Softening of edges of solids by surface tension

TL;DR

This paper investigates how surface tension causes soft solid edges to soften and round, especially at sharp corners, by analyzing a neo-Hookean elastic model under different angle conditions.

Contribution

It provides a theoretical analysis of edge softening in soft solids due to surface tension, including explicit calculations for different initial edge angles.

Findings

Edges become rounded due to surface tension effects.

Discontinuity in curvature appears at the softened edges.

Analysis covers both shallow and very sharp initial angles.

Abstract

Surface tension tends to minimize the area of interfaces between pieces of matter in different thermodynamic phases, be they in the solid or the liquid state. This can be relevant for the macroscopic shape of very soft solids, and lead to a roughening of initially sharp edges. We calculate this effect for a neo-Hookean elastic solid, with assumptions corresponding to actual experiments, namely the case where an initially sharp edge is rounded by the effect of surface tension felt when the fluid surrounding the soft solid (and so surface tension) is changed at the solid/liquid boundary. We consider two opposite limits where the analysis can be carried to the end, the one of a shallow angle and the one of a very sharp angle. Both cases yield a discontinuity of curvature in the state with surface tension although the initial state had a discontinuous slope.