Hydrogel menisci: Shape and interaction

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 neighboring 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*=
√ (γρg) that is based on surface tension γ and gravity ρg. Materials with shear modulus larger than G* exhibit a solid-like
response while softer materials are more liquid-like.