to -1.85 s (of Figure 16) showing the shapes of the voltage signal from bubbles transiting a microfluidic channel.

Figure 18 shows a cross-sectional view of an exemplary channel 1800 with sensor 1850and particle 1870.

DETAILED DESCRIPTION

Despite the promise that microfluidic technologies would revolutionize healthcare and diagnostics, relatively few microfluidic devices are in commercial development today because they often rely on capital-intensive optical systems and other peripheral equipment, limiting throughput.

Provided herein are devices and methods for detecting, quantifying, measuring, and identifying fluids, fluid flow, and particles in the fluids using electrical signals obtained from one or more strain sensors. In some embodiments, the strain sensor can be located on the wall of a channel through which the fluid is flowing. In some embodiments, the electrical signals from the strain sensor are based on deformation of a channel wall. In some embodiments, the sensor does not contact the fluid or other analyte such as a particle in the fluid.

In some embodiments, the methods do not require optical-based

characterization of fluid flow and analytes. Instead, the methods use measurement of the minute deformations that occur when fluid or particles flow past deformable walls, known as elastohydrodynamic phenomenon (see, e.g., Figure 1).

In some embodiments, embedded in a channel wall is one or more strain sensors that measures the changing deformation of the channel wall as fluid flows past it. In some embodiments, the strain sensors can be made of metallic nanoparticles that have been evaporated onto single-layer graphene and can measure strains as low as 0.001% [7-9] Some exemplary strain sensors and exemplary methods for making strain sensors useful in some embodiments of the invention are described in U.S. Pat. No. 9,863,885, which is incorporated by reference herein in its entirety. In some embodiments, the sensors do not require microfabricating structures and do not need to physically contact or interact with the fluid to retain their high sensitivity. In some embodiments, thin-film strain sensors made from palladium nano islands deposited on single-layer graphene [7] can be embedded in the bulk of an elastomer in close proximity to a channel wall. A composite film can measure changes in the electrical resistance caused by deformation of the wall (exemplary schematics shown in Figures 1A and 9). Fluid flowing against a soft wall, such as PDMS, can deform the channel in relation to the fluid flow rate (v) and viscosity. Ultra-sensitive graphene nanoisland sensors placed inside the channel can transduce minute elastohydrodynamic deformation into a voltage signal. Air bubbles and solid particles can also cause deformations along the channel wall. In Figure 1A, an exemplary PDMS wall is shown being deformed by a liquid (left panel), a gas (center panel), and a solid (right panel). In Figure 9, an exemplary wall is shown being deformed by a liquid (left panel), a gas (center panel), and a solid (right panel). A fluid flowing against a soft wall can deform the channel in relation to the fluid flow rate (v) and viscosity. For example, a deformation of a wall can be relative to an initial height of a channel (ho). For example, a deformation of a wall can be relative to an initial width of a channel (Wo). In some embodiments, this deformation can be related to the fluid flow [13] or to the properties of a flowing particle. [16,18] Couplings that occur between fluid flow and elastic structures are known as elastohydrodynamic phenomena. [19,37-39] In contrast with other methods of measuring and sorting objects in microfluidic channels, some methods described herein do not place an obstacle in the pathway of an analyte. Some of the current techniques of mechanical sensing require analytes to be flowed over cantilevers

[24,25] or around mechanical features, [26,27] such as spirals. Cantilever measurements, however, still require lasers to capture small deflections of the tip and must be rigorously isolated from vibration. Differentiating analytes based on mechanical features, either through biasing flow around features (e.g., deformability- based cell margination)[28-30] or through collisions into obstacles (e.g.,

deterministic lateral displacement), [31] can be limited in throughput by the speed of the camera used for sorting and damage caused to the structures or to the analyte. To transduce the deformation of the walls that occurs on the micron scale (Figure IB), it was found that it was advantageous to use sensors that did not need to be placed in the fluid environment. In some embodiments, a change in an electrical property (e.g., resistance) detected using a sensor can be related (e.g., mathematically related) to a change in one or more properties of the system (e.g., fluid flow rate, viscosity, deformation of a channel wall). A composite metal-on-graphene piezoresistive sensor, can be fabricated by evaporating palladium onto single-layer graphene. A top view of an exemplary sensor is shown in Figure 4B.In some embodiments, these sensors can measure strains as low as 0.001%. [7,8]

In some embodiments, sensitivity at low strains can be attributed to a combination of phenomena, including strain-induced scattering between nanoislands initially in contact and modulation of the tunneling current between metallic nano- islands once separated, along with the intrinsic piezoresistance of graphene. [7] Some strain sensors can have high gauge factors [40,41] In some embodiments, the strain sensors herein have high sensitivity at low strains. In some embodiments, the strain sensors herein have minimal fabrication steps. In some embodiments, the strain sensors herein have low physical profiles. In some embodiments, the strain sensors herein have ultralow stiffness so as to have a negligible effect on the mechanical response of the sidewalls of the channels. In some embodiments, microfluidic devices are fabricated out of poly(dimethylsiloxane) (PDMS) containing a single, straight channel, with the strain sensor embedded near the channel. A schematic of an exemplary channel is shown in Figure 4C, and a top view brightfield microscopy image of an exemplary channel is shown in Figure 4B. In some embodiments, devices can differ in their cross-sectional dimensions (width ^c height). In some embodiments, devices can differ by the Young’s modulus of the channel material (e.g., PDMS) (e.g., achieved by varying the base-to-crosslinker ratio).

In some embodiments, given a sufficiently soft material (e.g., with an elastic modulus of about 50 kPa to about 100 MPa (e.g., less than about 100 MPa, less than about 50 MPa, less than about 25 MPa, less than 10 about MPa, less than about 5 MPa, less than about 3 MPa, less than about 2 MPa, less than about 1 MPa, less than about 500 kPa, less than about 100 kPa, about 50 kPa to about 50 MPa, about 50 kPa to about 25 MPa, about 50 kPa to about 10 MPa, about 50 kPa to about 5 MPa, about 50 kPa to about 3 MPa, about 50 kPa to about 2 MPa, about 50 kPa to about 1 MPa, about 50 kPa to about 500 kPa, about 50 kPa to about 100 kPa, about 100 kPa to about 100 MPa, about 100 kPa to about 50 MPa, about 100 kPa to about 25 MPa, about 100 kPa to about 10 MPa, about 100 kPa to about 5 MPa, about 100 kPa to about 3 MPa, about 100 kPa to about 2 MPa, about 100 kPa to about 1 MPa, about 100 kPa to about 500 kPa, about 500 kPa to about 100 MPa, about 500 kPa to about 50 MPa, about 500 kPa to about 25 MPa, about 500 kPa to about 10 MPa, about 500 kPa to about 5 MPa, about 500 kPa to about 3 MPa, about 500 kPa to about 2 MPa, about 500 kPa to about 1 MPa, about 1 MPa to about 100 MPa, about 1 MPa to about 50 MPa, about 1 MPa to about 25 MPa, about 1 MPa to about 10 MPa, about 1 MPa to about 5 MPa, about 1 MPa to about 3 MPa, about 1 MPa to about 2 MPa, about 2 MPa to about 100 MPa, about 2 MPa to about 50 MPa, about 2 MPa to about 25 MPa, about 2 MPa to about 10 MPa, about 2 MPa to about 5 MPa, about 2 MPa to about 3 MPa, about 3 MPa to about 100 MPa, about 3 MPa to about 50 MPa, about 3 MPa to about 25 MPa, about 3 MPa to about 10 MPa, about 3 to about 5 MPa, about 5 MPa to about 100 MPa, about 5 MPa to about 50 MPa, about 5 MPa to about 25 MPa, about 5 MPa to about 10 MPa, about 10 MPa to about 100 MPa, about 10 MPa to about 50 MPa, about 10 MPa to about 25 MPa, about 25 MPa to about 100 MPa, about 25 MPa to about 50 MPa, or about 50 MPa to about 100 MPa)), such as an elastomer, a fluid can deform the wall as it flows in the channel. As a fluid flows with increased velocity in a channel, the fluid can increase pressure on the wall, deforming the channel even more. A fluid flowing at the same velocity, but at higher viscosity, can also deform the channel [10,11] The relationship between the channel geometry, viscosity, fluid velocity and the elastic modulus of the channel have been developed in microfluidic devices confined by thin [12] and thick layers [13] A pressure sensor at the inlet or outlet of the channel can be used for the same purpose, like ones already developed in the literature, but there can be limitations between detecting a total device pressure, instead of an inline (or in situ) pressure profile [14,15] For example, in inlet/outlet pressure sensors, transient changes - like an air bubble passing in the fluid - could report essentially the same pressure even though the channel walls will deform in response to the compressible fluid. In addition, for constant flow rates, a particle passing along the channel can cause deformations in the wall [16] These deformations can be related to the size, motion and elastic properties of the particle [17,18] However, there has been relatively little experimental verification of these recently developed theories up to this point [19,20] There are several devices in the literature that rely on mechanical-based sensing. Some devices use either mechanical-based sensors [21-23] - such as flowing analytes over cantilevers [24,25] - or differentiate analytes based on mechanical properties, such as flowing around spiral features [26,27] When flowing analytes over cantilevers, the cantilevers still need to be measured using a laser and sensitive are sensitive to vibration and will require isolation systems. Differentiating analytes based on mechanical properties, either through biasing flow around features (e.g. deformability-based cell margination) [27-30], or through collisions into obstacles (e.g. deterministic lateral displacement) [31,32], can be limited in throughput by damage caused to the structures or to the analyte, or both. These devices, however, still require an optical verification of the process, which is both expensive and can be only operated as fast as a camera. In addition, MEMS micropatteming is often required for each device, and these delicate features can become damaged quickly, or become ineffective at certain flowrates, limiting throughput.

