Dynamics and "Phase Behavior" of Foams and Concentrated Emulsions

摘要Eli Ruckenstein CTS-9522710纽约州立大学水牛泡沫和浓液乳状液的稳定性是其在任何实际应用中使用的必要前提。重力驱动的连续相排水主要通过高原边界水道(在相邻气泡之间形成)的相互连接的网络进行，在决定其稳定性方面起着关键作用，因为排水和坍塌之间存在相当大的相互作用。因此，系统地研究排水对于理解这些系统中的不稳定性是很重要的。提出了考虑连续相和分散相分离的排水统一理论处理方法。这个问题将以两种方式处理：一种是传统的宏观方法，其中平衡是在包含大量气泡的体差分元素上计算的；另一种是微观方法，其中分散相液滴由Voronoi多面体表示，详细的平衡被写在复杂网络中的每个高原边界通道上。后一种方法将使我们能够清楚地确定分散相的多分散性对排水过程的影响。将尝试将这两种方法的结果联系起来，以制定一个在计算上更容易处理的修正的宏观模型。对方程的检验表明，根据浓乳化液的初始状态，可以确定在建立排水平衡之前分离出哪一相，该平衡对应于高原边界吸力和重力之间的平衡。应该强调的是，这种平衡不是热力学的；然而，液液浓缩乳状液预计将在很长一段时间内保持这种机械平衡。将尝试根据系统的初始状态建立相图。给出了简单的实验来验证理论预测。

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.