Nonlinear Rayleigh–Taylor instability in an accelerated soap film: Nonlinear Rayleigh–Taylor instability in an accelerated soap film - Stewart, Peter S.; Roy, Alasdair T.; Hilgenfeldt, Sascha (Journal of engineering mathematics, 2025)
Rupture and fragmentation of thin liquid films are of great importance in manufacturing, agriculture, disease transmission, and other fields. An individual rupture event typically results from the nonlinear growth of small perturbations excited by the classical Rayleigh–Taylor mechanism and opposed by surface tension on the film interfaces. We study an initially uniform liquid film accelerated in the direction perpendicular to its interfaces, constructing a new reduced description of the flow in the limit of large surface tension consisting of three coupled (nonlinear) partial differential equations. This system is linearly unstable to disturbances of small wavenumber; we derive a simplified asymptotic description to gain analytical understanding of the nonlinear development until rupture. An initial phase of exponential film thinning leads to the accumulation of liquid in a central bulge. At a well-defined time, a localised pinch-off mechanism, driven by a mismatch in the interfacial curvature at the edge of the bulge, results in a self-similar thinning that breaks the film in finite time. Across a wide parameter range, the resultant droplet formed from the central bulge contains a significant fraction of the initial film volume.