Provided herein are channels. In some embodiments, a channel can include one or more walls defining at least a portion of a fluid flow channel. In some embodiments, a channel can have four walls. In some embodiments, a channel can have three walls. In some embodiments, the one or more walls can enclose a fluid flow channel along its length (e.g., a fluid flow channel can be a tube). In some embodiments, the one or more walls can partially enclose a fluid flow channel along its length (e.g., a fluid flow channel can be open on at the top). In some embodiments, a channel can include one or more inner walls. In some embodiments, an inner wall is about 10 nm to about 10 pm (e.g., about 10 nm to about 1 pm, about 10 nm to about 50 nm, about 50 nm to about 100 nm, about 100 nm to about 500 nm, about 500 nm to about 1 pm, about 1 to about 8 pm, about 1 to about 7 pm, about 1 to about 6 pm, about 1 to about 5 pm, about 1 to about 4 pm, about 1 to about 3 pm, about 1 to about 2 pm, about 2 to about 10 pm, about 2 to about 8 pm, about 2 to about 6 pm, about 2 to about 4 pm, about 4 to about 6 pm, about 6 to about 10 pm, about 6 to about 8 pm, or about 8 to about 10 pm). In some embodiments, a channel can include one or more outer walls. In some embodiments, a sensor can be positioned between an inner wall and an outer wall of a channel. For example, in some embodiments, a channel can have a fluid flow channel at least partially defined by three outer walls and one inner wall. In some such embodiments, an outer wall can be positioned on the inner wall, where the inner wall is positioned between the fluid flow channel and the outer wall. An exemplary channel 200 is shown in cross-section in Figure 2A. Walls 210, 211, and 212, having thicknesses ti, t ₂ , and t3, respectively, partially enclose a fluid flow channel 220 having a wall-less portion 218. In some embodiments, walls 210, 211, and 212 can be separate units in any appropriate configuration. In some embodiments, walls 210, 211, and 212 can be separate units, configured as shown by the dashed lines in Figure 2A. In some embodiments, walls 210, 211, and 212 can be a single unit. In some embodiments, one or more strain sensors as disclosed herein (not shown) can be positioned across wall-less portion 218. Fluid flow channel 220 has an initial height (ho) and an initial width (Wo). Walls 210, 211, and 212 can be, independently, inner or outer walls. Another exemplary channel 201 is shown in cross-section in Figure 2B. Walls 210, 211, and 212, having thicknesses ti, 12, and t3, respectively, partially enclose a fluid flow channel 220. In some embodiments, walls 210, 211, and 212 can be separate units in any appropriate configuration. In some embodiments, walls 210, 211, and 212 can be separate units, configured as shown by the dashed lines in Figure 2B. In some embodiments, walls 210, 211, and 212 can be a single unit. Walls 210, 211, and 212 can be, independently, inner or outer walls. Wall 213, having a thickness t4, encloses fluid flow channel 220 in this cross-sectional view, and has an inner surface 213a and an outer surface 213b. Wall 213 can be an inner wall or an outer wall. Fluid flow channel 220 has an initial height (ho) and an initial width (Wo). In some embodiments, one or more strain sensors as disclosed herein (not shown) can be embedded in wall 213, and/or positioned on at least a portion of surface 213a and/or 213b. Another exemplary channel 202 is shown in cross-section in Figure 2C. Walls 210, 211, and 212, having thicknesses ti, 12, and t3, respectively, partially enclose a fluid flow channel 220. In some embodiments, walls 210, 211, and 212 can be separate units in any appropriate configuration. In some embodiments, walls 210, 211, and 212 can be separate units, configured as shown by the dashed lines in Figure 2C. In some embodiments, walls 210, 211, and 212 can be a single unit. Walls 210, 211, and 212 can be, independently, inner or outer walls.

Inner wall 213, having a thickness t4, encloses fluid flow channel 220 in this cross- sectional view. Inner wall 213 is positioned between fluid flow channel 220 and outer wall 214. Fluid flow channel 220 has an initial height (ho) and an initial width (Wo). In some embodiments, one or more strain sensors as described herein (not shown) can be embedded in or positioned on wall 213 or wall 214. In some embodiments, one or more strain sensors as described herein (not shown) can be positioned on inner surface 213a and/or outer surface 213b of wall 213. In some embodiments, one or more strain sensors as described herein (not shown) can be positioned between inner wall 213 and outer wall 214. In some embodiments, one or more strain sensors as described herein (not shown) can be positioned on outer surface 214b of outer wall 214. In some embodiments of any of the channels disclosed herein, thicknesses ti, 12, t3, t4, and t5 can be any appropriate thickness. In some embodiments, any of thicknesses ti, 12, t3, t4, and ts can be, independently, between about 10 nm to about 1 cm (e.g., about 10 nm to about 1 pm, about 10 nm to about 50 nm, about 50 nm to about 100 nm, about 100 nm to about 500 nm, about 500 nm to about 1 pm, about 1 pm to about 5 pm, about 5pm to about 10 pm, about 10 pm to about 50 pm, about 50 pm to about 100 pm, about 100 pm to about 500 pm, about 500 pm to about 1 mm, about 1 pm to about 1 mm, about 1 mm to about 5 mm, about 5 mm to about 10 mm, about 10 mm to about 50 mm. about 50 mm to about 100 mm, about 100 mm to about 500 mm, or about 1 mm to about 1 cm). A channel can include one or more inlets to a fluid flow channel. A channel can include one or more outlets to a fluid flow channel. In some embodiments, an inlet and an outlet can define the length (/.) of a fluid flow channel. An inlet can be any appropriate shape. An inlet can be any appropriate size. An outlet can be any appropriate shape. An outlet can be any appropriate size. In some embodiments, a channel can include one or more microfluidic valves. In some embodiments, a channel can include one or more reaction chambers.

A fluid flow channel can be a fluid flow channel for any appropriate substance. In some embodiments, a fluid can flow through a fluid flow channel. In some embodiments, a gas (e.g., as a bubble or as a stream) can flow through the fluid flow channel. In some embodiments, the fluid flow channel can be a channel for the flow of multiple substances (e.g., a liquid and a solid (e.g., a liquid and a particle or a liquid and a cell), a liquid and a gas, or a gas and a solid). In some embodiments, a fluid flow channel can have a cross-section of any appropriate shape. For example, in some embodiments, a fluid flow channel can have a rectangular cross-section (see, e.g., Figures 2A-2C). In some embodiments, a fluid flow channel can have a square cross-section. In some embodiments, a fluid flow channel can have a circular cross- section. A fluid flow channel can have a cross-section characterized by any appropriate parameters. For example, a fluid flow channel can have a circular cross- section characterized by an initial radius. For example, a fluid flow channel can have a rectangular or a square cross-section characterized by an initial height and an initial width (see, e.g., Figures 2A-2C). In some embodiments, a fluid flow channel can have a cross-section of any appropriate size. For example, in some embodiments, a fluid flow channel can have a cross-section of about 25 pm ² to about 500000 pm ² (e.g., about 25 to about 400000 pm ² , about 25 to about 300000 pm ² , about 25 to about

250000 pm ² , about 25 to about 200000 pm ² , about 25 to about 150000 pm ² , about 25 to about 100000 pm ² , about 25 to about 50000 pm ² , about 25 to about 25000 pm ² , about 25 to about 10000 pm ² , about 25 to about 5000 pm ² , about 25 to about 2500 pm ² , about 25 to about 1000 pm ² , about 25 to about 500 pm ² , about 25 to about 100 pm ² , or about 25 to about 50 pm ² , about 50 to about 500000 pm ² , about 50 to about 400000 pm ² , about 50 to about 300000 pm ² , about 50 to about 250000 pm ² , about 50 to about 200000 pm ² , about 50 to about 150000 pm ² , about 50 to about 100000 pm ² , about 50 to about 50000 pm ² , about 50 to about 25000 pm ² , about 50 to about 10000 pm ² , about 50 to about 5000 pm ² , about 50 to about 2500 pm ² , about 50 to about 1000 pm ² , about 50 to about 500 pm ² , about 50 to about 100 pm ² , about 100 to about

500000 pm ² , about 100 to about 400000 pm ² , about 100 to about 300000 pm ² , about 100 to about 250000 pm ² , about 100 to about 200000 pm ² , about 100 to about 150000 pm ² , about 100 to about 100000 pm ² , about 100 to about 50000 pm ² , about 100 to about 25000 pm ² , about 100 to about 10000 pm ² , about 100 to about 5000 pm ² , about 100 to about 2500 pm ² , about 100 to about 1000 pm ² , about 100 to about 500 pm ² , about 500 to about 500000 pm ² , about 500 to about 400000 pm ² , about 500 to about 300000 pm ² , about 500 to about 250000 pm ² , about 500 to about 200000 pm ² , about 500 to about 150000 pm ² , about 500 to about 100000 pm ² , about 500 to about 50000 pm ² , about 500 to about 25000 pm ² , about 500 to about 10000 pm ² , about 500 to about 5000 pm ² , about 500 to about 2500 pm ² , about 500 to about 1000 pm ² , about 1000 to about 500000 pm ² , about 1000 to about 400000 pm ² , about 1000 to about 300000 pm ² , about 1000 to about 250000 pm ² , about 1000 to about 200000 pm ² , about 1000 to about 150000 mih ² , about 1000 to about 100000 mih ² , about 1000 to about 50000 mih ² , about 1000 to about 25000 mih ² , about 1000 to about 10000 mih ² , about 1000 to about 5000 mih ² , about 1000 to about 2500 mih ² , about 2500 to about 500000 mih ² , about 2500 to about 400000 mih ² , about 2500 to about 300000 mih ² , about 2500 to about 250000 mih ² , about 2500 to about 200000 mih ² , about 2500 to about 150000 mih ² , about 2500 to about 100000 mih ² , about 2500 to about 50000 mih ² , about 2500 to about 25000 mih ² , about 2500 to about 10000 mih ² , about 2500 to about 5000 mih ² , about 5000 to about 500000 mih ² , about 5000 to about 400000 mih ² , about 5000 to about 300000 mih ² , about 5000 to about 250000 mih ² , about 5000 to about 200000 mih ² , about 5000 to about 150000 mih ² , about 5000 to about 100000 mih ² , about 5000 to about 50000 mih ² , about 5000 to about 25000 mih ² , about 5000 to about 10000 mih ² , about 10000 to about 500000 mih ² , about 10000 to about 400000 mih ² , about 10000 to about 300000 mih ² , about 10000 to about 250000 mih ² , about 10000 to about 200000 mih ² , about 10000 to about 150000 mih ² , about 10000 to about 100000 mih ² , about 10000 to about 50000 mih ² , about 10000 to about 25000 mih ² , about 25000 to about 500000 mih ² , about 25000 to about 400000 mih ² , about 25000 to about 300000 mih ² , about 25000 to about 250000 mih ² , about 25000 to about 200000 mih ² , about 25000 to about 150000 mih ² , about 25000 to about 100000 mih ² , about 25000 to about 50000 mih ² , about 50000 to about 500000 mih ² , about 50000 to about 400000 mih ² , about 50000 to about 300000 mih ² , about 50000 to about 250000 mih ² , about

50000 to about 200000 mih ² , about 50000 to about 150000 mih ² , about 50000 to about 100000 mih ² , about 100000 to about 500000 mih ² , about 100000 to about 400000 mih ² , about 100000 to about 300000 mih ² , about 100000 to about 250000 mih ² , about 100000 to about 200000 mih ² , about 100000 to about 150000 mih ² , about 150000 to about 500000 mih ² , about 150000 to about 400000 mih ² , about 150000 to about

