Electrical contactless microfluidic flow quantification

Interrogation of fluid flow is essential to microfluidics and downstream lab-on-a-chip and medical applications. Known microfluidic flow measurement methods, such as calorimetry,^1,2 streaming potential,^3,4 moving electrical double layer,^5–7 and interfacial charge transfer,⁸ require to place a transducer in the fluidic channel to be in contact with the fluid. Contactless microfluidic flow measurement—i.e., interrogation of the microfluidic flow without using a transducer in contact with the flow or using a dedicated component placed deliberately to the fluid tubing system—is noninvasive, nonperturbative, and free of fouling and electrochemical erosion effects, offering considerable promise to applications, including healthcare and energy.^9,10 However, existing contactless liquid-flow sensing technologies are limited to bulk liquids,^11–13 such as water in pipelines; known approaches for remote measurement of the microfluidic flow require to place a dedicated component in the microfluidic channel⁹ or the fluid system¹⁴ and to interrogate the component remotely, which are, therefore, pseudo-contactless (see supplementary material, Table S1). Therefore, an efficacious approach to real contactless quantification of the microfluidic flow remains lacking. Here, we demonstrate contactless microfluidic flow measurement based on the non-contact probing of the ubiquitous contact electrification of a continuous microfluidic flow with fluid channel walls. We measured the flow electrification-induced electric potential variation by using a probe electrode to at a distance up to 5 cm from a microfluidic flow. The contactless measurement delivers a resolution of 0.26 ± 0.01 μL min⁻¹ (in a 1-Hz bandwidth) at a distance of ∼1 cm, comparable to state-of-the-art contact low-level (<10 μL min⁻¹) flow measurement technologies.^15–18 The relationship between the response of the electrode and the probe-channel distance is well in agreement with a line-charge model. Remarkably, to use a monolayer graphene-coated probe electrode as an alternative to typical bare metal probe electrode improves the contactless flow-quantification noise level, rendering an enhancement in the overall flow-sensory resolution by 36.4%.

The measurement setup is based on a metal probe electrode at a distance from a microfluidic flow channel where phosphate buffer solution (1 × PBS, ionic strength = 150 mM, pH = 7.0) flows [Fig. 1(a)]. To fabricate the microfluidics chip (see supplementary material, Fig. S1), a 200-μm thick acrylic sheet was sandwiched between two layers of 126-μm thick medical grade double sided tape (Adhesives Research 8939). Then, a 400-μm wide microfluidic channel was defined on the sandwiched structure by using a laser cutter, forming a structured microfluidic chip. The top side of the chip was bonded to a 2-mm thick acrylic cover and the bottom side to a fused silica substrate (University Wafer, 1943). The flow pathway, excepting the substrate, is entirely based on electrochemical inert materials. A flow of PBS with a precisely controlled flow rate was driven through the microfluidic channel by using a syringe pump (Harvard Apparatus 70–3009). The probe electrode (tungsten, 24 μm in diameter) was wired to an electrometer (Keithley 6517b) in the voltmeter mode, which acquires the electric potential at the probe electrode relative to ground by using a unity-gain buffer followed by a resistor-feedback amplifier. Prior to measurement, the noninverting input of the voltmeter was initially connected to a dissipative resistor. When a measurement commenced, the noninverting input was disconnected from the dissipating resistor and connected to the probe.

Figure 1(b) shows the responses—the time rates of the voltage change measured by the probe electrode as functions of time—for various flow rates. The voltage variation interrogated by the probe electrode is primarily induced by charges in the areas of the fused silica substrate (see supplementary material, Fig. S2) that is in contact with the fluid and <1 nm from the interfaces between the fluid and the acrylic channel walls, because the electric potential arising from charges that are not in those areas is screened by mobile ions in the PBS (the Debye screening effect). The responses are clearly constant over time, indicating continuous contact electrification of the flow and the fused silica substrate. To extract the values of the responses, the time rates of voltage change are fit by constant. The response–flow rate relationship is linear over a range of three orders of magnitude in flow rate, as shown in Fig. 1(c), providing an ideal dynamic range for contactless microfluidic flow characterization. The slope of the linear fitting, 27.6 ± 0.6 μV μL⁻¹, is the flow-sensory sensitivity. The noise level of the measurement is 10.8 μV min⁻¹, leading to a resolution (noise level divided by sensitivity) of 0.39 ± 0.01 μL min⁻¹.

The responses of the probe electrode depend on the distance between the probe electrode and the microfluidic channel systematically, as shown in Fig. 1(d). The association of the response to the distance can be well understood by modeling the charges on the fused silica along the edge of the microfluidic channel as line charge.¹⁹ Under this model, the sensitivity (⁠$s$⁠) for the flow measurement can be written as

