Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems

Viscous flows through compliant conduits apply forces at the solid-liquid interface, leading to deformation of the cross-section, which affects the flow rate--pressure drop relation. Conventionally, calculating this relation requires solving the coupled elastohydrodynamic problem of flow and deformation. Instead, we employ reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate--pressure drop relation in deformable channels, using a domain perturbation expansion that only requires the fluid flow solution and the elastic deformation due to the fluid stress distribution in an undeformed channel.