300000 mih ² , about 150000 to about 250000 mih ² , about 150000 to about 200000 mih ² , about 200000 to about 500000 mih ² , about 200000 to about 400000 mih ² , about 200000 to about 300000 mih ² , about 200000 to about 250000 mih ² , about 250000 to about 500000 mih ² , about 250000 to about 400000 mih ² , about 250000 to about 300000 mih ² , about 300000 to about 500000 mih ² , about 300000 to about 400000 mih ² , or about 400000 to about 500000 mih ² ). In some embodiments, a cross-section of a fluid flow channel can be characterized by a height and a width. A diagram showing an exemplary channel with a fluid flow channel with a cross section having a height and a width is shown in Figure 4D. Additional exemplary channels with fluid flow channels each having a height and a width are shown in Figures 2A-2C. A cross- section of a fluid flow channel can have any appropriate height. In some

embodiments, a cross-section of a fluid flow channel can have a height of about 5 to about 1000 pm (e.g., about 5 to about 10 pm, about 5 to about 25 pm, about 5 to about 50 pm, about 5 to about 100 pm, about 5 to about 200 pm, about 5 to about 300 pm, about 5 to about 400 pm, about 5 to about 500 pm, about 5 to about 750 pm, about 10 to about 25 pm, about 10 to about 50 pm, about 10 to about 100 pm, about 10 to about 200 pm, about 10 to about 300 pm, about 10 to about 400 pm, about 10 to about 500 pm, about 10 to about 750 pm, about 10 to about 1000 pm, about 25 to about 50 pm, about 25 to about 100 pm, about 25 to about 200 pm, about 25 to about 300 pm, about 25 to about 400 pm, about 25 to about 500 pm, about 25 to about 750 pm, about 25 to about 1000 pm, about 50 to about 100 pm, about 50 to about 200 pm, about 50 to about 300 pm, about 50 to about 400 pm, about 50 to about 500 pm, about 50 to about 750 pm, about 50 to about 1000 pm, about 100 to about 200 pm, about 100 to about 300 pm, about 100 to about 400 pm, about 100 to about 500 pm, about 100 to about 750 pm, about 100 to about 1000 pm, about 200 to about 300 pm, about 200 to about 400 pm, about 200 to about 500 pm, about 200 to about 750 pm, about 200 to about 1000 pm, about 300 to about 400 pm, about 300 to about 500 pm, about 300 to about 750 pm, about 300 to about 1000 pm, about 400 to about 500 pm, about 400 to about 750 pm, about 400 to about 1000 pm, about 500 to about 750 pm, about 500 to about 1000 pm, about 750 to about 1000 pm, about 5 pm, about 10 pm, about 25 pm, about 50 pm, about 100 pm, about 200 pm, about 300 pm, about 400 pm, about 500 pm, about 750 pm, or about 100 pm). A cross-section of a fluid flow channel can have any appropriate width. In some embodiments, a cross-section of a fluid flow channel can have a width of about 5 to about 1000 pm (e.g., about 5 to about 10 pm, about 5 to about 25 pm, about 5 to about 50 pm, about 5 to about 100 pm, about 5 to about 200 pm, about 5 to about 300 pm, about 5 to about 400 pm, about 5 to about 500 pm, about 5 to about 750 pm, about 10 to about 25 pm, about 10 to about 50 pm, about 10 to about 100 pm, about 10 to about 200 pm, about 10 to about 300 pm, about 10 to about 400 pm, about 10 to about 500 pm, about 10 to about 750 mih, about 10 to about 1000 mih, about 25 to about 50 mih, about 25 to about 100 mih, about 25 to about 200 mih, about 25 to about 300 mih, about 25 to about 400 mih, about 25 to about 500 mih, about 25 to about 750 mih, about 25 to about 1000 mih, about 50 to about 100 mih, about 50 to about 200 mih, about 50 to about 300 mih, about 50 to about 400 mih, about 50 to about 500 mih, about 50 to about 750 mih, about 50 to about 1000 mih, about 100 to about 200 mih, about 100 to about 300 mih, about 100 to about 400 mih, about 100 to about 500 mih, about 100 to about 750 mih, about 100 to about 1000 mih, about 200 to about 300 mih, about 200 to about 400 mih, about 200 to about 500 mih, about 200 to about 750 mih, about 200 to about 1000 mih, about 300 to about 400 mih, about 300 to about 500 mih, about 300 to about 750 mih, about 300 to about 1000 mih, about 400 to about 500 mih, about 400 to about 750 mih, about 400 to about 1000 mih, about 500 to about 750 mih, about 500 to about 1000 mih, about 750 to about 1000 mih, about 5 mih, about 10 mih, about 25 mih, about 50 mih, about 100 mih, about 200 mih, about 300 mih, about 400 mih, about 500 mih, about 750 mih, or about 100 mih).

The one or more walls of a channel can be flexible. In some embodiments, the one or more walls can have an elastic modulus of equal to or less than about 100 MPa (e.g., less than about 100 MPa, less than about 50 MPa, less than about 25 MPa, less than 10 about MPa, less than about 5 MPa, less than about 3 MPa, less than about 2 MPa, less than about 1 MPa, less than about 500 kPa, less than about 100 kPa, 50 kPa to about 100 MPa, about 50 kPa to about 50 MPa, about 50 kPa to about 25 MPa, about 50 kPa to about 10 MPa, about 50 kPa to about 5 MPa, about 50 kPa to about 3 MPa, about 50 kPa to about 2 MPa, about 50 kPa to about 1 MPa, about 50 kPa to about 500 kPa, about 50 kPa to about 100 kPa, about 100 kPa to about 100 MPa, about 100 kPa to about 50 MPa, about 100 kPa to about 25 MPa, about 100 kPa to about 10 MPa, about 100 kPa to about 5 MPa, about 100 kPa to about 3 MPa, about 100 kPa to about 2 MPa, about 100 kPa to about 1 MPa, about 100 kPa to about 500 kPa, about 500 kPa to about 100 MPa, about 500 kPa to about 50 MPa, about 500 kPa to about 25 MPa, about 500 kPa to about 10 MPa, about 500 kPa to about 5 MPa, about 500 kPa to about 3 MPa, about 500 kPa to about 2 MPa, about 500 kPa to about 1 MPa, about 1 MPa to about 100 MPa, about 1 MPa to about 50 MPa, about 1 MPa to about 25 MPa, about 1 MPa to about 10 MPa, about 1 MPa to about 5 MPa, about 1 MPa to about 3 MPa, about 1 MPa to about 2 MPa, about 2 MPa to about 100 MPa, about 2 MPa to about 50 MPa, about 2 MPa to about 25 MPa, about 2 MPa to about 10 MPa, about 2 MPa to about 5 MPa, about 2 MPa to about 3 MPa, about 3 MPa to about 100 MPa, about 3 MPa to about 50 MPa, about 3 MPa to about 25 MPa, about 3 MPa to about 10 MPa, about 3 to about 5 MPa, about 5 MPa to about 100 MPa, about 5 MPa to about 50 MPa, about 5 MPa to about 25 MPa, about 5 MPa to about 10 MPa, about 10 MPa to about 100 MPa, about 10 MPa to about 50 MPa, about 10 MPa to about 25 MPa, about 25 MPa to about 100 MPa, about 25 MPa to about 50 MPa, or about 50 MPa to about 100 MPa). In some cases, an elastic modulus can be adjusted by varying the base-to-cross linker ratio in a polymer used for fabrication. In some embodiments, the walls of a channel can be made of an elastomer. The one or more walls of a channel can be made of any appropriate material. In some embodiments, the one or more walls can include poly(dimethylsiloxane) (PMDS). In some embodiments, the one or more walls can include a polymer including one or more dimethylsiloxane monomers. In some embodiments, the one or more walls can include poly(ethylene glycol) diacrylate (PEGDA). In some embodiments, the one or more walls can include a polymer including one or more ethylene glycol monomers.

In some embodiments, the one or more walls can include poly(methyl methacrylate) (PMMA). In some embodiments, the one or more walls can include a polymer including one or more methyl methacrylate monomers. In some embodiments, the one or more walls can include polyurethane (PU). In some embodiments, the one or more walls can include a polymer including one or more urethane monomers. In some embodiments, the one or more walls can include a polymer selected from the group consisting of PMDS, PEGDA, PMMA, PU, and mixtures thereof. In some embodiments, the one or more walls can include a polymer including a monomer selected from the group consisting of dimethylsiloxane, ethylene glycol, methyl methacrylate, urethane, and mixtures thereof. In some embodiments, a channel can be made of a single type of material, for example, PMDS. In some embodiments, a channel can be made of more than one type of material.

In some embodiments, a channel can include one or more (e.g., 2, 3, 4, 5, 6, 7,

8, 9, 10, or more) strain sensors. In some embodiments, when two or more strain sensors are used, they are independently configured (e.g., as any appropriate strain sensor, or as any of the strain sensors described herein). In some embodiments, the strain sensor can include a supporting layer and a metallic layer on and in contact with the supporting layer. Figure 3C shows a close-up view of a portion of an exemplary strain sensor 350, including supporting layer 351 and metallic nanoislands (352a, 352b). The supporting layer can be any appropriate supporting layer. In some embodiments, the supporting layer is a zero band-gap material. In some embodiments, the supporting layer is a graphene layer. In some embodiments, the supporting layer is a hexagonal boron nitride layer. In some embodiments, the supporting layer is molybdenum disulfide layer. The supporting layer can be any appropriate thickness. For example, the supporting layer can have a thickness of about 0.3 nm to about 5 nm (e.g., about 0.3 to about 0.5 nm, about 0.3 to about 0.6 nm, about 0.3 to about 0.9 nm, about 0.3 to about 1 nm, about 0.3 to about 2 nm, about 0.3 to about 3 nm, about 0.3 to about 4 nm, about 0.5 to about 0.6 nm, about 0.5 to about 0.9 nm, about 0.5 to about 1 nm, about 0.5 to about 2 nm, about 0.5 to about 3 nm, about 0.5 to about 4 nm, about 0.5 to about 5 nm, about 0.6 to about 0.9 nm, about 0.6 to about 1 nm, about 0.6 to about 2 nm, about 0.6 to about 3 nm, about 0.6 to about 4 nm, about 0.6 to about 5 nm, about 0.9 to about 1 nm, about 0.9 to about 2 nm, about 0.9 to about 3 nm, about 0.9 to about 4 nm, about 0.9 to about 5 nm, about 1 to about 2 nm, about 1 to about 3 nm, about 1 to about 4 nm, about 1 to about 5 nm, about 2 to about 3 nm, about 2 to about 4 nm, about 2 to about 5 nm, about 3 to about 4 nm, about 3 to about 5 nm, about 4 to about 5 nm, about 0.3 nm, about 0.5 nm, about 0.6 nm, about 0.9 nm, about 1 nm, about 2 nm, about 3 nm, about 4 nm, or about 5 nm). In some

embodiments, the metallic layer can include a plurality of metallic nanoislands.

