Domain Relaxation in Polymer Langmuir Layers

We report on an experimental, theoretical and computational study of a molecularly thin polymer Langmuir layer on the surface of a subfluid. When stretched (by a transient stagnation flow), the monolayer takes the form of a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape relaxes to the minimum energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is thin. We model these experiments by taking previous descriptions of the full hydrodynamics (primarily those of Stone \& McConnell and Lubensky \& Goldstein ), identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem where motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. The problem has a boundary integral formulation which allows us to numerically simulate the tether relaxation; comparison with the experiments allows us to estimate the line tension in the system.