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Abstract The investigation in a previous paper (Oldroyd 1953) of the elastic and viscous properties of a dilute emulsion of one incompressible viscous liquid in another, when subjected to small variable rates of strain, is extended to include the possibility of an interfacial film being present everywhere between the two components, which resists deformation as a result of internal friction or of elasticity. When the film is purely viscous its presence has no effect on the type of elastico-viscous behaviour of the emulsion, although the values of the viscosity, relaxation time and retardation time of the system are altered. When the film is ideally elastic, the viscosity in slow steady flow is the same as that of a suspension of solid particles, and two relaxation times and two retardation times are required to describe the elastico-viscous behaviour of the emulsion completely. When the interfacial film shows more complicated elastic and viscous properties combined, these can be described by means of two operators (expressible in terms of d/dt) taking the place of elastic moduli. A viscosity operator describing the macroscopic elastic and viscous properties of the emulsion is calculated in terms of the elasticity operators of the film in the general case.
J. G. Oldroyd (Tue,) studied this question.