Metallic nanoislands can be include any appropriate metal or alloy. In some embodiments, the metallic nanoislands comprise, gold, silver, or palladium. In some embodiments, the metallic nanoislands are chemically inert. In some embodiments, the metallic nanoislands do not significantly change the band gap of the supporting layer (e.g., a graphene layer). In some embodiments, the metallic nanoislands comprise palladium. In some embodiments, the metallic nanoislands are palladium nanoislands. Metallic nanoislands can have any appropriate thickness. For example, metallic nanoislands can have a thickness of about 2 nm to about 20 nm (e.g., about 2 to about 5 nm, about 2 to about 10 nm, about 2 to about 15 nm, about 5 to about 10 nm, about 5 to about 15 nm, about 5 to about 20 nm, about 10 to about 15 nm, about 10 to about 20 nm, about 15 to about 20 nm, about 2 nm, about 5 nm, about 10 nm, about 15 nm, or about 20 nm). In some embodiments, a strain sensor can be a strain sensor as described in U.S. Patent No. 9,863,885, herein incorporated by reference in its entirety. In some embodiments, the metallic nanoislands can include nanospheres. In some embodiments, the metallic nanoislands do not include nanospheres. In some embodiments, the metallic nanoislands have predominantly a granular morphology. In some embodiments, the metallic nanoislands have a granular morphology. In some embodiments, the metallic nanoislands can be characterized by sharp tips and gaps. In some embodiments, a distance between edges of nanoislands in the metallic layer can be on the order of molecular dimensions. In some embodiments, the distance between edges of nanoislands in the metallic layer can be between about 3 nm and 2 A.

In some embodiments, a strain sensor can be configured so that it is in contact with the content of the fluid flow channel. In some embodiments, a strain sensor can be configured so that it is not in contact with the content of the fluid flow channel. In some embodiments, a strain sensor can be embedded in the one or more walls of a channel. Atop view of an exemplary channel including a strain sensor 300 is shown in Figure 3A. A fluid flow channel 320 having an initial width Wo is defined by one or more walls (e.g., 310, 312) that are formed by elastomer layer 360. The length, L, of fluid flow channel 320 is defined by inlet and outlet ports 330a and 330b. Spanning fluid flow channel 320 is strain sensor 350, connected to two electrodes 340a and 340b. In some embodiments, strain sensor 350 can extend across at least a portion of fluid flow channel 320, and/or beyond fluid flow channel 320. A cross-sectional view of an exemplary channel 301 including a strain sensor is shown in Figure 3B. Walls 310, 311, and 312, having thicknesses ti, h, and t3, respectively, partially enclose a fluid flow channel 320. Walls 310, 311, and 312 can be, independently, inner or outer walls. Inner wall 313, having a thickness t4, encloses fluid flow channel 320 in this cross-sectional view. Inner wall 313 is positioned between fluid flow channel 320 and outer wall 314. Fluid flow channel 320 has an initial height (ho) and an initial width (Wo). A strain sensor 350 is embedded in inner wall 313. Sensor 350 is separated from fluid flow channel 320 by thickness te. Sensor 350 has a thickness ti. Sensor 350 is separated from outer wall 314 by thickness te. Sensor 350 is connected to electrodes 340a and 340b, which extend beyond the channel.

Figure 3C shows a close-up view of a portion of strain sensor 350, including substrate 351 and metallic nanoislands (352a, 352b).

In some embodiments, a strain sensor can be in contact with the fluid flow channel (e.g., in Figure 3B, te can equal 0) In some embodiments, a strain sensor embedded in the one or more walls of a channel can be separated from the fluid flow channel (see, e.g., te in Figure 3B) by about 10 nm to about 10 pm (e.g., about 10 nm to about 1 pm, about 10 nm to about 50 nm, about 50 nm to about 100 nm, about 100 nm to about 500 nm, about 500 nm to about 1 pm, about 1 to about 8 pm, about 1 to about 7 pm, about 1 to about 6 pm, about 1 to about 5 pm, about 1 to about 4 pm, about 1 to about 3 pm, about 1 to about 2 pm, about 2 to about 10 pm, about 2 to about 8 pm, about 2 to about 6 pm, about 2 to about 4 pm, about 4 to about 6 pm, about 6 to about 10 pm, about 6 to about 8 pm, or about 8 to about 10 pm). In some embodiments, a strain sensor can be positioned between an inner wall and an outer wall of a channel (e.g., t ₄ = te and te = 0). In some such embodiments, a strain sensor can be separated from the fluid flow channel by about 1 to about 3 pm. Without being bound by any particular theory, it is believed that embedding a strain sensor in the one or more walls of a channel can dampen ambient vibrations, allowing a channel as described herein to be used without additional isolation from vibration. For example, Figures 5A and 5B show exemplary data collected in the absence of additional isolation from vibration. In some embodiments, a strain sensor can span a fluid flow channel. Schematics of exemplary channel is shown in Figures 3A, 3B, and 4A. In some embodiments, a strain sensor can be configured to provide an electrical impedance profile associated with the flow through the fluid flow channel. In some embodiments, a strain sensor can be configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel. In some embodiments, the sensor can be oriented so that the graphene layer is between the fluid flow channel and the metallic nanoislands. In some embodiments, the sensor can be oriented so that the metallic nanoislands are between the fluid flow channel and the graphene layer. In some embodiments, a channel can include one or more electrodes electrically connected to one or more metallic nanoislands. In some embodiments, a channel can include two electrodes, attached to opposite ends of a strain sensor spanning a fluid flow channel (see, e.g., Figures 3A and 3B). Electrodes can be made of any appropriate material. In some embodiments, a channel can include one or more leads electrically connected to the electrodes. In some embodiments, a channel can include one lead electronically connected to each electrode.

Also provided herein are microfluidic devices. In some embodiments, a microfluidic device can include one or more (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, or more) channels as described herein. In some embodiments, two or more (e.g., 3, 4, 5, 6, 7, 8, 9, 10, or more) channels can be set up in parallel. In some embodiments, two or more (e.g., 3, 4, 5, 6, 7, 8, 9, 10, or more) channels can be set up in sequence. In some embodiments, a microfluidic device can include a first substrate. In some

embodiments, a channel as described herein can be disposed on the first substrate. A first substrate can be any appropriate first substrate. In some embodiments, a microfluidic device can include one or more sample reservoirs. In some embodiments, a microfluidic device can include one or more sample collection reservoirs (e.g., one or more cell collection reservoirs). Cell collection reservoirs can be present for collecting and pooling cells of a specific subtype once a desired phenotypic identification has been reached. The cell collection reservoirs can serve as waste reservoirs, or as collection units for further analysis of the cells.

In some embodiments, microfluidic devices provided herein can have a channel network including one or more sensors, wherein the channel network includes one or more channels as described herein in which sample flows from an upstream portion at a sample reservoir to a downstream portion away from the sample reservoir in a downstream direction. In some embodiments, a channel as described herein can operably connect a sample reservoir to a sample collection reservoir (e.g., using a fluid flow channel). In some embodiments, a microfluidic device can include one or more inlet ports. In some embodiments, a microfluidic device can include one or more outlet ports. In some embodiments, a channel as described herein can operably connect an inlet port to an outlet port (e.g., using a fluid flow channel). In some embodiments, a channel as described herein can operably connect a sample reservoir to an outlet port (e.g., using a fluid flow channel). In some embodiments, a channel as described herein can operably connect an inlet port to a sample collection reservoir (e.g., using a fluid flow channel). In some embodiments, a microfluidic device can include a channel including one or more strain sensors as described herein disposed downstream of a sample reservoir. In some embodiments, a microfluidic device can include a channel including one or more strain sensors as described herein disposed downstream of an inlet port. In some embodiments, a microfluidic device can include a channel including one or more strain sensors as described herein disposed upstream of a sample collection reservoir. In some embodiments, a microfluidic device can include a channel including one or more strain sensors as described herein disposed upstream of an outlet port. In some embodiments, a microfluidic device can include one or more microfluidic valves.

The channels can be independently configured as any channel described herein. In some embodiments, a microfluidic device can include one or more inlet ports. In some embodiments can include one or more microfluidic valves. In some embodiments, a microfluidic device can be configured to provide an electrical impedance profile associated with the flow of fluid through one or more fluid flow channels. In some embodiments, a microfluidic device can be configured to provide an electrical resistance profile associated with the flow of fluid through one or more fluid flow channels.

In some embodiments, microfluidic devices are provided that are configured to concurrently identify, from a single sample of cells, two or more cell subtypes. For example, in some embodiments, provided are microfluidic devices that are configured to identify, from a single sample of cells, circulating tumor cells and cells that are not circulating tumor cells.

Also provided herein are systems. In some embodiments, a system can include one or more (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, or more) channels as described herein. The channels can be independently configured as any channel described herein. In some embodiments, a system can include one or more inlet ports. In some embodiments can include one or more microfluidic valves. In some embodiments, a system can be configured to provide an electrical impedance profile associated with the flow of fluid through one or more fluid flow channels. In some embodiments, a system can be configured to provide an electrical resistance profile associated with the flow of fluid through one or more fluid flow channels.

Also provided are methods of fabricating a channel, a microfluidic device, or a system as described herein. Nanoisland-on-graphene sensors (e.g., with palladium nanoislands) can be made by any appropriate method, for example, the methods described in U.S. Patent No. 9,863,885. For example, palladium nanoislands can be made by an evaporation of palladium onto single-layer graphene, backed on copper foil. Palladium can be evaporated onto as-is graphene at a rate of about 0.03 A/s to achieve a final layer thickness of about 8 nm (e.g., as registered by a quartz crystal microbalance). The morphology of nanoparticles produced by this process can be discrete, loosely connected particles (“nanoislands”).

