Formation of Labyrinth Patterns in Langmuir Films

A Langmuir film is a molecularly thin fluid layer on the surface of a subfluid. When dipole dipole forces are negligible, bounded films relax to energy minimizing circular domains. We investigate numerically the case where dipole dipole interactions are strong enough to deform the domain into highly distorted labyrinth type patterns. Our numerical method is designed to achieve higher accuracy and better stability than previous work and exploits an analytic formulation that removes a singularity in the dipole dipole forces without resorting to a small cutoff parameter. We calculate the relaxation rates for a linearly perturbed circular domain, and we verify them numerically. We are also able to numerically reproduce experimentally observed circle to dogbone transitions with minimal area loss