Coupled electromagnetohydrodynamic and heterogeneous reactive solute transport in non-Newtonian third-grade fluid flow through a microchannel

In this work, we investigated the microfluidic solute dispersion in electromagnetohydrodynamics (EMHD) flow of third-grade fluid in parallel plates microchannel. On account of the complex non-linearity of the Navier-Stokes equation, a series solution is introduced for the derivation of an analytical expression for a velocity distribution. For microscale system design, optimizing surface area and mass transfer efficiency is crucial. Skin friction contours aid in this evaluation. Additionally, the time-dependent convection–diffusion equation is analyzed using Aris’s method of moments to formulate the moment equations, which are solved through an implicit finite difference scheme. The mean concentration distribution of the tracers is calculated using the first four central moments expressed in a Hermite polynomial. Moreover, the two-dimensional concentration distribution is represented using contour plots, with the analysis based on Gill’s work on asymptotic expansions. From our investigation, it is apparent that higher values of the third-grade parameters ($\sigma$) improve the non-Newtonian characteristics and result in an obstruction to solute transport in the microchannel. Strong boundary absorption significantly accelerates tracer depletion in the microchannel, leading to an exponential reduction in contaminant retention over time. A higher electric field leads to a strong electroconductive effect to facilitate the mobility and velocity of charged particles that interact intensively with the medium, resulting in increased mixing and improved solute transport. Such a system strongly affects the ion separation process based on both charge and size, so increasing the strength of conduction field separation becomes more efficient. The analysis presents a highly complex understanding of solute dispersion control through a microfluidic system, offering modern application of the mechanism in drug delivery, blood flow, lab-on-a-chip devices, and cell separation.