Channels and microfluidic devices can be fabricated by any appropriate method. For example, a microfluidic device can be constructed by casting an elastomer (e.g., poly(dimethylsiloxane) (PDMS)) casted onto a reverse of a channel constructed out of a photopolymerizable polymer (e.g., SU-8 photopolymerizable polymer) on a silicon wafer. Multiple castings (e.g., 2 or 3) can be used. The ratio of base: cross-linker can be any appropriate ratio. In some embodiments, the ratio of base: cross-linker can be a ratio of about 5: 1 to about 30: 1 (e.g., about 5: 1, about 10: 1, about 12: 1, about 15: 1, about 20: 1, about 25: 1, or about 30: 1). In a first casting, the elastomer can be cast up to a thin layer (~ < 2 pm) covering the reverse of a channel and cured (e.g., at 65 °C for 1 hr). In some embodiments, taking advantage of a tacky layer, the metal nanoislands-on-graphene sensor can be placed onto this thin layer above the channel by cutting a small rectangle (~5 mm ^c 10 mm) spanning short axis of the channel. In some embodiments, after a brief setting period (e.g., 30 min at room temperature), the copper backing can be wet-etched (e.g., with a 10% w/w ammonium persulfate solution (APS) for 5 hours at room temperature). After etching, the etchant can rinsed carefully with DI water. Electrodes (e.g., copper wire or aluminum foil electrodes) can be attached to the nanoisland sensors (e.g., using conductive carbon paint (Dag-T-502 Carbon Paint, Ted Pella) or EGaln (Eutectic Gallium-Indium, Sigma Aldrich)). In some embodiments, with the sensor in place and electrodes leading far from the channel, a second casting of PDMS can be poured over the assembly and cured (e.g., to completion at 65°C for 2 h). After the PDMS is cured, holes can punched for an inlet an outlet and plasma bonded (e.g., using Harrick Plasma, ambient O2/N2 plasma to a glass slide and cured on a hot-plate for 1 h at 100 °C). A brightfield image of the sensor, which is offset from the channel by one micron, is shown in

Figures 14A and 14B.

In some embodiments, with, e.g., a softer formulation of 20: 1 PDMS, a release

(or sacrificial) layer of a 5% w/w solution of PMMA:anisole can help detach PDMS from the mold. The PMMA:anisole solution can be spin-cast onto the wafer at 1500 RPM (« 1 pm thickness) and heated for 5 min at 100 °C. Then, after proceeding with the device fabrication, acetone can be used to promote release of the PDMS.

Sensitive, non-contact, sterile and in-situ measurements of channel deformation according to some embodiments of devices and methods described herein can measure different phenomena. In some embodiments, these techniques can be inherently orthogonal to current methods, and many current devices that rely on optical-based techniques could gain added functionality with minimal drawback to such device.

Also provided herein are methods of sensing in microfluidic devices by measuring the minute deformation caused by fluid flow on the side channels. In some embodiments, the methods use graphene decorated with a percolated network of palladium“islands” (nanoislands) as an ultra-sensitive piezoresistive sensor. In some embodiments, for pure fluids, such as water, changes in the electrical resistance of the sensor due to flow rate can be related across multiple devices by considering the deformation of the channel due to fluid flow. In some embodiments, this relationship can enable calibration of a device provided herein to measure deformation of a channel dynamically. In some embodiments, the methods can be used to measure the passing of air bubbles through the channels, which can induce the viscoelastic deformation of the channel walls.

Also provided herein are methods of detecting deformation in at least a portion of a channel as described herein through which a fluid is flowing, comprising measuring one or more electrical signals from the strain sensor caused by the deformation. An exemplary undeformed channel including a strain sensor is shown in Figure 3B. A cross-sectional view of an exemplary deformed channel 1800 is shown in Figure 18. Walls 1810, 1811, and 1812, having thicknesses ti, t2, and t3, respectively, partially enclose a fluid flow channel 1820. Walls 1810, 1811, and 1812 can be, independently, inner or outer walls. Inner wall 1813, having a thickness t4, encloses fluid flow channel 1820 in this cross-sectional view. Inner wall 1813 is positioned between fluid flow channel 1820 and outer wall 1814. A strain sensor 1850 is embedded in inner wall 1813. A particle 1870 is shown in fluid flow channel 1820. The presence of particle 1850 can change the height ho (e.g., by Ah) and/or width Wo (e.g., by AW) of fluid flow channel 1820. When fluid flow channel 1820 is deformed, Sensor 1850 is likewise deformed. Without being bound by any particular theory, it is believed that deformation of sensor 1820 can cause alterations in one or more electrical signals from sensor 1850. Sensor 1850 is connected to electrodes 1840a and 1840b, which extend beyond the channel. In some embodiments, a change in height or width can be positive. In some embodiments, a change in height or width can be negative.

Also provided herein are methods of measuring deformation in at least a portion of a channel as described herein through which a fluid is flowing, comprising measuring one or more electrical signals from the strain sensor caused by the deformation. In some embodiments, the one or more electrical signals can be a voltage. In some embodiments, measuring can include continuous measuring. In some embodiments, measuring can include discontinuous measuring.

In some embodiments, the method can further comprise detecting one or more particles in the fluid. In some embodiments, the particles can be rigid. In some embodiments, the particles can be deformable. In some embodiments, the one or more particles can be a gas bubble. In some embodiments, the one or more particles can be a solid particle. In some embodiments, the one or more particles can be a biological cell. In some embodiments, the method can further include determining one or more properties of at least one of the particles. In some embodiments, the one or more properties can be selected from the group consisting of rigidity, deformability, size, flow rate, and identity. In some embodiments, the method further includes quantifying the particles based on the detecting of the particles. In some embodiments, the strain sensor does not directly contact the particle. In some embodiments, the strain sensor does not directly contact the fluid. In some embodiments, the methods described herein can be used to identify one or more contents of the fluid flow channel. In some embodiments, the method can further include determining the identity of the gas bubble based on the one or more electrical signals. In some embodiments, the method can further include determining the identity of the solid particle based on the one or more electrical signals. In some embodiments, the method can further include determining the identity of the biological cell based on the one or more electrical signals.

In some embodiments of any of the methods described herein, the method can further include calculating a flow rate of the fluid based on the one or more electrical signals.

Also provided herein are methods of measuring a fluid flow rate. In some embodiments, the method can include passing a fluid through any of the channels described herein, detecting deformation in at least a portion of the channel by measuring one or more electrical signals from the strain sensor, and measuring the fluid flow rate based on the one or more electrical signals. In some such

embodiments, the viscosity of the fluid is known.

Also provided herein are methods of measuring a viscosity of a fluid. In some embodiments, the method can include passing a fluid through any of the channels described herein, detecting deformation in at least a portion of the channel by measuring one or more electrical signals from the strain sensor, and measuring the viscosity based on the one or more electrical signals. In some such embodiments, the flow rate of the fluid is known. In some embodiments, such methods can determine whether a fluid is Newtonian or non-Newtonian.

Also provided herein are methods for high throughput particle sorting. In some embodiments, the method can include passing a fluid containing a plurality of particles through any of the channels described herein, detecting deformation caused by a particle in at least a portion of the channel by measuring one or more electrical signals from the strain sensor, identifying one or more properties of the particle based on the one or more electrical signals, and sorting the particle based on the one or more properties. In some embodiments, wherein the particle can be a biological cell.

Accordingly, also provided herein are methods for sorting of biological cells. In some embodiments, the method can include passing a sample including cells comprising a circulating tumor cell and a cell that is not a circulating tumor cell from a subject through any of the channels described herein, detecting deformation caused by the cells in at least a portion of the channel by measuring one or more electrical signals from the strain sensor, identifying the cell as a circulating tumor cell or a cell that is not a circulating tumor cell based on the one or more electrical signals, and sorting the cell based on the identifying. The method can, in some embodiments, further include independently collecting cells of one or more subtypes to create one or more pools of cells having the same subtype.

Also provided herein are methods of modeling a blood vessel. Without being bound by any particular theory, it is believed that changes in blood vessel pressure can cause changes in cellular responses. In some embodiments, the method can include passing a sample through any of the channels described herein, and detecting a cellular response in one or more cells in contact with the channel.

Also provided herein are methods of detecting the presence or absence of a bubble in a fluid. In some embodiments, method can include passing a fluid through any of the channels described herein, detecting deformation caused by a bubble in at least a portion of the channel by measuring one or more electrical signals from the strain sensor, and identifying the presence or absence of a bubble based on the detecting. In some embodiments, the method further comprises detecting the size of a bubble in a fluid based on the detecting. In some embodiments, this method could be carried out on lab reagents, e.g., chromatography solutions. In some embodiments, this method could be carried out on therapeutic solutions, e.g., blood, IV solutions, and the like.

In some embodiments, any of the methods described herein can be carried out without the use of without the use of a camera or laser. In some embodiments, any of the methods described herein can be carried out on a benchtop. In some embodiments, any of the methods described herein can be less computationally intensive than other methods of detecting deformation in a wall of a channel.

In some embodiments, a minute deformation can be transduced into a change in electrical resistance using an ultrasensitive piezoresitive film composed of metallic nanoislands on graphene. In some embodiments, changes in the resistance of a sensor can be related to the theoretical deformation of a channel at varying flow rates. In some embodiments, given a flow rate, the imposed channel deformation by a fluid can be related using the relationships developed by Gervais et al. [13] (used here) or Christov et al.[l2]The channel deformation is (and shown in Figure 5C):

where Q is the flow rate, ho is the initial channel height, E is the elastic modulus of the channel walls in the device, L is the length of the channel, z is the axial position along the device, m is the fluid viscosity, W is the width of the channel, p(z) is the pressure distribution along the channel, and a is a proportionality constant with a range from 0.5 to 15 [11]

Devices can be compared in the proportional response in deformation as the channel dimensions, or flow rates, are changed. The a value can be chosen to be one, otherwise, a could be calculated from simulations. The schematic device is shown in and sample calculations of the channel shape Figure 4D (top), and profile are shown in Figure 4D (bottom) and Figure 15.

The deformation of the walls in a channel could be used to measure a variety of phenomenon, such as fluid flow rates, the viscoelastic relaxation of the channel walls in the presence of air bubbles, channel deformation caused by particles and cells, or a combination thereof.

Also provided herein are methods of sensing the transit of fluids, gases, particles, and cells as they flowed through a microfluidic channel. In some embodiments, methods can be performed without the use of a camera or laser, i.e., “optics-free” microfluidics. In some embodiments, the methods can include monitoring the deformation of one or more walls caused by an analyte passing through a channel. In some embodiments, an analyte does not have to make contact with the channel walls to induce a deflection. In some embodiments, air bubbles can be used to induce a perturbation on elastomeric channel walls and the viscoelastic relaxation of the walls of the channel can be measured.

In some embodiments, a viscoelastic time constant can be calculated for the channel wall material (e.g., 11.3 ± 3.5 s ¹ for PDMS). In some embodiments, the calculated viscoelastic time constant agrees favorably with such measurement obtained by other techniques.

In some embodiments, the methods can detect solid particles, such as silica particles, as well as biological cells, such as human mesenchymal stem cells, as they passed through the channels. In some embodiments, the methods described herein can provide a convenient, continuous, and non-contact measurement of rigid and deformable particles without the use of a laser or camera.

