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Small-deformation theory for a surfactant-covered drop in linear flows

Published online by Cambridge University Press:  10 April 2009

PETIA M. VLAHOVSKA ,
JERZY BŁAWZDZIEWICZ  and
MICHAEL LOEWENBERG
PETIA M. VLAHOVSKA*
Affiliation:
Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA
JERZY BŁAWZDZIEWICZ
Affiliation:
Department of Mechanical Engineering, Yale University, New Haven, CT 06520-8284, USA
MICHAEL LOEWENBERG
Affiliation:
Department of Chemical Engineering, Yale University, New Haven, CT 06520-8286, USA
*
†Email address for correspondence: petia.vlahovska@dartmouth.edu
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Abstract

A small-deformation perturbation analysis is developed to study the effect of surfactant on drop dynamics in viscous flows. The surfactant is assumed to be insoluble in the bulk-phase fluids; the viscosity ratio and surfactant elasticity parameters are arbitrary. Under small-deformation conditions, the drop dynamics are described by a system of ordinary differential equations; the governing equations are given explicitly for the case of axisymmetric and two-dimensional imposed flows. Analytical results accurate to third order in the flow-strength parameter (capillary number) are derived (i) for the stationary drop shape and surfactant distribution in simple shear and axisymmetric straining flows, and (ii) for the rheology of a dilute emulsion in shear flow which include a shear-thinning viscosity and non-zero normal stresses. For drops with clean interfaces, the small-deformation theory presented here improves the results of Barthès-Biesel & Acrivos (J. Fluid Mech., vol. 61, 1973, p. 1). Boundary integral simulations are used to test our theory and explore large-deformation conditions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 624 , 10 April 2009 , pp. 293 - 337
Copyright
Copyright © Cambridge University Press 2009

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References

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