Interfacial effects on droplet dynamics in Poiseuille flow

Jonathan T. Schwalbe*, Frederick R. Phelan, Petia M. Vlahovska, Steven D. Hudson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

Many properties of emulsions arise from interfacial rheology, but a theoretical understanding of the effect of interfacial viscosities on droplet dynamics is lacking. Here we report such a theory, relating to isolated spherical drops in a Poiseuille flow. Stokes flow is assumed in the bulk phases, and a jump in hydrodynamic stress at the interface is balanced by Marangoni and surface viscous forces according to the Boussinesq-Scriven constitutive law. Our model employs a linear equation of state for the surfactant. Our analysis predicts slip, cross-stream migration and droplet-circulation velocities. These results and the corresponding interfacial parameters are separable: e.g., cross-stream migration occurs only if gradients in surfactant concentration are present; slip velocity depends on viscosity contrast and dilatational properties, but not on shear Boussinesq number. This separability allows a new and advantageous means to measure surface viscous and elastic forces directly from the drop interface.

Original languageEnglish (US)
Pages (from-to)7797-7804
Number of pages8
JournalSoft Matter
Volume7
Issue number17
DOIs
StatePublished - Sep 7 2011

ASJC Scopus subject areas

  • Chemistry(all)
  • Condensed Matter Physics

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