Abstract
We investigate the linear and weakly nonlinear behaviors of a gel-like elastic interface separating two viscous fluids moving in two dimensions (2D). Induced by fluid suction or injection, a 2D Stokes flow takes place and the interface deforms due to the interplay between viscous and elastic forces. By modeling the elastic boundary as having a curvature-dependent bending rigidity and by employing a perturbative mode-coupling approach, we study the linear stability of the interface and the formation of nonlinear patterned structures. In addition to capturing a number of interesting linear properties, we have identified the emergence of suction-driven, nonlinear polygonal-like patterns presenting either convex or concave edges that can develop peculiar near-cusp fingers.
- Received 12 June 2020
- Accepted 12 October 2020
DOI:https://doi.org/10.1103/PhysRevFluids.5.104005
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