Multiphysics modeling for pressure-thermal sensitive hydrogels

Some smart hydrogels, like poly(N-isopropylacrylamide) (PNIPA) hydrogels, are sensitive to both stimulus hydrostatic pressure and temperature. The model for thermal-sensitive only hydrogels has been well established in the past two decades. In this work, by combining Flory's mean-field theory and Poisson-Nernst-Planck nonlinear equations, we develop a multiphysics model coupling chemo-electro-thermal-mechanical fields which can quantitatively calculate both hydrostatic pressure and thermal sensitivity of hydrogels in an electrolyte bathing solution. Considering PNIPA hydrogels as an example, the proposed model is validated by comparing the numerical results with experimental results reported in the literature. We investigate the influences of initial fixed-charge density, temperature, hydrostatic pressure, and bathing solution concentration on the volume expansion ratio of the hydrogels. Moreover, the concentration of mobile ions and distribution of electric potential within the hydrogel body and bathing solution are quantitatively predicted. The model and results obtained in this paper can be used to better understand the response of smart hydrogels sensitive to both hydrostatic pressure and temperature.