Elasto-compliance of harmonically stimulated soft micro-gaps during electro-magneto-kinetic flows

In this article, we develop and solve an analytical model to understand the elasto-hydrodynamic force response of a deformable, soft substrate, under dynamic loading; wherein the microfluidic gap between the substrate and load is subjected to electro-magneto-hydrodynamic interactions. As a simple physical system, we model the coupled fluid-structure-interaction characteristics when a rigid, small cylinder is permitted to impinge harmonically on an infinitely large elastic, soft substrate, and an oscillatory, squeeze flow establishes in the micro-gap formed between the two. We discuss the different observations and mechanics in terms of the governing Dukhin, Hartmann, and electroviscous numbers. The influence of electromagnetic stimuli on the flow, and its implications vis-à-vis the substrate compliance is the focus of the article. We reveal that for pure magnetohydrodynamics of the gap electrolyte, the transverse magnetic field and the induced streaming potential resist outward squeeze flow, thereby generating substantial amplifications in the force response. On the contrary, the effect of electro-magneto-hydrodynamics on the force response was strongly affected by the orientation and intensity of the transverse electric field. Notably, such variations depended significantly on the electrokinetic parameters, oscillation frequency, and substrate stiffness, whose effects were intertwined with the transverse and streaming potential electric fields. Further, possibilities of squeeze flow reversal due to opposing electromagnetic forces is observed, which may again modulate the compliance of the substrate in different mannerisms.