The swelling and shrinking of spherical thermo-responsive hydrogels

TL;DR

This paper models the swelling and shrinking behavior of spherical thermo-responsive hydrogels using a poro-elastic framework, revealing different dynamic regimes and providing simplified analytical tools for predicting their response to temperature changes.

Contribution

It introduces a poro-elastic model for spherical thermo-responsive hydrogels, characterizes different swelling/shrinking behaviors, and develops an analytical approximation for front dynamics.

Findings

Identification of different swelling/shrinking regimes

Development of an analytical front dynamics model

Efficient prediction of hydrogel response for applications

Abstract

Thermo-responsive hydrogels are a promising material for creating controllable actuators for use in micro-scale devices, since they expand and contract significantly (absorbing or expelling fluid) in response to relatively small temperature changes. Understanding such systems can be difficult because of the spatially- and temporally-varying properties of the gel, and the complex relationships between the fluid dynamics, elastic deformation of the gel and chemical interaction between the polymer and fluid. We address this using a poro-elastic model, considering the dynamics of a thermo-responsive spherical hydrogel after a sudden change in the temperature that should result in substantial swelling or shrinking. We focus on two model examples, with equilibrium parameters extracted from data in the literature. We find a range of qualitatively different behaviours when swelling and shrinking, including cases where swelling and shrinking happen smoothly from the edge, and other situations which result in the formation of an inwards-travelling spherical front that separates a core and shell with markedly different degrees of swelling. We then characterise when each of these scenarios is expected to occur. An approximate analytical form for the front dynamics is developed, with two levels of constant porosity, that well-approximates the numerical solutions. This system can be evolved forward in time, and is simpler to solve than the full numerics, allowing for more efficient predictions to be made, such as when deciding dosing strategies for drug-laden hydrogels.