Transient analysis of swelling-induced large deformations in polymer gels (original) (raw)
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When exposed to an external solvent, a dry polymeric network imbibes the solvent and undergoes large deformation. The resulting aggregate is known as a hydrogel. This swelling process is diffusion driven and thus results in differential swelling during transient swelling. When subjected to external geometrical constraints, such as being rigidly fixed or attachment to a compliant substrate, wrinkles have been shown to appear due to mechanical instabilities. In the case of free swelling, there are no external constraints to induce the instabilities accounting for wrinkling patterns. However, during the transient swelling process, the swelling differential between the gel on the exterior and the interior causes compressive stresses and gives rise to mechanical instabilities. It is also observed that the time dependence of the swelling profile causes the wrinkles to evolve with time. In this work, we investigate this interesting phenomenon of transient wrinkle mode evolution using the f...
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Abstract A gel is an aggregate of polymers and solvent molecules. The polymers crosslink into a three-dimensional network by strong chemical bonds and enable the gel to retain its shape after a large deformation. The solvent molecules, however, interact among themselves and with the network by weak physical bonds and enable the gel to be a conduit of mass transport. The time-dependent concurrent process of large deformation and mass transport is studied by developing a finite element method.
SIAM Journal on Applied Mathematics, 2011
We develop a general theory of the swelling kinetics of polymer gels, with the view that a polymer gel is a two-phase fluid. The model we propose is a free boundary problem and can be used to understand both contraction and swelling, including complete dissolving or dehydration of polymeric gels. We show that the equations of motion satisfy a minimum energy dissipation rate principle similar to the Helmholz minimum dissipation rate principle which holds for a Stokes' flow. We also show, using asymptotic analysis and numerical simulation, how the equilibrium swelled state and the swelling rate constant are related to the free energy and rheological properties of the polymer network.
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SIAM Journal on Applied Mathematics, 2008
In this article, we analyze a model of the incipient dynamics of gel swelling, and perform numerical simulations. The governing system consists of balance laws for a mixture of nonlinear elastic solid and solvent yielding effective equations for the gel. We discuss the multiscale nature of the problem and identify physically realistic regimes. The mixing mechanism is based on the Flory-Huggins energy. We consider the case that the dissipation mechanism is the solid-solvent friction force. This leads to a system of weakly dissipative nonlinear hyperbolic equations. After addressing the Cauchy problem, we propose physically realistic boundary conditions describing the motion of the swelling boundary. We study the linearized version of the free boundary problem. Numerical simulations of solutions are presented too.
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Mathematical Modeling of Hydrogels Swelling Based on the Finite Element Method
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In recent years, hydrogels have been introduced as new materials suitable for applications in areas such as biomedical engineering, agriculture, etc. The rate and degree of hydrogel swelling are important parameters that control the diffusion of drugs or solvents inside a polymer network. Therefore, the description of the dynamic swelling process of the hydrogels is very important in applications that require precise control of the absorption of solvents inside the hydrogel structure. To date, most of the numerical models developed for describing the swelling process are based in the finite difference methods. Even though numerical models supported in finite differences can be easily implemented, their use is limited to samples with very simple shapes. In this paper, a new model based on the finite element method is proposed. The diffusion equation is solved in a time-deformable grid. An original procedure is proposed to numerically solve the non-linear algebraic equation system that permits computing a new grid for each time-step. Hydrogel samples of different shapes were prepared in order to conduct experimental tests to validate the numerical proposed model. Numerical results show that the new model is able to describe the mass and shape changes in the hydrogel samples in time. An application of the numerical model to determine the relation between diffusion coefficients and density in Polyacrylamide samples allows verifying the versatility of the model.