CENTRO DE INVESTIGACIONES EN FISICA E INGENIERIA DEL CENTRO DE LA PROVINCIA DE BUENOS AIRES
Unidad Ejecutora - UE
Stability of a liquid ring on a substrate
ALEJANDRO GONZÁLEZ; JAVIER A. DIEZ; LOUR KONDIC
JOURNAL OF FLUID MECHANICS
CAMBRIDGE UNIV PRESS
Lugar: Cambridge; Año: 2013 vol. 718 p. 246 - 246
We study the stability of a viscous incompressible fluid ring on a partially wetting substrate within the framework of long-wave theory. We discuss the conditions under which a static equilibrium of the ring is possible in the presence of contact angle hysteresis. A linear stability analysis (LSA) of this equilibrium solution is carried out by using a slip model to account for the contact line divergence. The LSA provides specific predictions regarding the evolution of unstable modes. In order to describe the evolution of the ring for longer times, a quasi-static approximation of Wentzel-Kramers-Brillouin (WKB) type is implemented. This approach assumes a quasi-static evolution and takes into account the concomitant variation of the instantaneous growth rates of the modes responsiblefor either collapse of the ring into a single central drop or breakup into a number of droplets along the ring periphery. We compare the results of the LSA and WKB with those obtained from non-linear numerical simulations using a complementary disjoining pressure model. We find remarkably good agreement between the predictions of the twomodels regarding the expected number of drops forming during the breakup process.