Kinetics of swelling and shrinking of gels

TLDR

The kinetics of swelling and shrinking of gels is theoretically generalized and experimentally studied. The study formulates a new relation, alongside Tanaka and Fillmore’s differential equation, to solve the kinetics of gels of arbitrary shape. The authors use the new theory to derive explicit solutions for long cylinder and large disk gels. The solutions predict that long cylinder and large disk gels have effective diffusion constants 1.5 and 3 times smaller than a spherical gel, relaxation times 2.0 and 5.7 times longer, identical kinetics along the z and radial axes, and these predictions are experimentally confirmed.

Abstract

The kinetics of swelling and shrinking of gels is theoretically generalized and experimentally studied. A new relation, in addition to the differential equation developed by Tanaka and Fillmore, is formulated to solve the kinetics of gels having arbitrary shape. Using our new theory, we provide explicit solutions for long cylinder and large disk gels. These solutions predict that the effective diffusion constants of long cylinder and large disk gels are 1.5 and 3 times smaller than that of a spherical gel. The relaxation times of long cylinder and large disk gels with small shear modulus μ are approximately 2.0 and 5.7 times longer than that of a sphere, where the diameters of the cylinder and the sphere and the thickness of the disk are the same. The theory also concludes that the experimentally measured kinetics of a long cylinder and disk gels along the z axis and the radial axis are the same. The results have been excellently confirmed by the experiments.