Modeling fluid--structure interactions in shallow microchannels

Rectangular microfluidic conduits with deformable walls are some of the simplest and most extensively studied microfluidic devices, primarily due to their practical design applications in a variety of fields like biology, medical diagnostics (e.g., lab-on-a-chip), nanotechnology, etc. Experimentally, these devices are found to deform into a non-rectangular cross-section due to fluid--structure interactions occurring at the channel walls. These deformations significantly affect the flow profile, which results in a non-linear relationship between the flow rate and the pressure drop, which cannot be explained by a `generalised Poiseuille flow solution'. To this end, we perform a numerical study of these fluid--structure interactions and their effect on the flow rate and the pressure drop occurring in microfluidic conduits with a single deformable wall. The behavior of several shallow conduit systems ($\ell\gg w\gg h$) with rigid base and side walls and a soft top wall (e.g., PDMS) is simulated under laminar flow conditions using the commercial software suite ANSYS. Simulation results are compared against experimental pressure drop--flow rate data from the literature and also newly developed analytical expressions for the wall deformation, the pressure and the normalized flow rate.