Some theoretical investigations on the flow of fluids with special reference to emulsions

Abstract

The principal result of the analysis is that a localized reduction in interfacial tension does lead to an interfacial instability. For small reductions, the interfacial growth is linear in t and proportional to W itself, but when it is large and comparable to ??, the dependence upon ? is much faster. But this type of instability is mild and quite different from the exponential growth of the disturbance when its dynamical tension becomes negative locally. The present calculations, it must be added, have certain limitations. It treats a model of the physical system which is simple enough mathematically and realistic enough physically. But a quantitative agreement with all the practical results is not to be expected. The linearization of the hydrodynamic equations renders the solution valid only for the initial stages of the instability. Factors like the viscosities of the liquids, presence of interfacial films, etc., will modify the quantitative features of the instability. Nevertheless, the basic qualitative conclusions regarding the phenomena arising from a local reduction of interfacial tension remain unaltered.