Analysis of a model for pH-sensitive hydrogels

A mathematical model comprising conservation of mass, momentum, and ions for a hydrogel subject to alterations of the solution pH is derived, analyzed, validated and presented. Good agreement between model predictions and their experimental counterpart are achieved. To gain a physical insight into the deformation behavior of the pH-sensitive hydrogel, a scaling analysis coupled with a parametric study is carried out for key physical and operational parameters. The results suggest the significance of initial fixed-charge density, solution ionic strength, Poisson ratio and Young modulus in determining swelling degree of the hydrogel. In addition, it is noted that changes in acid dissociation constant and temperature lead to a notable shift in equilibrium swelling curves. Permeability and size of the hydrogel were found to significantly affect the deformation kinetics: A hydrogel with higher permeability and/or smaller size exhibits faster deformation. These findings and the characteristic scales could provide important guidelines in designing systems utilizing pH-sensitive hydrogels.