Effects of viscoelastic rheology and dynamic slip-on fluid–structure interaction in a compliant tube under oscillatory flow

This study examines the effects of rheology and dynamic slip-on fluid–structure interaction (FSI) between a thin, slender, deformable tube and an oscillatory flow. The nonlinear coupling between the fluid and the structure leads to flow rectification, which is analyzed as a function of the governing dimensionless parameters. The fluid is modeled using the Oldroyd-B constitutive equation, while the structural response of the tube is described by a reduced Donnell–Mushtari shell theory. Lubrication theory is employed to simplify the governing equations by neglecting convective inertial terms, while retaining arbitrary Womersley and Deborah numbers, as well as a slip Deborah number that accounts for slip relaxation effects. The system dynamics arise from the competition between fluid viscoelasticity and structural elasticity, leading to memory effects that significantly influence the response under oscillatory forcing. A harmonic pressure gradient imposed at the inlet produces a time-dependent pressure response, followed by a gradual relaxation toward equilibrium, indicating the balance between elastic and dissipative mechanisms. The coupled FSI problem is solved numerically using finite differences and a Crank–Nicolson scheme. The resulting pressure–flow phase portraits show that increasing the solvent fraction modifies the phase lag between the pressure gradient and the flow response. Additionally, variations in the Deborah and Womersley numbers govern transitions between viscous, elastic, and inertial regimes. Under purely oscillatory forcing, the system can exhibit flow rectification, highlighting the combined roles of viscoelasticity, structural compliance, and dynamic slip.