Rheo-soluto-dynamics of confined Stokes-second-problem type electro-magneto-kinetic flows

This study presents an analytical investigation of electro-magneto-hydrodynamic (EMHD) flow and solute transport in a parallel-plate microchannel filled with a viscoelastic (Jeffrey) fluid. The system mimics a confined Stokes’ second problem, with harmonically oscillating walls and externally applied magnetic and electric fields. The microchannel connects two reservoirs with constant but different concentrations of an electro-neutral solute. The electric potential distribution is obtained by solving the Poisson–Boltzmann equation using Debye–Hückel linearization under the thin electric double layer (EDL) assumption. Using this, we solve the momentum equation incorporating Lorentz forces to obtain the velocity field. The species transport equation is then analyzed using the Chatwin approximation to evaluate the effective dispersion coefficient. Our results reveal that introducing a magnetic field enhances the peak velocity by up to 4.5% and increases the effective dispersion coefficient by nearly 40% for Jeffrey fluids. Additionally, asymmetry in wall zeta potentials, higher Schmidt numbers, and increasing Womersley number significantly improve mass transport rates. These findings provide design insights for microfluidic devices such as lab-on-a-chip systems, drug delivery platforms, and biosensors, where enhanced control over flow and mixing is crucial.