Exemplary Embodiments:

Embodiment 1 is a channel comprising:

one or more walls having an elastic modulus of 100 MPa or less and defining at least a portion of a fluid flow channel; and

a first strain sensor comprising a supporting layer and a metallic layer on and in contact with the supporting layer, wherein the metallic layer comprises a plurality of metallic nanoislands.

Embodiment 2 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 50 MPa or less.

Embodiment 3 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 25 MPa or less.

Embodiment 4 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 10 MPa or less.

Embodiment 5 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 5 MPa or less.

Embodiment 6 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 3 MPa or less.

Embodiment 7 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 2 MPa or less. Embodiment 8 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of 1 MPa or less.

Embodiment 9 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 100 MPa.

Embodiment 10 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 50 MPa.

Embodiment 11 is the channel of embodiment 1 , wherein the one or more walls have an elastic modulus of between about 50 kPa and 25 MPa.

Embodiment 12 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 10 MPa.

Embodiment 13 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 5 MPa.

Embodiment 14 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 3 MPa.

Embodiment 15 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 2 MPa.

Embodiment 16 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 50 kPa and 1 MPa.

Embodiment 17 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 1 MPa and 10 MPa.

Embodiment 18 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 1 MPa and 5 MPa.

Embodiment 19 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 1 MPa and 3 MPa.

Embodiment 20 is the channel of embodiment 1, wherein the one or more walls have an elastic modulus of between about 1 MPa and 2 MPa.

Embodiment 21 is the channel of any one of embodiments 1-20, wherein the supporting layer comprises graphene.

Embodiment 22 is the channel of any one of embodiments 1 -20, wherein the supporting layer comprises hexagonal boron nitride.

Embodiment 23 is the channel of any one of embodiments 1 -20, wherein the supporting layer comprises molybdenum disulfide. Embodiment 24 is the channel of any one of embodiments 1-23, wherein the metallic layer comprises palladium, gold, or silver.

Embodiment 25 is the channel of any one of embodiments 1 -24, wherein the nanoislands comprise palladium, gold, or silver.

Embodiment 26 is the channel of embodiment 25, wherein the nanoislands are palladium nanoislands.

Embodiment 27 is the channel of any one of embodiments 1 -26, wherein the strain sensor is embedded in said wall.

Embodiment 28 is the channel of any one of embodiments 1-27, wherein the strain sensor is not in contact with the fluid flow channel.

Embodiment 29 is the channel of any one of embodiments 1-28, wherein the strain sensor is separated from the fluid flow channel by about 1 to about 10 pm.

Embodiment 30 is the channel of any one of embodiments 1-28, wherein the strain sensor is separated from the fluid flow channel by about 1 to about 5 pm.

Embodiment 31 is the channel of any one of embodiments 1-28, wherein the strain sensor is separated from the fluid flow channel by about 1 to about 3 pm.

Embodiment 32 is the channel of any one of embodiments 1-31, wherein the strain sensor spans the fluid flow channel.

Embodiment 33 is the channel of embodiment 32, wherein the strain sensor is perpendicular to the long axis of the fluid flow channel, the fluid flow channel having a long axis.

Embodiment 34 is the channel of any one of embodiments 1-33, wherein the supporting layer is between the fluid flow channel and the metallic layer.

Embodiment 35 is the channel of any one of embodiments 1-33, wherein the metallic layer is between the fluid flow channel and the supporting layer.

Embodiment 36 is the channel of any one of embodiments 1-35, further comprising one or more electrodes electrically connected to one or more of said metallic nanoislands.

Embodiment 37 is the channel of embodiment 36, further comprising one or more leads electrically connected to said electrodes. Embodiment 38 is the channel of any one of embodiments 1-37, wherein the wall comprises an inner wall and an outer wall and the strain sensor is situated between said inner wall and said outer wall.

Embodiment 39 is the channel of any one of embodiments 1-38, wherein the strain sensor further comprises a polymeric layer.

Embodiment 40 is the channel of any one of embodiments 1-39, wherein the one or more walls comprise a polymer.

Embodiment 41 is the channel of embodiment 40, wherein the polymer is selected from the group consisting of poly(dimethylsiloxane) (PMDS), poly(ethylene glycol) diacrylate (PEGDA), poly(methyl methacrylate), polyurethane, and combinations thereof.

Embodiment 42 is the channel of any one of embodiments 1-41, wherein the fluid flow channel has a cross-section with an area of about 25 pm ² to about 500000 pm ² .

Embodiment 43 is the channel of embodiment 42, wherein the fluid flow channel has a cross-section with an area of about 2500 to about 150000 pm ² .

Embodiment 44 is the channel of any one of embodiments 1-43, wherein the fluid flow channel has a rectangular cross-section, the cross-section characterized by a height and a width.

Embodiment 45 is the channel of embodiment 44, wherein the fluid flow channel has a square cross-section.

Embodiment 46 is the channel of embodiment 44 or embodiment 45, wherein the height of the cross-section is about 5 to about 1000 pm.

Embodiment 47 is the channel of embodiment 46, wherein the height of the cross-section is about 50 to about 300 pm.

Embodiment 48 is the channel of any one of embodiments 44-47, wherein the width of the cross-section is about 5 to about 1000 pm.

Embodiment 49 is the channel of embodiment 48, wherein the width of the cross-section is about 50 to about 750 pm.

Embodiment 50 is the channel of any one of embodiments 1-49, further comprising an inlet and an outlet. Embodiment 51 is the channel of any one of embodiments 1-50, wherein the strain sensor is configured to provide an electrical impedance profile associated with the flow of fluid through the fluid flow channel.

Embodiment 52 is the channel of any one of embodiments 1-51, wherein the strain sensor is configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel.

Embodiment 53 is the channel of any one of embodiments 1-52, further comprising one or more additional strain sensors, each independently comprising a supporting layer and a metallic layer on and in contact with the supporting layer, wherein the metallic layer comprises a plurality of metallic nanoislands.

Embodiment 54 is a microfluidic device comprising one or more channels according to any one of embodiments 1-53.

Embodiment 55 is the device of embodiment 54, further comprising one or more reaction chambers.

Embodiment 56 is the device of any one of embodiments 54-55, further comprising one or more inlet ports.

Embodiment 57 is the device of any one of embodiments 54-56, further comprising one or more microfluidic valves.

Embodiment 58 is a system comprising one or more channels according to any one of embodiments 1-53.

Embodiment 59 is the system of embodiment 58, wherein the system is configured to provide an electrical impedance profile associated with the flow of fluid through the fluid flow channel.

Embodiment 60 is the system of embodiment 58, wherein the system is configured to provide an electrical resistance profile associated with the flow of fluid through the fluid flow channel.

Embodiment 61 is a method of detecting deformation in at least a portion of a channel according to any one of embodiments 1-53 through which a fluid is flowing, comprising measuring one or more electrical signals from the strain sensor caused by the deformation.

Embodiment 62 is the method of embodiment 61, wherein the one or more electrical signals is a voltage. Embodiment 63 is the method of any one of embodiments 61-62, wherein the measuring comprises continuous measuring.

Embodiment 64 is the method of any one of embodiments 61-63, further comprising detecting one or more particles in the fluid.

Embodiment 65 is the method of embodiment 64, wherein the one or more particles are rigid or deformable.

Embodiment 66 is the method of any one of embodiments 64-65, wherein the one or more particles is a gas bubble.

Embodiment 67 is the method of any one of embodiments 64-65, wherein the one or more particles is a solid particle.

Embodiment 68 is the method of any one of embodiments 64-65, wherein the one or more particles is a biological cell.

Embodiment 69 is the method of any one of embodiments 64-68, further comprising determining one or more properties of at least one of the particles.

Embodiment 70 is the method of embodiment 69, wherein the one or more properties are selected from rigidity, deformability, size, flow rate, and identity.

Embodiment 71 is the method of any one of embodiments 64-70, further comprising quantifying the particles based on the detecting of the particles.

Embodiment 72 is the method any one of embodiments 64-71, wherein the strain sensor does not directly contact the particle.

Embodiment 73 is the method of any one of embodiments 61-71, wherein the strain sensor does not directly contact the fluid.

Embodiment 74 is the method of embodiment 66, further comprising determining the identity of the gas bubble based on the one or more electrical signals.

Embodiment 75 is the method of embodiment 67, further comprising determining the identity of the solid particle based on the one or more electrical signals.

Embodiment 76 is the method of embodiment 68, further comprising determining the identity of the biological cell based on the one or more electrical signals. Embodiment 77 is the method of any one of embodiments 61-77, further comprising calculating a flow rate of the fluid based on the one or more electrical signals.

Embodiment 78 is a method for high throughput particle sorting comprising: passing a fluid containing a plurality of particles through a channel according to any one of embodiments 1-53;

detecting deformation caused by a particle in at least a portion of the channel by measuring one or more electrical signals from the strain sensor;

identifying one or more properties of the particle based on the one or more electrical signals;

sorting the particle based on the one or more properties.

Embodiment 79 is the method of embodiment 78, wherein the particle is a biological cell.

EXAMPLES

Materials and Methods

Device Fabrication. Microfluidic devices were constructed by casting poly(dimethylsiloxane) (PDMS) casted onto a reverse of a channel constructed out of SU-8 photopolymerizable polymer on a silicon wafer. This process occurred in two castings of PDMS in either a ratio of 15: 1 or 20: 1 rato (base: cross-linker). In the first casting, the PDMS was cast up to a thin layer (~ < 2 pm) covering the channel and cured at 65 °C for 1 hr. Taking advantage of the tacky PDMS layer, the metal nanoislands-on-graphene sensor was placed onto this thin layer above the channel by cutting a small rectangle (~5 mm ^c 10 mm) spanning short axis of the channel. After a brief setting period of 30 min at room temperature, the copper backing was wet-etched with a 10% w/w ammonium persulfate solution (APS) for 5 hours at room temperature. After etching, the etchant (blue, due to the copper ions) was rinsed carefully with DI water. Then, copper wire or aluminum foil electrodes were attached to the nanoisland sensors using conductive carbon paint (Dag-T-502 Carbon Paint, Ted Pella) or EGaln (Eutectic Gallium-Indium, Sigma Aldrich). [46] With the sensor in place and electrodes leading far from the channel, a second casting of PDMS was poured over the assembly and cured to completion at 65 °C for 2 h. After the PDMS was cured, two holes were punched for the inlet and outlet and plasma bonded (Harrick Plasma, ambient O2/N2 plasma) to a glass slide and cured on a hot-plate for 1 h at 100 °C. A brightfield image of the sensor, which is offset from the channel by one micron, is shown in Figures 14A and 14B.

