(276f) Rupture of Draining Foam Films Due to Random Pressure Fluctuations

A generalized formalism for the rupture of a draining foam film due to imposed random pressure fluctuations, modeled as a Gaussian white noise, is presented in which the flow inside the film is decomposed into a flow due to film drainage and a flow due to imposed perturbation. The evolution of amplitude of perturbation is described by a stochastic differential equation. The rupture time distribution is calculated from the sample paths of perturbation amplitude as the time for this amplitude to equal one half the film thickness and is calculated for different amplitudes of imposed perturbations, film thickness, electrostatic interactions, viscosities and interfacial mobilities. The rupture time distribution is unimodal with a sharp peak at small times and a long tail thus resulting in a large mean rupture time. The probability of film rupture is high for thicker films especially at smaller times as a result of faster growth of perturbations in a thick film due to smaller disjoining pressure gradient. Larger viscosity , surface viscosity and Marangoni number result in slower growth of perturbation of a draining film thus leading to larger rupture time. It is shown that a composite rupture time distribution combining short time simulation results with equilibrium distribution is a good approximation.