Experimental investigation of the flow rate--pressure drop relation of a viscoelastic Boger fluid in a deformable channel

TL;DR

This study combines experiments and theory to analyze how viscoelastic Boger fluids behave in deformable channels, revealing that both wall compliance and fluid viscoelasticity reduce pressure drop, aiding microfluidic system design.

Contribution

It provides a validated experimental-theoretical framework for weakly viscoelastic Boger fluids in deformable channels, highlighting the effects of wall compliance and fluid viscoelasticity on flow dynamics.

Findings

Wall compliance and viscoelasticity decrease pressure drop.

Theoretical predictions match experimental results for weakly viscoelastic flows.

Rigid channel experiments show similar pressure drops for Boger and Newtonian fluids.

Abstract

We study the steady flow-induced deformation between an incompressible non-Newtonian fluid and a three-dimensional (3D) deformable channel. Specifically, we provide a comprehensive experimental--theoretical framework for such flows of constant-viscosity viscoelastic (i.e., Boger) fluids, which allows us to quantify the influence of the fluid's viscoelasticity on the flow rate--pressure drop ($q-\Delta p$) relation. For a flow-rate-controlled regime and weakly viscoelastic flow, we find excellent agreement between the theoretical prediction and experimental results, specifically providing an experimental demonstration of how both wall compliance and fluid viscoelasticity decrease the pressure drop. To definitively demonstrate the coupled effect of wall compliance and fluid viscoelasticity (change of cross-sectional area and curving of streamlines), we perform experiments in an equivalent rigid channel, showing that both the Boger fluid and a viscosity-matched Newtonian fluid have the same pressure drop. Thus, the experimentally verified theory for the $q-\Delta p$ relation of weakly viscoelastic flows of Boger fluids in compliant channels can now be used for the design of microfluidics and soft hydraulic systems operating with complex fluids.