A Transient Simulation for Analysis of Volume Transition of pH-Sensitive Hydrogel in Micro-Channel

Abstract

Based on Donnan’s equilibrium, a simple chemo-mechanical model is developed to study the transient swelling behavior of the pH-sensitive hydrogel for design and optimization of smart hydrogel-based BioMEMS device. The model is mathematically composed of several governing equations, including Fick’s law which describes the diffusion process in the buffer solution, the fixed charge density formula associated with pH value of the buffer solution, and mechanical equation which gives the swelling ratio responding to pH. The model also considers several chemical conditions, including Donnan’s equilibrium condition which gives Donnan partitioning ratio relating to the concentrations of ionic species in the interior hydrogel and the external solution, the electroneutrality condition in the interior hydrogel and bathing solution as well. The model is capable of predicting the kinetics process of the smart hydrogel immersed in buffer solution with change in pH. The simulation of the diffusion-swelling behavior of the pH-sensitive hydrogel is presented, and the responsive deformation of the smart hydrogel to the solution pH is discussed in detail.