An exploration of electroosmotically inspired peristaltic flow of Bingham fluid along a vertical channel with Ohmic heating

Abstract

Transport and deposition of submicron particles in peristaltic flows with non-Newtonian fluids play a crucial role in physiological processes such as targeted drug delivery and biomedical filtration, where controlled particle transport is required. Consideration is given to the particle deposition in buoyancy inspired electroosmotic peristaltic motion inside a vertical channel containing viscoplastic (Bingham) fluid. Transverse magnetic field is assumed to have uniform strength and the resulting Joule heating is retained for heat transfer analysis. The imposition of boundary slip produces non-linearity in the boundary conditions for axial velocity. The governing equations are derived under lubrication approximations and transformed to a wave frame of reference using the Galilean transformations. The governing differential equations are numerically computed utilizing the NDsolve function integrated within Mathematica 12.0. Key parameters influencing the flow dynamics include the slip coefficient, Bingham number, Helmholtz–Smoluchowski velocity, Grashof numbers and magnetic field strength. Interestingly, boundary layers form near the cylinder walls which become thinner when yield stress is considered. Fluid motion decelerates significantly upon increasing fluid’s yield stress. In line with pervious works, the thermophoretic force increases particle distribution towards the cold wall. An intensification in the buoyance force markedly affects the axial flow and temperature field.