W. R. Schowalter, C. Chaffey, Howard Brenner
Feb 1, 1968
Journal of colloid and interface science
Abstract A rheological constitutive equation has been derived for a dilute emulsion composed of droplets of a neutrally buoyant, incompressible, Newtonian fluid dispersed in and immiscible with another incompressible Newtonian fluid. Because the extent of departure of the droplets from spherical shape depends upon the shear rate, such an emulsion necessarily manifests non-Newtonian behavior. The constitutive equation was found by utilizing the known solution of the creeping motion equations for the fluid motion in the regions interior and exterior to a single droplet. Boundary conditions for the fluid motion are a homogeneous shear flow at an infinite distance from the drop, and agreement with the interfacial tension boundary condition, correct to first order in the deformation, at the drop surface. Landau and Lifshitz's scheme was employed to establish the macrorheology of a dilute emulsion from this known microrheological behavior. The result is a constitutive equation which exhibits properties, such as normal stresses, associated with fluids possessing a degree of elasticity. Comparison is made with earlier theories of suspension and emulsion viscosity.