Formation of Labyrinth Patterns in Langmuir Films

available for noncommercial, educational purposes, provided that this copyright statement appears on the reproduced materials and notice is given that the copy-ing is by permission of the author. To disseminate otherwise or to republish re-quires written permission from the author. A Langmuir film is a molecularly thin fluid layer on the surface of a sub-fluid. 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 de-signed 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 experimen-tally observed circle to dog-bone transitions with minimal area loss