Theory of gel electrophoresis in high fields: Evolution of a population of hernias

We consider long polyelectrolytes that are initially at rest in a gel and suddenly submitted to a strong electric field. The evolution of the conformation regime is described up to the final disengagement from the initial tube. Just after the field has been applied, the chain adopts a comb-like conformation with several “hernias”, which evolve in competition with each other. As long as the conformation has many hernias, the distribution of their size follows a self-similar law, first described by Deutsch. The number of hernias decreases, and ultimately the chain disengages from its initial tube. Various predictions for the conformation of the chain in this last stage and for time constants are proposed. In particular, the disengagement times are found to follow a self-similar law in the size of the chains.