Three-Dimensional Multiphase Peristaltic Flow Through a Porous Medium with Compliant Boundary Walls (Contemporary Mathematics, 2024)
In this communication, we focus on the peristaltic propulsion of multiphase fluid flowing in a three-dimensional rectangular channel with compliant walls. The flow is influenced by porosity and magnetic effects, and the formulation is based on lubrication theory. The governing equations for both fluid and particulate phases are derived for continuity and momentum, assuming a long wavelength (λ → ∞) and a creeping flow regime (Re → 0). Exact solutions of the partial differential equations for both solid and liquid velocities are obtained using the eigenfunction expansion method. We analyze the influence of several relevant parameters on the velocities and profiles graphically. It is found that fluid velocity increases with greater damping and mass effects. Conversely, wall tension and wall elastance have an inverse effect on velocity distribution. While wall tension tends to reduce the size of the boluses, wall stiffness tends to enhance the trapping of boluses. Additionally, the size of the trapped bolus increases due to the combined effects of the magnetic field and porosity.
Keywords: multi-phase flow, magnetohydrodynamics, peristaltic flow, porous medium, compliant wall