On Using Electric Circuit Models to Analyze Electric Field Distributions in Insulator-Based Electrokinetically Driven Microfluidic Devices.

Predicting the electric field distribution inside microfluidic devices featuring an embedded array of electrical insulating pillars is critical for applications that require the electrokinetic manipulation of particles (e.g., bacteria, exosomes, microalgae, etc.). Regularly, these predictions are obtained from finite element method (FEM)-based software. This approach is costly, time-consuming, and cannot effortlessly reveal the dependency between the electric field distribution and the microchannel design. An alternative approach consists of analytically solving Laplace's equation subject to specific boundary conditions. This path, although precise, is limited by the availability of suitable coordinate systems and can only solve for the simplest case of a single pair of pillars and not for a rectangular array of pillars. Herein, we propose and test the hypothesis that the electric field across a longitudinal path within the microchannel can be estimated from an electric circuit model of the microfluidic device. We demonstrate that this approach allows estimating the electric field for whatever pillar shape and array size. Estimations of the electric field extracted from a commercial FEM-based software were used to validate the model. Moreover, the circuit model effortlessly illustrates the relationships between the electric field and the geometrical parameters that define the microchannel design.