A coupled theory of fluid permeation and large deformations for elastomeric materials

By Shawn A. Chester, L. Anand. 2010

401 citations recorded by the source corpus.

Abstract An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model for the free energy based on a Flory–Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical–mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. As representative examples of application of the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained, stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii) consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across elastomeric membranes.

Subfields: Biomedical Engineering, Fluid Flow and Transfer Processes, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/6d6ad69ae643cb1aa790a3229a01f6ffed31dc12

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Zhigang Suo
2. Shengqiang Cai
3. Zishun Liu
4. T. Y. Ng
5. W. Toh
6. Rui Huang
7. Chad M. Landis
8. Xuanhe Zhao

In Fluid Flow and Transfer Processes

1. W. Toh
2. Zishun Liu
3. T. Y. Ng
4. Zhigang Suo
5. Shengqiang Cai

In Materials Chemistry

1. Zhigang Suo
2. Shengqiang Cai
3. W. Toh
4. Zishun Liu
5. Chad M. Landis
6. T. Y. Ng
7. Rui Huang
8. Xuanhe Zhao

Citations in the corpus

• Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels (2011, methodology): “Following previous works (e.g., Hong et al., 2008; Chester and Anand, 2010), this paper combines the thermodynamic theory of Gibbs and the Flory–Huggins statistical-mechanical model.”
• A nonlinear, transient finite element method for coupled solvent diffusion and large deformation of hydrogels (2015, background): “On the other hand, a variety of nonlinear approaches have been proposed for coupling large deformation and transport processes in gels (Dolbow et al., 2004; Hong et al., 2008; Birgersson et al., 2008; Doi, 2009; Chester and Anand, 2010; Duda et al., 2010; Wang and Hong, 2012).”
• Dynamics of swelling and drying in a spherical gel (2015, neutral): “For relatively small volume changes, the dynamics of swelling have been studied using both simple linear models [24–30] and fully nonlinear models [4, 6, 31, 32], but no study has yet combined the fully nonlinear and transient mechanics of swelling with the extreme volume changes that are one of the”
• Advances in Mechanics of Soft Materials: A Review of Large Deformation Behavior of Hydrogels (2015, methodology): “By considering entropy imbalance, Chester and Anand [2011] extended the coupled theory for fluid permeation in elastomeric materials [Chester and Anand, 2010] to account for thermal response in temperature-sensitive hydrogels.”