Control of axial dispersion in polymeric flows: Magnetic effect versus electro-osmotic effect

Since Taylor’s seminal work on the dispersion of soluble matter, the modelling and control of solute dispersion have received considerable attention. This study investigates the solute dispersion in polymer solutions driven by unsteady magnetohydrodynamic (MHD)-oscillatory electro-osmotic flow within a microtube, aiming to reveal the transport mechanisms in complex rheological media through microscale flow. Firstly, based on the Debye–Hückel approximation, analytical solutions for the electric potential and velocity distributions of mixed MHD-electrohydrodynamic flows are rigorously derived. Subsequently, using Sankarasubramanian & Gill’s generalised dispersion model (1970 Proc. R. Soc. Lond. A , vol. 316, pp. 341–350), mathematical models are developed to systematically investigate the temporal evolution of hydrodynamic dispersion. By investigating the synergistic modulation of electrokinetic and magnetic fields, we identify three distinct flow regimes, namely the electric-field-dominant, competitive transition and magnetic-field-limited regimes, and quantitatively define their boundaries and evolution with the oscillatory Reynolds number italic Re Re $\textit{Re}$ and Deborah number upper D e D e $De$ , thus allowing accurate flow regime classification. Moreover, a non-monotonic critical response governing solute dispersion is observed over a wide range of oscillatory Reynolds numbers, which provides a novel control paradigm for microfluidic mixing and separation. Additionally, through a comparative analysis of fractional Maxwell, classical Maxwell and Newtonian fluids, we show that microscopic structural relaxation plays a crucial role in macroscopic solute transport under multi-field coupling. Our findings help to reveal flow mechanisms for precise mass transport control in electromagnetically coupled systems, advancing the development of microfluidic devices and biomedical detection technologies.