A finite volume method with interface capacitance insertion on quad-tree meshes for impedance analysis in microfluidic devices

In this work, we introduce an enhanced Finite Volume Method (FVM) designed for the quasi-electrostatic analysis of microfluidic devices in the frequency domain. Addressing the critical need for accurate modeling of double-layer capacitances at electrode-electrolyte interfaces, we propose a novel approach for interface capacitance insertion. This is pivotal for impedance spectroscopy applications in microfluidic devices where such interfaces are present. By leveraging Quad-Tree meshing, our method adeptly manages the substantial geometrical scale variations inherent in microfluidic channels. This integration allows for efficient computation of multi-port impedances, facilitating the comprehensive evaluation of electrical parameters within these devices. Our approach not only bridges the gap left by traditional FVM and commercial software but also provides a robust framework for design space exploration and optimization of microfluidic structures and electrode geometries. The effectiveness of the proposed method is demonstrated through numerical convergence analysis and practical application to a microfluidic channel cross-section for measurement of transepithelial electrical resistance (TEER), showcasing its potential for advancing biomedical device simulations.