Static response of deformable microchannels: A comparative modelling study

TL;DR

This study compares theoretical models and simulations of fluid-structure interactions in deformable microchannels, validating predictions of deformation and flow behavior across different elasticity regimes.

Contribution

It introduces a mathematical framework combining plate theory and lubrication approximation for microchannel deformation analysis, validated against detailed 3D simulations and experiments.

Findings

Good agreement between theory, simulation, and experiments for flow-pressure relations.

Validation of the decoupling of span-wise and flow-wise deformation.

Scaling laws for maximum displacement with pressure and material parameters.

Abstract

We present a comparative modelling study of fluid-structure interactions in microchannels. Through a mathematical analysis based on plate theory and the lubrication approximation for low-Reynolds-number flow, we derive models for the flow rate-pressure drop relation for long shallow microchannels with both thin and thick deformable top walls. These relations are tested against full three-dimensional two-way-coupled fluid-structure interaction simulations. Three types of microchannels, representing different elasticity regimes and having been experimentally characterized previously, are chosen as benchmarks for our theory and simulations. Good agreement is found in most cases for the predicted, simulated and measured flow rate-pressure drop relationships. The numerical simulations performed allow us to also carefully examine the deformation profile of the top wall of the microchannel in any cross section, showing good agreement with the theory. Specifically, the prediction that span-wise displacement in a long shallow microchannel decouples from the flow-wise deformation is confirmed, and the predicted scaling of the maximum displacement with the hydrodynamic pressure and the various material and geometric parameters is validated.