Curvature-Mediated Forces on Elastic Inclusions in Fluid Interfaces

Heterogeneous fluid interfaces often include two-dimensional solid domains that mechanically respond to changes in interfacial curvature. While this response is well-characterized for rigid inclusions, the influence of solid-like elasticity remains essentially unexplored. Here, we show that an initially flat, elastic inclusion embedded in a curved, fluid interface will exhibit qualitatively distinct behavior depending on its size and stiffness. Small, stiff inclusions are limited by bending and experience forces directed up gradients of Gaussian curvature, in keeping with prior findings for rigid discoids. By contrast, larger and softer inclusions are driven down gradients of squared Gaussian curvature in order to minimize the elastic penalty for stretching. Our calculations of the force on a solid inclusion are shown to collapse onto a universal curve spanning the bending- and stretching-limited regimes. From these results, we make predictions for the curvature-directed motion of deformable solids embedded within a model interface of variable Gaussian curvature.