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On the accuracy in the determination of diffusivity constants in hydrogels by numerical simulation

Abstract:

The accuracy of the numerical schemes used for discretizing the diffusion equation is of great importance for determining the value of the diffusivity constant that best represents the diffusion of a solvent in a hydrogel. In this paper we compare the values obtained for the diffusivity constant of a solvent in a hydrogel, by using two different methodologies based on finite difference and finite element schemes respectively. These methodologies consider the discretization of the diffusion equation to model the process of penetration of the solvent in the hydrogel, while modeling the volume change of the hydrogel. The specific application of both approaches is performed on cylindrical samples of polyacrylamide hydrogels. Diffusivity constants were determined by fitting the numerical pbkp_redictions with experimental results. Numerical results show that huge differences in the values of diffusivity constant were obtained depending on the numerical method used, requiring, therefore, a thorough review of the methodologies used so far. Additionally, little influence of the uncertainty of parameters in diffusivity law was observed in the estimated diffusivity; specific values of the radius / thickness ratio corresponding to slower swelling process were calculated, and finally the effect of variations in the equilibrium concentration in swelling dynamics was determined.