Dynamics and rheology of complex interfaces. I

When a concentrated mixture of two immiscible fluid is sheared, a rather complex interface is formed due to the coagulation, rupture, and deformation of droplets. The dynamics and rheological properties of such system is discussed. A semiphenomenological kinetic equation is proposed which describes the time evolution of droplet size and orientation, and also the macroscopic stress in a flow field. The rheological properties are shown to be quite unusual: for example, the steady-state viscosity is independent of the shear rate, while the normal stress difference is nonzero and proportional to the magnitude of the shear rate.