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The influence of surfactant adsorption on the motion of a fluid sphere in a tube. Part 1. Uniform retardation controlled by sorption kinetics

Published online by Cambridge University Press:  26 April 2006

Zunqing He ,
Zeev Dagan  and
Charles Maldarelli
Zunqing He
Affiliation:
Levich Institute for Physicochemical Hydrodynamics, Department of Chemical Engineering, City College of New York, New York, NY 10031, USA
Zeev Dagan
Affiliation:
Department of Mechanical Engineering, City College of New York, New York, NY 10031, USA
Charles Maldarelli
Affiliation:
Levich Institute for Physicochemical Hydrodynamics, Department of Chemical Engineering, City College of New York, New York, NY 10031, USA
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Abstract

This paper presents a study of the steady, axisymmetric, creeping translation of a fluid sphere in a tube for the case in which surfactant is adsorbed onto the fluid sphere interface. Marangoni stresses caused by the convective redistribution of surfactant are computed perturbatively in the limit of sorption-controlled uniform retardation, and fully converged numerical solutions of the creeping-flow equations including the Marangoni stress are obtained by a collocation technique.

The results indicate that when the fluid sphere moves in a liquid which is at rest at infinity, the Marangoni stress retards the particle velocity. This retardation generally increases with the sphere to tube diameter ratio up to a value of approximately 0.6, whereupon the retardation begins to level off or even become reduced. When the sphere is suspended in a Poiseuille flow, stagnation rings develop on the sphere surface, and the Marangoni stresses that derive from this surface convection pattern can accelerate the fluid particle when the particle velocity is small with respect to the Poiseuille centreline velocity, but in the same direction as that velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 1 - 32
Copyright
© 1991 Cambridge University Press

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