For softer formulations of 20: 1 PDMS, it was found that a release (or sacrificial) layer of a 5% w/w solution of PMMA:anisole helped detach PDMS from the mold. The PMMA:anisole solution was spin-cast onto the wafer at 1500 RPM (« 1 pm thickness) and heated for 5 min at 100 °C. Then, after proceeding with the typical device fabrication, acetone can be used to promote release of the PDMS. A schematic of the device is in Figure 4A and a picture of the graphene-interface spanning a fluid-filled channel is in Figure 4C.

Palladium NanoIsland-on-Graphene Sensors. Palladium nanoislands were made by an incomplete evaporation of palladium onto single-layer graphene (GrollTex, Inc.), backed on copper foil. As detailed previously [7], palladium was evaporated onto as-is graphene at a rate 0.03 A/s to achieve a final layer thickness of 8 nm as registered by a quartz crystal microbalance, but the morphology consisted of discrete, loosely connected particles (“nanoislands”) (see Figure 4B).

Device Characterization Fluid was controlled for constant flow rate using a PID-controlled, isocratic fluid pump for size-exclusion chromatography (e.g., from a GPC/SEC column) (Agilent). Sensor resistance was measured using a Kiethley source-measure unit (261 lb) at approximately 20 readings/s during fluid calibration using the SEC. For the particle measurements, an oscilloscope (RTB2K, Rhode & Schwarz) was used to achieve kilohertz sampling. High-speed video was taken using a scientific camera (Basler acAl 920-150uc) imaging a 300 ^c 280 pixel window with a custom-built magnification stage at 820 FPS.

Cell culture and staining. Human mesenchymal stem cells (hMSCs, Lonza, PT-2501) were seeded in a T75 flask at 5000 cells/cm ² in growth media (Lonza, PT- 3001). These cells were incubated under standard conditions and then detached by adding 2 ml of Trypsin (Gibco, Thermo Fisher Scientific) when the confluence reached to around 90%. 8 mL of media was added to quench the Trypsin when more than 90% cells were detached from the flask. Then, 100 pL DiR (Thermo Fisher Scientific) in DMSO was added to the cell suspension and mixed by gentle pipetting. The cell staining was confirmed with an epifluorescence microscope (Evos, Life Technologies). The cells were then centrifuged at 1000 rpm for 5 min. After removal of the supernatant, the cell pellet was resuspended in media for immediate use or in 10% Formalin (Sigma Aldrich) for later use.

Results

Channel Deformation Due to Flow Rate. Figure 5 shows exemplary measurement of changes in resistance due to changes in flow rate. The resistance of the sensor was continuously measured at varying flow rates (Figure 5A-B) using a PID- controlled flow rate through a commercial GPC/SEC device (Agilent). The device responded to changes in flow rate, with lower resistances at lower flow rates. Figure 5B shows the device changing quickly to imposed changes in flow rate of the device. Typical resistance changes were of order 0.1%, which roughly translated to approximately -tens of Ohms.

The raw data can be seen in Figure 5A and Figure 5B, which were taken with the device directly on a bench without isolation from vibration. Most ultra-sensitive sensors suffer from unwanted detection of ambient vibration. Embedding the sensor in the viscoelastic elastomer dampened these ambient vibrations, which enabled the sensor to measure the submicron deformations in the channel with a signal well above the background mechanical noise.

A change of 0.1% in resistance during flow rate measurements corresponds to increments of absolute resistance on the order of 10 W.

Given a flow rate, the imposed channel deformation can be related using the relationship developed by Gervais et al. [13] (used here) or Christov et al. [12] The relationship between flow rate and channel deformation is shown in Figure 5C for four different devices, two of which (750 pm ^c 200 pm, channel width times height) have the same geometry but different elastic moduli by varying the PDMS mixing ratio. Figure 5C shows an exemplary theoretical relationship between fluid flow rate and channel deformation for different exemplary devices tested, which is a function of channel geometry and the elastic modulus, calculated with the derivation by Gervais et al. [13] Naming convention on devices are Width ( W) ^c Channel Height (H) in microns, followed by the elastic modulus of the device. Note the 1/10 factor on the 50 x 50 pm device (dashed line).

The channel deformation is given as:

Where Q is the flow rate, ho is the initial channel height, E is the elastic modulus of the device, L is the length of the channel (taken to be the device, see Ref. [12]), z axial position along the device (with the sensor located at z = zsensor ), m is the fluid viscosity, W is the width of the channel, p(z) is the pressure distribution along the channel and a is a proportionality constant with a range from 0.5 to 15 [11] (see, e.g., Ref. [11] and [12] for more details).

The channel deformation may also be given as:

where Q is the flow rate, ho is the initial channel height, E is the elastic modulus of the channel walls in the device, L is the length of the channel, z is the axial position along the device, m is the fluid viscosity, W is the width of the channel, p(z) is the pressure distribution along the channel, and a is a proportionality constant with a range from 0.5 to 15 [11] (see, e.g., refs 11 and 12 for more details).

Parameters for a sample calculation are given in Table 1.

Table 1. Model parameters to calculate channel deformation

Devices were compared in the proportional response in deformation as the channel dimensions, or flow rates, were changed. The a value was chosen to be one, otherwise, a would be calculated from simulations. The schematic device is shown in and sample calculations of the channel shape Figure 4D (top), and profile are shown in Figure 4D (bottom) and Figure 15.

There are three possible contributions to determine the maximum frequency of acquisition: (1) the response time of the nanoislands on graphene sensor, (2) the response time of the elastic channel, (3) and the resistance profile caused by a bubble. As graphene can operate in kHz frequencies[47], limitations likely arise some combination of the elasticity of the channel and ability to resolve overlapping resistance profiles from multiple bubbles.

Based on the viscoelastic relaxation constant of 11.3 s ¹ , a conservative time required for the channel deformation to reset back to its original configuration can be estimated. The interface will return to 95% of its original configuration after 0.266 seconds or 3.77 Hz. As described herein, much higher frequencies at 33 Hz have been achieved (Figure 15 and Figure 16).

It is noted that it was not necessary to have a channel width that is much greater than the channel height, and it was assumed the exemplary devices can still be considered using the same derivation (see appendix of Ref. [12]). However, the linear relationship between flow rate and deformation was observed (see, e.g., Figure 5C and Eqs. (2) and (5)), which occurs at relatively low pressures for device geometries in Figure 5D-F. A linear relationship between channel deformation and flow rates in the 50 x 50 pm device at the flow rates tested and accessible by the GPC pump is not expected (Figure 5G), which is reflected in the least-squares fit. Figures 3D-3G show exemplary percent change in resistance at different flow rates, plotted against the theoretical deformation at the wall for several devices in varying geometries and elastic modulus. Note the relationship between deformation and flow rate is linear for Figures 3D-3F but non-linear for Figure 3G. Gain and linearity given by slope and r ² values, respectively. Verifying Resistance Changes Due to Elastohydrodynamic Phenomenon. When compensating for the gain, given as the slope m, (Figures 5D-G), a master curve of all devices plotting the change in resistance as a function of the imposed flow rate can be created, as shown in Figures 6 and 10. In Figure 6, the flow rate, fluid viscosity, sensor position and channel height can be incorporated into a channel deformation, using Ref.

[13] The exemplary strain sensor measures channel deformation by changing resistance change, normalized by the gain m in Figure 5). Three channel geometries in the linear regime between deformation and flow rate are shown, with an inset showing the 50 x 50 pm device, which is operating in a non-linear regime. The devices operating in the linear regime (750 ^c 200 pm at 2 MPa, 750 ^c 200 pm at 1 MPa and 300 ^c 300 pm at 1 MPa) reasonably collapse onto a single line of slope 0.78, against a theoretical value of one. It is hypothesized that a combination of non-idealities in the device and theory that account for this. First, the value of a (Eq. (2) and (5)) varies from device to device, and a was set equal to one because the primary interest is in calibrating the exemplary devices. Second, the exemplary devices are not constructed with a high aspect ratio, which simplifies the mathematics, and the widths are similar to the height. Finally, the sensor is embedded at ~l-3 pm into the device (‘into’ being along the y- axis of Figure 4D), which is a similar length of the elastic deformations on the wall, which could result in non-linear relationships between surface deformation and the deformation at the sensor. Despite these offsets, it was found that the aggregate relationship between flow rate and deformation for the devices in the linear regime remains linear (r ² = 0.95).

For high pressures, such as in the device with a relatively small 50 ^c 50 pm cross-sectional area, the relationship between deformation and flow rate became noticeably nonlinear. Thus, in Figures 5D-5G, the relationship between changes in resistance and deformation are linear for the three devices with a larger cross-sectional area but not the 50 pm ^c 50 pm device (Figure 5G) A normalized change in resistance was obtained, which normalizes the sensitivity of the nano-islands on graphene sensor and the distance of the sensor from the fluid channel, by multiplying the change the resistance by its slope, m, compared to a reference slope, mo, of the device with dimensions 750 pm ^c 200 pm, E = 2 MPa. This value, m/mo, is denoted as the“gain” in Figures 6 and 10. Plotted on the y axis is normalized change in resistance of the palladium nano-island strain sensor, which is proportional to the strain. Plotted on the x axis of Figure 10, are the experimental conditions in the form of Ah/ho, which relates the strain in the channel assuming elastohydrodynamic deformation, given by Eqs. 2 and 5. A collapse of the data was observed in the linear regime onto a single master plot with a slope of 0.78, which is in close agreement to a theoretical value of 1. This demonstrates that the sensor is sensing deformation due to elastohydrodynamic phenomenon. The deviation from the theoretical value could be due to differences between the devices and theory [13]: the devices here do not have a limiting dimension, and for the purposes of demonstrating trends in strain with flow rate, the fitting parameter, a, has been taken to be 1. In addition, the distance between the sensor to the channel can vary between devices (~l-3 pm), which decreases the strain as the sensor is further in the bulk (the strain on the sensor, however, remains proportional to the deformation on the sidewalls). [42] Christov et al. solved for a without requiring simulations, but this approach had a thin, deformable layer on top of the channel, whereas the devices here have a semi-infinite layer on top. [12]

Channel Deformation and Viscoelastic from Air Bubbles. The transient changes in channel deformation due to air bubbles (~30-50 pL) was measured in a 300 x 300 mih at 1 MPa device. In contrast to optical methods of previous studies [14,15], the exemplary devices can monitor dynamic events in the channel (~ 10 kHz sampling rates) at far higher rates that accessible to most cameras (~20-l00 Hz) and without optical limits (micron-or-less wall deformation). Figures 7 and 11 show exemplary measurement of air bubbles and channel viscoelasticity with

elastohydrodynamic deformation. Figures 7A and 11A show exemplary relatively large changes in resistance as a bubble transits across the sensor. In comparison to the fluid flow, this is somewhat surprising because the pressure drop across a 30-50 pL bubble, such as the ones generated by the artificial bubble generator is approximately -5-50 Pa for flow velocities of 1 mm/s to 10 mm/s, given by Eq. (3) [33]

DR = 4.52

Where LR is the change in pressure across the air bubble, y is the surface tension (air-water), r is the radius of channel (approximate for square geometries) and Ca is the capillary number (Ca = mU/y, m is the fluid viscosity and V is the characteristic fluid velocity).

