Numerical simulation and stability analysis of solutocapillary effect in ultrathin films
1 Perm National Research Polytechnic University, Lysva branch, 618902, ul. Lenina, 2, Lysva, Permskii krai, Russia
2 Perm State Pedagogical University, ul. Sibirskaya 24, 614990, Perm, Russia
Received: 29 June 2016
Revised: 14 August 2016
Published online: 2 May 2017
Polar fluids, like water or polydimethylsiloxane, are widely used in technical and medical applications. Capillary effects arising from surface tension gradients can be significant in thin liquid films. The present paper is dedicated to investigation of capillary flow due to a surfactant added to a polar liquid under conditions when intermolecular forces and disjoining pressure play an important role. Evolution equations are formulated for a film profile and the surfactant concentration. Stability analysis shows that the Marangoni effect destabilizes the film, and oscillatory modes appear at slow evaporation rates. We find that the film has four stability modes of at slow evaporation: monotonic stable, monotonic unstable, oscillatory stable, and oscillatory unstable, depending on the wave number of disturbances.
© EDP Sciences, Springer-Verlag, 2017