Dispersion of solute under electro-magneto-hydrodynamically assisted flow through tube with spatially varying magnetic field

The present study investigates solute concentration distribution of passive solute particles in an electro-magneto-hydrodynamically (EMHD) assisted flow of a Newtonian fluid. The flow is driven by pressure gradient, axial and radial electric fields, and spatially varying magnetic fields. Unlike conventional studies that assume low zeta potential ζ≤1 and uniform magnetic fields, the present work considers high zeta potential ζ>1, that realistically represent biomedical applications, together with a non-uniform magnetic field. Mei's multiscale homogenization technique is employed, and analytical approximate solution up to third-order of the advection–diffusion equation with first-order bulk reaction and convective damping effects due to inter-particle collisions are obtained. Comparative analysis with numerical solutions and stochastic Brownian dynamics simulations shows good agreement. Velocity results indicate that in the absence of the transverse electric field (S=0), flow exhibits significant velocity suppression accompanied by a pronounced dip phenomenon across the tube radius. The lateral electric forcing dominates over the constant viscous Lorentz force up to a critical Hartmann number Ha∗, beyond which the net volumetric flow rate decreases. The threshold of Ha∗ shifts with the magnetic non-uniformity parameter (A), yielding a Ha∗−S spectrum. Solute distribution under a uniform magnetic field dominates axial spreading and produces a downstream tail, whereas a non-uniform magnetic field suppresses the tail and promotes a near-Gaussian longitudinal profile with enhanced peak concentration. Parametric effects on dispersion coefficient, skewness, and kurtosis are also quantified. A high-dimensional regression model of dispersion coefficient demonstrates satisfactory results. Overall, it provides a framework for solute dispersion in EMHD-based systems.