Calculation of the effect of inertia on the dynamic viscosity of dilute emulsions in a pure straining motion

The dynamic viscosity of a dilute emulsion is calculated for a pure straining motion. The emulsion consists of almost spherical drops of a Newtonian fluid immersed in another Newtonian fluid. The oscillating velocity field of the flow is derived from the Navier-Stokes equation, in which the linear inertia term is included, whereas the non-linear one is neglected. The dynamic viscosity is determined with the aid of a cell model. The results are calculated numerically and typical results are presented graphically. The influence of inertia on the dynamic viscosity appears to be appreciable. Special cases presented in the literature, frequency or density zero and rigid spheres, are confirmed.