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The double layer–capillary stability of an annular electrolyte fluid surrounding a dielectric-fluid core in a tube

Published online by Cambridge University Press:  26 April 2006

E. Georgiou ,
D. T. Papageorgiou ,
C. Maldarelli  and
D. S. Rumschitzki
E. Georgiou
Affiliation:
The Levich Institute and Department of Chemical Engineering, City College of CUNY, 140th Street at Convent Avenue, New York, NY 10031, USA
D. T. Papageorgiou
Affiliation:
The Levich Institute and Department of Chemical Engineering, City College of CUNY, 140th Street at Convent Avenue, New York, NY 10031, USA
C. Maldarelli
Affiliation:
The Levich Institute and Department of Chemical Engineering, City College of CUNY, 140th Street at Convent Avenue, New York, NY 10031, USA
D. S. Rumschitzki
Affiliation:
The Levich Institute and Department of Chemical Engineering, City College of CUNY, 140th Street at Convent Avenue, New York, NY 10031, USA
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Abstract

In this paper we examine the linear stability of an annular film surrounding a dielectric-fluid core in a tube in the presence of double layers of charges at the film core and at the film–tube interfaces, when the fluid-fluid interface is of low tension. In the absence of electrostatic forces, the surface tension force arising from the circumferential curvature destabilizes, and that from the axial curvature stabilizes the system. The competition is such that waves larger than the unperturbed interface circumference are unstable and those shorter are stable. For charged layers in the film, two cases are examined: (i) double-layer repulsion where the volume charge density is everywhere of the same sign and (ii) double-layer attraction where the diffusive layers next to the film interfaces are of opposite signs. In the first case, double-layer repulsion and surface tension lowering stabilize the destabilizing action of the circumferential component of the surface tension force, and a window of stability can exist. In the case of double layers of opposite signs, double-layer attraction destabilizes the system, and growth rates larger than those caused by pure capillarity can arise. Finally, for the case of a core bounded by an infinite electrolyte, surface tension lowering stabilizes the destabilizing action of the circumferential component of the surface tension force and destabilizes the longitudinal one, although the magnitudes of these effects may differ. As a result the thread can become unstable to waves shorter than the interface circumference.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 149 - 174
Copyright
© 1991 Cambridge University Press

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