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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 cut-off 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 dog-bone transitions with minimal area loss.