The Elastic and Viscous Properties of Emulsions and Suspensions

A calculation is made of the elastic properties of a dilute emulsion of one incompressible viscous liquid in another, arising from the interfacial tension between the two phases. A linear relation between the stress tensor, the rate-of-strain tensor and their first time derivatives defines the behaviour at small rates of strain; the three constants involved are expressed as functions of the viscosities of the two components, the drop size (assumed small and uniform), the interfacial tension and the concentration. The relaxation time and retardation time for the system vary directly as the drop diameter and inversely as the interfacial tension. The effect of slip at the interfaces, which might be associated with the presence of a film of a third component introduced as a stabilizer, is also calculated. The values of the rheological constants are appreciably altered if the frictional coefficient specifying the degree of slipping is sufficiently small, but the type of elastic behaviour is unchanged. In the case of a suspension of elastic solid particles in a viscous liquid, slip at the solid-liquid interfaces can cause a change in the type of elastic behaviour.