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Stability of a liquid ring on a substrate

Published online by Cambridge University Press:  08 February 2013

Alejandro G. González ,
Javier A. Diez  and
Lou Kondic
Alejandro G. González*
Affiliation:
Instituto de Física Arroyo Seco, Universidad Nacional del Centro, de la Provincia de Buenos Aires, Pinto 399, 7000, Tandil, Argentina
Javier A. Diez
Affiliation:
Instituto de Física Arroyo Seco, Universidad Nacional del Centro, de la Provincia de Buenos Aires, Pinto 399, 7000, Tandil, Argentina
Lou Kondic
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
*
†Email address for correspondence: [email protected]
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Abstract

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 is implemented. This approach assumes a quasi-static evolution and takes into account the concomitant variation of the instantaneous growth rates of the modes responsible for 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 the quasi-static model approach with those obtained from nonlinear numerical simulations using a complementary disjoining pressure model. We find remarkably good agreement between the predictions of the two models regarding the expected number of drops forming during the breakup process.

JFM classification

Drops and Bubbles: Breakup/coalescence Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 246 - 279
Copyright
©2013 Cambridge University Press

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