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

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. (C) 2004 Elsevier Ltd. All rights reserved.