Swelling Dynamics of a Gel Undergoing Volume Transition

The swelling dynamics of a gel undergoing the volume transition is studied theoretically for one dimensional case. It is assumed that there is a sharp interface between the swollen region and the unswollen region. The position of the interface and the volume change of the gel is calculated as a function of time by numerical simulation and analytical calculation. It is shown that (i) the characteristic time of the swelling is proportional to L 2 0 ζ/ |σ c | ( L 0 , ζ and σ c being the gel size, the friction constant and the transition stress respectively), which diverges at the equilibrium transition temperature and that (ii) the volume of the gel increases in proportion to \(√t\) until it reaches the final volume.