A theory of constrained swelling of a pH-sensitive hydrogel

Citations Over TimeTop 10% of 2010 papers

Abstract

Many engineering devices and natural phenomena involve gels that swell under the constraint of hard materials. The constraint causes a field of stress in a gel, and often makes the swelling inhomogeneous even when the gel reaches a state of equilibrium. This paper develops a theory of constrained swelling of a pH-sensitive hydrogel, a network of polymers bearing acidic groups, in equilibrium with an aqueous solution and mechanical forces. The condition of equilibrium is expressed as a variational statement of the inhomogeneous field. A free-energy function accounts for the stretching of the network, mixing of the network with the solution, and dissociation of the acidic groups. Within a Legendre transformation, the condition of equilibrium for the pH-sensitive hydrogel is equivalent to that for a hyperelastic solid. The theory is first used to compare several cases of homogenous swelling: a free gel, a gel attached to a rigid substrate, and a gel confined in three directions. To analyze inhomogeneous swelling, we implement a finite element method in the commercial software ABAQUS, and illustrate the method with a layer of the gel coated on a spherical rigid particle, and a pH-sensitive valve in microfluidics.

Related Papers

• → A review on the nonlinear dynamics of hyperelastic structures(2022)111 cited
• → A study on hyperelastic models for micromorphic solids(2023)3 cited
• → Blow-up issues for the hyperelastic rod equation(2022)2 cited
• → Hyperelastic Model Selection of Tissue Mimicking Phantom Undergoing Large Deformation and Finite Element Modeling for Elastic and Hyperelastic Material Properties(2011)2 cited
• Orthotropic-hyperelastic Material Model and Numerical Simulation of Biological Parenchyma(2011)