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Issue 17, 2011
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Interfacial effects on droplet dynamics in Poiseuille flow

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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

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Publication details

The article was received on 27 Jan 2011, accepted on 10 Mar 2011 and first published on 12 Apr 2011


Article type: Paper
DOI: 10.1039/C1SM05144J
Citation: Soft Matter, 2011,7, 7797-7804
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    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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