Numerical model of flow in distensible microfluidic network

Abstract

This chapter presents a model for the steady laminar flow of an incompressible fluid through a distensible microfluidic network. First, the laminar flow through a single distensible vessel is modeled. The deformation of the vessel in response to an internal pressure is determined by numerically solving the plane-strain equations, and the resistance of the deformed vessel is found by numerically solving the Navier–Stokes equations over the deformed cross-section. A relation is generated to correlate the fluidic resistance of each vessel to its internal pressure. The microfluidic network is modeled as a resistor network and solved iteratively as the resistance of each vessel is altered in response to internal pressure. This model is shown to compare favorably with experimental results. Furthermore, the model presented is highly simplified as it assumes linear elastic behavior of the polymer, small strains limited to two dimensions, and assumes that the vessels remain straight while deforming.