Issue 17, 2011

Interfacial effects on droplet dynamics in Poiseuille flow

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.

Graphical abstract: Interfacial effects on droplet dynamics in Poiseuille flow

Associated articles

Article information

Article type
Paper
Submitted
27 Jan 2011
Accepted
10 Mar 2011
First published
12 Apr 2011

Soft Matter, 2011,7, 7797-7804

Interfacial effects on droplet dynamics in Poiseuille flow

J. T. Schwalbe, F. R. Phelan, Jr., P. M. Vlahovska and S. D. Hudson, Soft Matter, 2011, 7, 7797 DOI: 10.1039/C1SM05144J

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