Channel Formation in Gels
N. G. Cogan, James P. Keener
Source abstract
We derive and give an analysis of a model of gel dynamics based on a two-phase description of the gel, where one phase consists of networked polymer and the second phase is the fluid solvent. It is found that for the gel to maintain an edge in a poor solvent, the function describing the osmotic pressure must be of a particular form. The model is used to study the behavior of a gel forced by a pressure gradient to move between two flat plates. The distribution of the network phase under these conditions is found to be nonuniform and dependent on the pressure gradient. There is a range of pressure gradients for which the network has regions of high and low volume fraction separated by a sharp boundary, indicative of a channel. We provide the bifurcation analysis of how these novel, singularly perturbed, channeled solutions occur.
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