Understanding solute dispersion in EMHD-EOF microchannels: The role of magnetic and electric field interactions

The analysis of solute transport in electromagnetohydrodynamic (EMHD) electroosmotic flow (EOF) is critical for optimizing microfluidic systems in applications such as lab-on-a-chip devices, electrokinetic separation, and biomedical transport processes. Despite extensive research on pressure-driven, electroosmotic, and magneto-electroosmotic flows, the combined effects of pressure gradient, electroosmosis, and EMHD on the dispersion of solutes remain largely unexplored. This study examines solute dispersion within a microchannel with parallel plates, subjected to a fully developed EMHD-EOF, driven by an axial/longitudinal electric field, a transverse electric field (TEF), and a vertical magnetic field (VMF). The governing advection–diffusion formulation is analytically approached using a homogenization procedure, and the results are validated against numerical solutions obtained via the finite difference discretization technique. Key findings indicate that in the absence of a TEF (S=0), the solute dispersivity decreases monotonically with increasing Hartmann number (Ha), whereas a non-monotonic trend emerges when S>0, identifying a critical Hartmann number (Hac). Increasing S enhances solute dispersivity, while increasing the Debye–Hückel parameter (K) confines solute to the channel core, reducing axial dispersion. Additionally, a higher pressure gradient (Ω) leads to increased solute dispersivity, and for Ha>Hac, the opposing Lorentz force causes solute accumulation near the centroid. These findings demonstrate that precise tuning of electric and magnetic fields enables control over solute residence time and dispersion, offering practical strategies for enhanced transport efficiency in microfluidic applications.