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

Petia M. Vlahovska*, Jerzy Bławzdziewicz, Michael Loewenberg

*Corresponding author for this work

Research output: Contribution to journalArticle

49 Scopus citations

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 Barth's-Biesel & Acrivos (J. Fluid Mech., vol. 61, 1973, p. 1). Boundary integral simulations are used to test our theory and explore large-deformation conditions.

Original languageEnglish (US)
Pages (from-to)293-337
Number of pages45
JournalJournal of fluid Mechanics
Volume624
DOIs
StatePublished - May 25 2009

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Small-deformation theory for a surfactant-covered drop in linear flows'. Together they form a unique fingerprint.

  • Cite this