INTERFACIAL EFFECTS ON DROPLET DYNAMICS IN POISEUILLE FLOW
Jonathan T. Schwalbe, Frederick R. Phelan, Jr., and Steven D. Hudson
Interfacial rheology governs many properties of emulsions, and here we report theory that accounts for and measures surface viscous and elastic forces. Stokes flow is assumed in 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 for a spherical drop in plane Poiseuille flow. These results and the corresponding interfacial parameters are separable: e.g., cross-stream migration occurs only if surfactant is present; slip velocity depends on viscosity contrast and dilatational Boussinesq number, but not shear Boussinesq number. The effects of interfacial viscosity are not greatly explored. Here we determine their effects on drop dynamics. We suggest that measurement of these quantities yields a new route to characterize the interfacial viscosities.