Uncovering the Contribution of Microchannel Deformation to Impedance-Based Flow Rate Measurements

Abstract

Changes in electrical impedance have previously been used to measure fluid flow rate in microfluidic channels. Ionic redistribution within the electrical double layer by fluid flow has been considered to be the primary mechanism underlying such impedance based microflow sensors. Here we describe a previously unappreciated contribution of microchannel deformation to such measurements. We found that flow-induced microchannel deformation contributes significantly to the change in electrical impedance of solutions, in particular to those solutions producing an electrical double layer in the order of a few tens of nanometers (i.e., containing relatively high ionic strength). Since the flow velocity at the measurement surface is near zero, due to the laminar nature of the flow, the contribution of the double layer under the conditions mentioned above should be negligible. In contrast, an increase in the fluid flow rate results in an increase in the microchannel cross-sectional area (because of higher local pressure), therefore, producing a decrease in solution resistance between the two electrodes. Our results suggest that microflow sensors based on the concept of elastic deformation could be designed for in situ monitoring and fine control of fluid flow in flexible microfluidics. Finally, we show that purposefully engineering a larger deformability of the microchannel, by changing the geometry and the Young's modulus of the microchannel, enhances the sensitivity of this flow rate measurement.

Static response of deformable microchannels: a comparative modelling study

“…vide a reliable quantitative displacement profile across the microchannel's cross-section. Only a few studies have employed the more accurate confocal microscopy [9,43]. On the other hand, our mathematical models do provide an analytical expression for the crosssectional displacement profile, and we can easily compare this result to our 3D direct numerical simulations.…”

Flow rate–pressure drop relation for deformable shallow microfluidic channels

“…A lubrication model captures the bulk of the transient response observed in experiments (Panda et al 2009), thereby verifying the scaling analysis of Dendukuri et al (2007); Mukherjee et al (2013) extended the one-dimensional lubrication model of Panda et al (2009) to account for electroosmotic flows. It is of interest to account for the effect of fluid-structure interactions in such flows because, for example, flow-wise cross-sectional variations affect electrokinetics and increase electrolyte dispersion (Ghosal 2002;Bahga et al 2012) and can be used to improve the sensitivity of impedance-based flow rate measurements (Niu et al 2017). More recently, Elbaz & Gat (2014 analyzed, using perturbation methods, sev-eral problems of axisymmetric axial viscous flows in soft cylinders, obtaining closed-form leading-order solutions of the transient response of the elastic shell and the corresponding time evolution of the fluid pressure.…”

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

“…PDMS, also known commercially as Sylgard 184, typically has a low tensile modulus [10], and PDMS-based micro-conduits are prone to deformation (bulging) under applied forces. Although early studies considered deformation to be a drawback, because it may restrict the structural viability of a device [11,12], the compliance of PDMS microchannels has been exploited to design microfluidic devices with specific functions, such as pressure-actuated valves [13], passive fuses [14], pressure sensors [15,16], strain sensors [17] and impedance-based flow meters with improved sensitivity [18].…”