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.
Date of this Version
Erk, Kendra; Schwalbe, Jonathan T.; Phelan, Frederick R. Jr.; Vlahovska, Petia M.; and Hudson, Steven D., "Interfacial effects on droplet dynamics in poiseuille flow" (2011). School of Materials Engineering Faculty Publications. Paper 2.