To investigate the origin of these large changes in resistance, the resistance was measured while taking high-speed video (Basler Ace, 820 FPS) for the case of an “infinitely -long” bubble, where a channel of fluid is cleared by air.

Potentially, the large signal changes in resistance originate from the channel relaxing in the presence of a compressible fluid (i.e. air), but previous data shows that channels relaxing inward towards their neutral height would result in a decrease in resistance. To investigate the origin of these large resistance changes, the resistance was measured while taking high-speed video (820 FPS) for the case of an“infinitely - long” bubble, where a channel of fluid is cleared by air. Figures 7B and 11B show exmplary calculated deformation due to a transiting“infinitely long” bubble. In

Figure 11B, the baseline with zero corresponded to the deformation of the open channel. By doing so, it was assumed that the deformation profile over the strain sensor was the same between a pure fluid and an air bubble; they presumably deform the walls with a different profile, but the magnitude of deformation on the sensor is similar. The sensor resistance and deformation is shown (micrometers) on the other y axis, as calculated from the fluid flow rate, by dividing the percent relative change in resistance ( Ro = 5.35 kQ) by 5.9 ^c 1CT ² m (Figure 5F). Figures 7B and 11B show exemplary resistance change due to a transiting‘infinitely long’ bubble. In region 0, the channel is flowing only water, and a small increase in flow rate was applied, indicated by the arrow, to serve as a calibration. This pulse highlights how large the signals are due to air bubbles, compared to changes in resistance due to flow rate, despite the - 5-50 Pa pressure drop associated with air bubbles. In region I, it was observed that the resistance begins to increase rapidly, and from the exemplary image in Figure 7C, this corresponds to the entire air-water interface transiting across the sensor. In region II, the exemplary image from Figure 7D shows that the fluid interface has passed the graphene sensor, which corresponds to the exemplary lengthy plateau in the resistance change in Figure 7B. This plateau, which has a modest negative linear slope, corresponds to clearing the channel of fluid with air, since the sensor is located in the middle of the channel. It was observed that clearing the channel with air at higher velocities results in a shorter plateau and vice versa. It was observed that clearing the channel with air at higher velocities results in a shorter plateau and vice versa. This process was mechanically noisy as the channel sputtered water, which is reflected in the deformation trace in Figure 7D.

Finally, Figure 7E shows exemplary channel relaxing in the absence of any motion, due to the viscoelastic nature of PDMS. Using a Kelvin-Voigt model of viscoelastic materials, the channel resistance (normalized by maximum resistance) was treated as a spring-dashpot (Figure 7F, dashed lines; another exemplary comparison is shown in Figure 12) responding to the channel pressure, represented as a square wave (solid lines in Figure 7F and Figure 12) with a width that spans region I to region II. A viscoelastic relaxation time constant, x, of 11.3 ± 3.5 s ¹ was obtained as well as viscosity (of the solid) of 0.20 ± 0.08 MPa*s, which compares reasonably to 7.2 s ¹ and 0.15 MPa*s respectively of literature values (hexane-extracted 10: 1 PDMS measured with an elastic modulus of 1.08 MPa) [19]

The maximum frequency of bubbles achieved was at 33 Hz (see Figure 16, Figure 17) and was limited by the capability to generate bubbles rapidly. This rate could potentially be increased because the maximum frequency was limited by the ability to generate bubbles, rather than to the mechanical response of the material.

Large Changes in Resistance due to Pinching of the Graphene Sensor. It was observed that large changes in resistance occurs when the air-water interface moves across the sensor. The strain profile caused by a moving air-water interface is unusual: most strain sensors experience a gradual change in deflection across the majority of the sensor, e.g., a strain sensor bent like a cantilever. It is hypothesized that large changes in the resistance of the sensor, through the PDMS side walls, occur due to relatively high compression (i.e., strain) in a narrow portion, around the air-water interface, as opposed to a gradual bend across the length of the entire sensor. It was hypothesized that the sensor is being pinched at the air-water interface. This pinching is in contrast to the typical usage of strain sensors, which are often used as a beam - clamped on one end with a deflection applied on the other end. This localized pinching could move small patches of nanoislands together, leaving behind large gaps where there are fewer nanoislands. This would result in a net loss of conductivity and increase in resistance. The channel deformation was calculated assuming the deformation caused by changes in fluid flow. When the channel is being deformed by fluid, the entire sensor is being strained, whereas a moving air-water interface applies strain in specific portions across the sensor as it transits across the sensor. Thus, while the resistance is an experimentally-measured value, the deformation of the channel can possibly be different. The linear conversion values between deformation and resistance change are provided.

Silica Particles and hMSC Measurements

As a particle transits through a channel, it causes the fluid to flow around the particle, deforming the walls of the channel. Measurements were taken of transiting particles of silica spheres, which are rigid, and human mesenchymal stem cells, which are deformable. The deformation of rigid particles (silica microspheres) and deformable objects (human mesenchymal stem cells) as they transited through the channel was examined. As a particle transits through a channel, it causes the fluid to flow around the particle, deforming the walls of the channel. [16,20,44] Figures 8 and 13 show exemplary measurement of deformation profiles of transiting silica particles and human mesenchymal stem cells.

Silica Particles. The change in resistance (converted to deformation, from the calibration) was measured as an 80 pm silica particle (PolySciences, Inc.) passed across a sensor in (exemplary data shown in Figure 8A and Figure 13A) and simultaneously recorded by video during this event (exemplary data shown in Figure 8B and Figure 13B). The silica spheres (Megabead, PolySciences, Inc., calibration grade, CV < 3%) were 80 pm in diameter and flowed through a device with cross-sectional dimensions of 300 pm x 300 pm, made with PDMS (E = 1 MPa). Figure 13A shows exemplary data showing a change in resistance and the calculated change in deformation as the silica sphere flowed past the sensor. These resistance changes were converted to channel deformation per calibration from Figure 10. Again, this assumes that the deformation caused by the particle and a pure fluid is the same, which is not necessarily true but gives a magnitude of channel deformation. An exemplary sequence of images showing the silica sphere past the sensor can be seen in Figure 12B. The channel was isolated from a sequence of images to show the particle flowing from left-to-right and over the sensor, with the boundaries highlighted by the dashed lines. It was observed that changes in deformation and resistance (see, e.g., Figure 8A; Figure 13A)) of the sphere follows a linear increase as the particle transits across the graphene sensor, reaches a maximum after approximately 0.03 seconds (30 ms). At this moment (see, e.g., Figure 8B, Figure 13B)), the particle is approximately 2/3 through the sensor (at length = 2.8 mm). It is not immediately clear why the maximum deformation is a sharp peak, but the presence of a peak suggests that the particle deforms the walls in front and behind the actual particle.. As the particle moves, it deforms the channel walls [16,17], which increases the resistance in the sensor. After the particle moves past a part of the channel, it will relax and the resistance in the sensor reduces to its equilibrium value. This relaxation is subject to viscoelastic delay from the channel walls. It follows that the maximum resistance would occur when the particle has maximized the deformation on the walls, including the portions of the channel that are relaxing from when the particle flowed across it. One hypothesis is that the particle deforms the channel ahead of the particle, shifting the maximum resistance towards the right of the sensor. This could also help explain why the resistance drops even before the particle has fully exited the channel.

Human Mesenchymal Cells. Mesenchymal Stem Cells (hMSCs, Lonza, PT- 2501) cultured in bovine serum albumin were directly flow into the device. Human- derived mesenchymal stem cells were trypsinized and then flown into the device to demonstrate a proof-of-principle in measuring the deformability of the side walls due to the transit of biological objects in a continuous manner. This capability could be advantageous in the high-throughput screening of cells that differ in mechanical properties only, such as the label-free detection of circulating tumor cells. [45] Cells were approximately 10-15 pm in diameter, and exemplary resistance and deformation on the sensor caused by a cell flowing in the 300 pm ^c 300 pm device is shown in Figure 13C. The cell is both smaller and softer than the silica particle, and a smaller signal from the sensor is observed.

In addition, the width of the signal exceeds the time that the cell was in the channel, as shown from the composite image of exemplary cell motion in a channel in Figure 13D. The velocity of the moving particle, whether cell or silica sphere, affects the amount of deformation on the wall, and particles that move too slowly will not be detectable. It was also observed that the cell caused a deformation that lasted longer than the duration where the cell transited across the sensor, which is similar to the situation with air bubbles. Consecutive measurements in narrow and large channel could, in principle, aid differentiating between cells, bubbles and particles. For example, air bubbles will elongate in narrow channels, whereas particles would not. In addition, development and verification of elastohydrodynamic theories may make it simpler to distinguish between air bubbles, particles and cells from deformation profiles. Future development of the theoretical elastohydrodynamic deformation profile may make it simpler to distinguish between air bubbles, rigid particles, and cells from the characteristic time-dependent resistance recorded by the sensor during transit of the object.

Conclusions

It was demonstrated that the deformation of the sidewalls in microfluidic channel can be used to measure a variety of phenomenon, such as the fluid flow rates, the viscoelastic relaxation of the channel side walls in the presence of air bubbles, and channel deformation caused by particles and cells. The advantages of using, e.g., palladium nanoisland-on-graphene to measure channel deformation center are the simplicity of voltage measurements and the fact that the sensor does not contact the analyte directly. High-throughput arrays of devices scale favorably because voltage readings are used in lieu of special optical equipment, conjugating molecules or special solutions. The sensor used here did not even require microfabrication. The non-contact measurements of channel deformation means that the device remains sterile and versatile in a range of experimental conditions, including temperatures and solutions. The only device requirement is that one of the channels walls, or a portion of the channel wall, is deformable which makes these measurements complementary to many existing sensing techniques for multi-modal measurements. This technique may enable new avenues of investigation in physics and biology. These devices can be used to experimentally verify novel elastohydrodynamic phenomenon, such as the passage of deformable particles in the presence of deformable walls, or the flow around a deformable junction in the channel. Within cell biology, this device is complementary to many existing optical techniques because it only requires that one of the channel walls is deformable. For example, this device could provide a method of continuously measuring the mechanical properties of cells.

OTHER EMBODIMENTS

It is to be understood that while the invention has been described in conjunction with the detailed description thereof, the foregoing description is intended to illustrate and not limit the scope of the invention, which is defined by the scope of the appended claims. Other aspects, advantages, and modifications are within the scope of the following claims.

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