Analysis of the Stability of a Stretched Polymer Gel Thread

The stability of a pre-stretched and fixed cylindrical thread of weakly crosslinked polymer gel against varicose perturbations has been analyzed. The influence of capillary forces, gel elasticity, and interactions on the dynamics of the perturbations has been investigated, and a criterion for thread instability has been formulated. A dispersion equation has been derived, and based on this equation, the fastest-growing mode of perturbations has been determined, along with its growth rate as a function of the macroscopic properties of the gel and the thread radius.