Modeling transient magnetohydrodynamic peristaltic pumping of electroconductive viscoelastic fluids through a deformable curved channel

Abstract

A mathematical model is presented to analyze the unsteady peristaltic flow of magnetized viscoelastic fluids through a deformable curved channel. The study simulates the bio-inspired pumping of electroconductive rheological polymers which possess both electroconductive and viscoelastic properties. The Jeffrey viscoelastic model is utilized which features both relaxation and retardation terms of relevance to real polymers. A magnetic body force is incorporated for the influence of static radial magnetic field. The mass and momentum conservation equations are formulated in an intrinsic coordinate system and transformed with appropriate variables into a nondimensional system between the wave and the laboratory frames, under lubrication (i.e., low Reynolds number and long wavelength) approximations. Kinematic and no-slip boundary conditions are imposed at the channel walls. A magnetic body force is incorporated for the influence of static radial magnetic field in the primary momentum equation. An analytic approach is employed to determine closed-form solutions for stream function, axial pressure gradient, and volumetric flow rate. Spatiotemporal plots for pressure distribution along the channel (passage) length are presented to study the influences of curvature parameter, relaxation-to-retardation time ratio (Jeffrey first viscoelastic parameter) and Hartmann number (magnetic field parameter). The effects of these parameters on radial velocity distributions are also visualized. Cases of trapping and reflux in a curved channel are discussed. Streamline distributions are included to study trapping phenomena and to investigate more closely the impact of curvature, magnetic field, and viscoelastic properties on bolus evolution. The reflux or retrograde motion of the particles is studied by particle advection based on Lagrangian viewpoint. The simulations provide new insight into the mechanisms of pumping of electroconductive non-Newtonian liquids in realistic geometries.