Multiphysics modeling of responsive characteristics of ionic-strength-sensitive hydrogel

A multiphysics model is developed in this paper for simulation of the volume transition mechanism of the smart hydrogel in response to the changes in the ionic strength of bathing solution as an important measure of the ionic concentration of that solution, which is termed the multi-effect-coupling ionic-strength-stimulus (MECis) model. In the present works, the ionic strength is treated as a main stimulus and incorporated into both the ionic convection-diffusion system in the Nernst-Planck flux and the fixed charge density equation characterized by Langmuir isotherm theory. Due to the diffusion and convection, the osmotic pressure is produced by the difference in the ionic concentration between the interior hydrogel and exterior solution, which drives the swelling of the smart hydrogel. The deformation of the ionic-strength-sensitive hydrogel is described by the momentum conservation law, in which the osmotic pressure is a main driving source. Apart from osmotic pressure, however, the repulsive force between the fixed charges is also considered in the mechanical equilibrium equation as another driving source for the swelling of the hydrogel. The simulation is conducted for one-dimensional steady-state problem, and then compared with the experimental data and other theories from open literature. The comparisons demonstrate that the MECis model can simulate well the swelling behavior of the ionic-strength-sensitive hydrogel qualitatively and quantitatively. Probably it is able to predict the responsive characteristics of the bathing solution including the distribution of diffusive ionic concentrations and electrical potential.