Interfacial Effects on Droplet Dynamics in Poiseuille Flow

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 forces (linearized with respect to local deviations of interfacial surfactant concentration) and surface viscous forces according to the Boussinesq--Scriven constitutive law. Interfacial diffusion is also included. 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. Modeling of other geometries will also be discussed.