ABSTRACT Eli Ruckenstein CTS-9522710 SUNY Buffalo The stability of foams and concentrated liquid-liquid emulsions is a necessary prerequisite for their utilization in any practical application. Gravity driven drainage of the continuous phase which takes place primarily through an interconnected network of Plateau border channels (formed between adjacent bubbles) plays a pivotal role in determining their stability since there is considerable interplay between drainage and collapse. A systematic study of drainage is therefore important in understanding the instability in these systems. A unified theoretical treatment of drainage is proposed which takes into account the separation of the continuous and dispersed phases. The problem will be treated in two ways: a conventional macroscopic approach in which balances are formulated over bulk differential elements containing a large number of bubbles and a microscopic approach in which the dispersed phase droplets are represented by Voronoi polyhedral and detailed balances are written over each Plateau border channel in the complex network. The latter approach will enable us to clearly identify the effect of the polydispersivity of the dispersed phase on the drainage process. An attempt will be made to relate the results from the two approaches to formulate a corrected macroscopic model which is computationally more tractable. Inspection of the equations suggests that it is possible to determine based on the initial state of concentrated emulsion which phase separates out before a drainage equilibrium, which corresponds to a balance between the Plateau border suction and gravity, is established. It should be emphasized that this equilibrium is not thermodynamic; liquid-liquid concentrated emulsions are, however, expected to remain in this mechanical equilibrium for a long time. An attempt will be made to establish a phase diagram based on the initial state of the system. Simple experiments are proposed to verify the theoretical predicti ons.
