A Lego Block Approach to Flow in Complex Microfluidic Networks

TL;DR

This paper introduces a modular analytical approach using 'Lego Blocks' to model flow in complex microfluidic networks, enabling efficient solutions for intricate geometries and disordered media with minimal computation.

Contribution

The authors develop a novel 'Lego Block' method combining Schwarz-Christoffel maps and segmentation techniques for analytical flow solutions in complex geometries.

Findings

Allows analytical modeling of complex microfluidic networks

Handles multiply connected domains effectively

Applicable to various flow problems modeled by Laplace's equation

Abstract

We present a new way to construct analytical solutions for flow in complex microfluidic channel networks, as well as planar disordered media. Using a combination of Schwarz-Christoffel maps and segmentation techniques inspired by integrated circuit analysis, we build a library of base building blocks which can be reassembled to model complex geometries, in the style of ``Lego Blocks''. Our approach requires minimal numerical computation, and can then generate analytical solutions for any combination of inlet and outlet flow rates. Moreover, our method can tackle multiply connected domains which are usually difficult to model using typical conformal transform approaches. The solutions are developed for microfluidic Hele-Shaw cell devices, but also apply to ideal flow and Darcy flow in complex geometries, or any other flow problem adequately modeled by Laplace's equation. We end by showing how the procedure can be used to model complex disordered media, fractal-like flow geometries, as well as problems of steady advection-diffusion in microfluidic mixers.