Microstructural evolution during complex laminar flow of liquid-liquid dispersions

This paper presents a general framework for modeling microstructural evolution in liquid-liquid dispersions undergoing complex mixing flows. The method is implemented using the theory of Wetzel and Tucker [J. Fluid Mech. 426 (2001) 199] for dilute dispersions with zero interfacial tension. The local microstructure is represented by a second-order tensor that describes droplet shape and orientation, and the global scheme treats this tensor as a spatial field variable. A coupled finite element solution for the global flow and microstructural field is developed. Sample solutions for an eccentric cylinder mixer reveal the effect of viscosity ratio and flow history on microstructural evolution. For the calculations presented, the coupling between microstructure and rheology has only a small effect on the global velocity and microstructural fields. Some numerical difficulties associated with high strains and specific flows are discussed.