We study the steady-flow-induced deformation between an incompressible non-Newtonian fluid and a three-dimensional 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 ($q$–$\mathrm{\Delta }p$) 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 effects 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 $q$–$\mathrm{\Delta }p$ 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.

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• Elastic deformation
• Flow-structure interactions
• Low Reynolds number flows
• Microfluidics
• Biological materials
• Complex fluids
• Microfluidic devices
• Non-Newtonian fluids