where $ε0$ is the vacuum permittivity, $ε$ is the relative permittivity of acrylic (∼3.4), $v$ is the fluid flow rate, $λ$ is the line charge density, $t$ is the time in second, $L$ is the length of the microfluidic channel (16.24 mm). As shown in Fig. 1(d), the magnitude of the sensitivity data is well fit by Eq. (1), with the best fitting parameter $|dλ/dt|=$ 9.39 ± 0.49 fC m⁻¹ s⁻¹, corresponding to a surface charge-density variation rate of 0.023 ± 0.001 nC m⁻² s⁻¹, given the width of the fluidic channel (400 μm). The discrepancy between the data and the fitting curve is associated with the uncertainties in determining the electrode-to-fluid-channel distances, particularly in (1) finding the line from the tip of the electrode vertical to the flow channel and (2) aligning the line so that it passes through the fluid channel given that the acrylic chip is 2.45-mm thick. Since for silica, a variation in surface charge density of 1 mC m⁻² corresponds to a variation of zeta potential of ∼5 mV,²⁰ the surface charge-density variation rate in our experiment (0.023 ± 0.001 nC m⁻² s⁻¹) corresponds to a zeta potential variation rate of ∼0.1 nV s⁻¹, or ∼0.4 μV h⁻¹. This is about an order of magnitude smaller than the zeta potential variation rate of silica at stable ionization state (∼10 μV h⁻¹),²¹ which may be understood by the Debye screening effect as demonstrated in supplementary material, Fig. S3.

We also fabricated devices of different channel widths based on fused-silica substrate. Supplementary material, Fig. S3 indicates that the flow-velocity sensitivity (in μV μL⁻¹) increases when the width of the microfluidic channel decreases. This is the result of two competing effects induced by the decrease in channel width: The increase in flow velocity and the decrease in areal charges on the fused silica substrate.

The flow-electrification scenario for the contactless flow-sensory voltage change suggests that the resolution of the flow measurement (the ratio of standard deviation to sensitivity) can be improved by replacing the bare metal probe electrode with an electrode covered by graphene, a single-atom thickness and flatness material with low electrical noise.^22–25 In addition, coating a metal electrode by graphene that is chemically inert can eliminate the noise of oxidizing reaction of the metal. To test this hypothesis, a graphene-coated probe electrode was prepared via chemical vapor deposition (CVD) using a procedure we have developed.⁸ As shown in Fig. 1(c), the relative response of the graphene-coated probe electrode is linear to the microfluidic flow rate with 35.0 ± 0.9 μV μL⁻¹ sensitivity and 9 μV min⁻¹ noise level (standard deviation), 26.7% and 19.5% improvements, respectively, in comparison with those of the bare metal probe electrode (27.6 ± 0.6 μV μL⁻¹ sensitivity and 10.8 μV min⁻¹ noise level). Note that the reduction in the noise level is intrinsic to graphene and the enhancement in the sensitivity is not graphene intrinsic and contributes a factor in the determination of the resolution (noise level divided by sensitivity). Given the noise level and the sensitivity, the flow-sensory resolution of our approach using the graphene-coated electrode is 0.26 ± 0.01 μL min⁻¹ (in a 1-Hz bandwidth), which is a 36.4% improvement from that of the bare metal probe electrode (0.39 ± 0.01 μL min⁻¹). Such resolution for flow detection is comparable to the state-of-the-art low-level flow measurement technologies,^15–18 while our approach is contactless.

Based on the response–flow rate relationship [Fig. 1(c)] of the contactless microfluidic flow detection, we developed a program to automatically acquire voltage signal from the probe, compute time rate of voltage change (response) by taking numerical time derivative of the induced voltage, smooth the response using a real-time bandwidth-controllable Savitzky–Golay filter, and translate the smoothed response to flow rate via linear interpolation of the response–flow rate data. Figure 2(a) shows the real-time flow rate measured by a probe electrode (∼1 cm distance to the microfluidic channel) in response to a microfluidic flow with stepwise flow waveform switching between 0, 30, 60, and 90 μL min⁻¹ every 10 s. The real-time readout basically follows the set flow rate, with slight discrepancies within ∼1–2 s after the abrupt flow rate transitions, which may arise from the compressibility of the fluidic tubings. For a triangle flow waveform [Fig. 2(b)], the readout well follows the set flow rate with minimal discrepancy: The standard deviation and the Pearson product-moment correlation coefficient are 7.61 μL min⁻¹ and 0.994, respectively, representing excellent performance metrics of the contactless sensing technology in characterizing the microfluidic flow.

Our approach to contactless interrogation of the microfluidic liquid flow rate is based on the measurement of the characteristic electric potential generated by contact electrification between a microfluid flow and fluidic channel walls and is non-perturbative to the measured fluidic systems to any extent. The strategy can be used in an extremely broad range of applications due to the ubiquitous flow-channel contact electrification. The findings provide the promise of developing instrumentation for clogging-free, fouling-free, and non-perturbative flow interrogation that are difficult for conventional contact flow-sensory methods.^1–7 Since the measurement outcome of our approach is associated with the surface charge density of hydrolyzable components in a microfluidic device, the research also provides a pathway to contactless investigation of electrostatic and electrokinetic effects in microfluidic systems.

See the supplementary material for additional information on the image of a fused silica-substrate device used in our experiment, the measurement results of devices based on fused silica and acrylic substrates, the flow rate and flow-velocity sensitivities vs microfluidic channel width, and the summary of previous non-contact (only suitable for bulky water) or pseudo-contactless (relying on a dedicated component attached to fluid tubing) flow sensory methods.

This work was not directly funded. J.P. acknowledges support from Department of Defense (DoD), Air Force Office of Scientific Research (AFOSR) (No. FA9550-20-1-0125).