Electro-osmotic flow of hydromagnetic dusty viscoelastic fluids in a microchannel propagated by peristalsis

Abstract

A theoretical study is carried out to determine the electric and magnetohydrodynamics of a dusty Jeffrey fluid containing small particles propagating through a wavy asymmetric microchannel. A static transverse magnetic field is applied in the presence of an electric field. Slip effects are considered to examine the flow behavior. The dusty Jeffrey model is taken into account to review its response. The governing flow problem is modelled with the help of ionic Nernst Planck equation, Poisson–Boltzmann equation, and Debye length approximation. It is then transformed into a steady wave frame with the help of coordinate transformation. Using the lubrication approach (“long wavelength and zero's Reynolds number”) the normalized governing equations of fluid and particle-phase that corresponds to the second order coupled partial differential equations represents the contribution of Jeffrey fluid model. The linearized boundary value problem is solved analytically, and exact solutions are presented for axial velocity distribution, wall shear stress and pressure gradient. It is reported from the obtained results that the magnitude of the particle-phase is more as compared to fluid-phase for velocity field and shear stress however it is less for pressure gradient. The findings of the present model are applicable in designing the microfluidics devices for the use of various transport phenomena in micro level where particles as well as fluids are transported together. The present study can be further extended and applicable for three-dimensional profile with appropriate assumptions and modifications.