Controlled gel expansion through colloid oscillation

TL;DR

This paper models how colloids oscillate within a gel, causing controlled swelling and free-volume creation, with resonance behaviors influenced by material properties, offering insights into tunable gel expansion.

Contribution

It introduces a model linking colloid oscillation to gel swelling, revealing resonance phenomena and scaling laws, and shows how material parameters can tune the effect.

Findings

Resonance occurs at intermediate frequencies.

Elastic modulus and cross-linking density affect resonance.

Viscosity dampens the oscillation response.

Abstract

We model the behaviour of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local micro-cavity, containing the particle and any free volume created by its motion. This cavity exists only as long as the particle is actuated and, when present, reduces the local density of the material, leading to swelling. We show that the model exhibits rich resonance features, but is overall characterised by clear scaling laws at low and high driving frequencies, and a pronounced resonance at intermediate frequencies. Our model predictions suggest that both the magnitude and position of the resonance can be varied by varying the material's elastic modulus or cross-linking density, whereas the local viscosity primarily has a dampening effect. Our work implies appreciable free-volume generation is possible by dispersing a collection of colloids in the medium, even at the level of a simple superposition approximation.