Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number

Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is central problem in microfluidics. We analyze Newtonian fluid rectangular duct with soft top wall at steady state. The resulting fluid–structure formulated for both vanishing finite inertia. At leading-order small aspect ratio, lubrication approximation implies that pressure only varies streamwise direction. Meanwhile, wall's slenderness makes fluid–solid interface behave like Winkler foundation, displacement fully determined by local pressure. Coupling deformation averaging across cross section leads to one-dimensional reduced model. In case of inertia, effective deformed channel height defined rigorously eliminate spanwise dependence deformation. It shown previously used averaged concept acceptable approximation. From model, friction factor corresponding Poiseuille number are derived. Unlike rigid case, not constant but Compliance can increase up four. model inertia obtained assuming parabolic vertical variation velocity. To satisfy constraints along edges channel, weak tension introduced direction regularize Winkler-foundation-like Matched asymptotic solutions regularized