Magnetoelastic pattern formation in field-responsive fluids

We study the development of interfacial magnetoelastic patterns when an initially circular droplet of a field-activated fluid (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. Elasticity takes effect when the fluids are brought into contact and, due to a chemical reaction, the interface separating them becomes a gel-like elastic layer. By modeling the interface as an elastic membrane having a curvature-dependent bending rigidity, a perturbative mode-coupling theory is employed to investigate the weakly nonlinear dynamics of the system. In this context, we examine how the interface responds to the influence of magnetic, elastic, and yield stress forces. Our findings support the relevance of a curvature weakening effect, in the sense that magnetoelastic fingering structures tend to arise and protrude in regions of lower bending rigidity. We contrast the magnetoelastic patterns with the corresponding usual shapes of magnetic fluid interfaces without bending rigidity, but with surface tension.