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    Vlahovska, Petia M. 2010.


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  • Journal of Fluid Mechanics, Volume 624
  • April 2009, pp. 293-337

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

  • PETIA M. VLAHOVSKA (a1), JERZY BŁAWZDZIEWICZ (a2) and MICHAEL LOEWENBERG (a3)
  • DOI: http://dx.doi.org/10.1017/S0022112008005417
  • Published online: 10 April 2009
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.

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Email address for correspondence: petia.vlahovska@dartmouth.edu
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