Abstract
The instability of an elastic interface separating a ferrofluid and a nonmagnetic fluid subjected to an applied magnetic field perpendicular to the initially undisturbed interface is investigated in the effectively two-dimensional environment of a vertical, rectangular Hele-Shaw cell. By using a third-order mode-coupling perturbative scheme, and considering that the elastic interface has a curvature-dependent bending rigidity, the emergence of elastic ferrofluid peaks is detected at the onset of nonlinearities. In this context, the approximate profile of the interface is obtained. It is also shown that the morphology of the resulting peaks is sensitive to changes in a dimensionless magnetoelastic number (relative measure of magnetic and elastic forces), as well as in a bending rigidity fraction parameter, which expresses variations in the bending rigidity with the local interface curvature.
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