A 2-D model of Rayleigh instability in capillary tubes––surfactant effects

Abstract

The Rayleigh instability of stagnant liquid films lining the interior of capillary tubes is analyzed with the aid of a 2-D free surface flow model; this axisymmetric model is previously validated using already published theoretical and experimental results. The Galerkin-finite element method is used to transform the complete set of governing equations and boundary conditions into a discrete set, which is then simultaneously solved at each time step by Newton's method. Predictions of well known simplified models represented by nonlinear evolution equations derived on the one-dimensional flow assumption are compared with those obtained from the present one. The comparisons are made for pure liquids and also for liquids contaminated with insoluble surfactants; they show that the simpler models represent the free surface evolution reasonable well. However, the 1-D models generally underestimate the time needed to complete the unstable process that ends––if the film is thick enough––when the inner gas phase becomes disconnected due to the formation of liquid lenses regularly spaced; these discrepancies become larger when surface active agents are present. Surfactant effects and the wealth of information produced by the 2-D model are both evidenced through sample results presented at the end of the paper.