On the viscosity of dilute emulsions

The slow motion of a liquid droplet in a shear flow in the presence of surf actants is studied. The effects of the interfacial viscosity, Gibbs elastic ity, surface diffusion and bulk diffusion of surfactants in both phases are taken into account. The analytical solution of the problem for small Reyno lds and Peclet numbers gives a simple criterion for estimation of the tange ntial mobility of the droplet interface. By applying the standard procedure for averaging of the stress tensor flux at an arbitrary surface of the dil ute emulsion, an analytical formula for the viscosity of emulsions in the p resence of surfactants is derived. The result is a natural generalization o f the well-known formula of Einstein for the viscosity of monodisperse dilu te suspensions and of the expressions derived by Taylor and Oldroyd for the viscosity of monodisperse dilute emulsions taking into account the Marango ni effect, (C) 2001 Academic Press.