Hydrogel menisci: Shape, interaction, and instability

TL;DR

This paper investigates the complex shapes and interactions of hydrogel menisci caused by particle indentation, revealing how surface tension, elasticity, and pressure influence stability and particle interactions.

Contribution

It introduces a comprehensive analysis of hydrogel menisci shapes and interactions using a free energy approach, highlighting the role of a characteristic shear modulus in governing behavior.

Findings

Meniscus shapes result from a balance of surface tension, elasticity, and hydrostatic pressure.

A characteristic shear modulus $G^*$ determines the transition between solid-like and liquid-like responses.

The study elucidates the Rayleigh-Taylor instability in soft hydrogels.

Abstract

The interface of a soft hydrogel is easily deformed when it is in contact with particles, droplets or cells. Here we compute the intricate shapes of hydrogel menisci due to the indentation of point particles. The analysis is based on a free energy formulation, by which we also assess the interaction laws between neighbouring particles on hydrogel interfaces, similar to the "Cheerios effect". It is shown how the meniscus formed around the particles results from a competition between surface tension, elasticity and hydrostatic pressure inside the gel. We provide a detailed overview of the various scaling laws, which are governed by a characteristic shear modulus $G^*=\sqrt{\gamma\rho g}$ that is based on surface tension $\gamma$ and gravity $\rho g$. Stiffer materials exhibit a solid-like response while softer materials are more liquid-like. The importance of $G^*$ is further illustrated by examining the Rayleigh-Taylor instability of soft hydrogels.