Electro-magneto-kinetic thermo-fluid-structure-interactions of viscoelastic electrolytes through soft micro-confinements

Abstract

A coupled electro–magneto-hydrodynamic (EMHD) framework for a viscoelastic electrolyte (of Phan–Thien–Tanner (PTT) fluid rheology) flowing through a compliant micro-confinement with linearly elastic walls is developed. The flow is driven by a combination of an imposed pressure gradient, and externally applied electric and magnetic fields. Closed-form perturbation solutions are obtained for the velocity, pressure, wall deformation, and temperature. Fluid–structure interactions (FSI) are examined against four parameters: Debye-Huckel parameter (¯κ), Weissenberg number (Wi), Hartmann number (Ha), and electrical Reynolds number (S). We show that favourable pressure gradients drive wall contractions towards a converging channel, while adverse gradients cause wall expansion to a diverging geometry. Observations also show that ¯κ reduces the pressure requirement through electroosmotic pumping; Wi induces shear-thinning that flattens velocity profiles; Ha has a dual effect – assistive at low Ha, and resistive at higher Ha due to Lorentz drag; and S is consistently assistive, lowering the required pressure drop and enhancing near-wall transport. Thermal behaviour is characterized using three parameters—the Biot number (Bi), Peclet number (Pe), and wall-to-fluid conductivity ratio (k_r): higher Bi improves cooling via wall–environment exchange, larger Pe increases axial thermal advection and raises fluid temperature, and higher k_r facilitates heat removal and limits thermal buildup. Collectively, the insights provide a systematic approach for regulating hydrodynamic resistance and thermal loading in deformable EMHD microsystems, with potential applications in bio-lab-on-chip technologies and microscale thermal management platforms.