Applied Math Seminar Announcement

We investigate the deformation and breakup behavior of liquid droplets in a fluid-fluid multiphase system when the system experiences a mixed flow field. Under the assumptions of Newtonian fluid phases and constant interfacial tension, the deformation and breakup behavior of a droplet in steady linear shear flow and extensional flow have been investigated extensively. In industrial dispersing processes, however, the flow field is a mixture of shear and elongational flow. Moreover, a droplet in such a flow experiences transient rates of strain as it moves through the flow field. In order to understand better the relative efficiency of dispersing processes, we investigate the deformation behavior of a single droplet as it moves along a particle path in a mixed flow field. We consider a rotor-stator apparatus used for the processing of highly viscous systems and take the annular gap flow between two eccentric cylinders as one idealization of such a process flow which produces transient shear rates and relatively small elongation rates. In this numerical investigation, a boundary integral method is used to calculated the droplet deformation where the particle paths and velocity gradients are determined from a FEM-calculated flow field using numerical particle tracking techniques. We discuss the effect of processing parameters, such as geometry and strain rates, and the effect of fluid parameters, such as the viscosity ratio, on drop breakup. We find, for example, that a small change in geometry alone improves the dispersing ability of the eccentric cylinders due to the transient shear rates felt by the drop.

Complementary experiments are performed in flow cells which allow for the imposition of desired flow fields. The droplet is visually recorded by a CCD-camera as it moves in the flow field and its deformation is determined via image analysis. Comparisons are made between experiments and simulations.