Numerical analysis of Rayleigh instability in capillary tubes in the presence of soluble surfactants

DIEGO MARTIN CAMPANA; FERNANDO A. SAITA

Mar del Plata, Argentina

Workshop; Pan-American Advanced Studies Institute (PASI) on Interfacial Fluid Dynamics: From Theory to Applications; 2007

<!-- @page { size: 21cm 29.7cm; margin: 2cm } P { margin-bottom: 0.21cm } --> Annular liquids films coating the interior surface of a capillary are unstable to infinitesimal axisymmetric perturbations of wavelength greater than the interfacial perimeter. This phenomenon is very similar to the breakup of liquids jets, a problem that was first analyzed by Lord Rayleigh. While in the breakup of jets the instability forms drops, in a tube it can produce liquid bridges or lenses that close the conduit. This capillary instability has important consequences in several industrial processes, as well as in some aspects of human physiology (oil recovery, lung functioning) In the systems mentioned above the presence of surfactants is very common, they introduce new interfacial properties like surface elasticity —the so-called Marangoni effect. In order to analyze this problem we assume linear sorption kinetics and we solve continuity and Navier-Stokes equations together with the surfactant mass balance in the bulk and interface, simultaneously. The system of nonlinear highly coupled equations was solved using the finite element method and the spine technique in a fully implicit manner. Our numerical results were successfully validated with theoretical models (linear stability analysis) and numerical results of simplified models based on lubrication theory. The technique used here permits us to detect errors in the closures times predicted by the simplified models; they become more important when the elastic effects of surfactants are strong. Our results show that closure times change considerably when surfactants are somewhat soluble.