Non-Newtonian fluid–structure interaction: Flow of a viscoelastic Oldroyd-B fluid in a deformable channel

We analyze the steady non-Newtonian fluid–structure interaction between flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide theoretical framework for calculating leading-order effect fluid’s viscoelasticity on rate–pressure drop relation deformation channel’s elastic wall. first identify characteristic scales dimensionless parameters governing in slender shallow channels. Applying lubrication approximation employing perturbation expansion powers Deborah number De, derive closed-form expression pressure as function non-uniform shape channel weakly viscoelastic limit up to O(De). Coupling hydrodynamic deformation, interplay compliance fields, well relation. For flow-rate-controlled regime limit, show analytically that both deforming top wall decrease drop. Furthermore, reveal trade-off influence deformation. While increases decreases it.