Galanis Jennifer, Tsori Yoav
Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012304. doi: 10.1103/PhysRevE.88.012304. Epub 2013 Jul 15.
We deduce the mixing-demixing phase diagram for binary liquid mixtures in an electric field for various electrode geometries and arbitrary constitutive relation for the dielectric constant. By focusing on the behavior of the liquid-liquid interface, we produce simple analytic expressions for the dependence of the interface location on experimental parameters. We also show that the phase diagram contains regions where liquid separation cannot occur under any applied field. The analytic expression for the boundary "electrostatic binodal" line reveals that the regions' size and shape depend strongly on the dielectric relation between the liquids. Moreover, we predict the existence of an "electrostatic spinodal" line that identifies conditions where the liquids are in a metastable state. We finally construct the phase diagram for closed systems by mapping solutions onto those of an open system via an effective liquid composition. For closed systems at a fixed temperature and mixture composition, liquid separation occurs in a finite "window" of surface potential (or charge density). Higher potentials or charge densities counterintuitively destroy the interface, leading to liquid mixing. These results give valuable guides for experiments by providing easily testable predictions for how liquids behave in nonuniform electric fields.
我们推导了二元液体混合物在电场中，针对各种电极几何形状以及介电常数的任意本构关系的混合 - 去混合相图。通过关注液 - 液界面的行为，我们得出了界面位置对实验参数依赖性的简单解析表达式。我们还表明，相图包含在任何外加电场下都不会发生液体分离的区域。“静电双节线”边界的解析表达式表明，这些区域的大小和形状强烈依赖于液体之间的介电关系。此外，我们预测存在一条“静电旋节线”，它确定了液体处于亚稳态的条件。我们最终通过有效液体组成将封闭系统的解映射到开放系统的解，构建了封闭系统的相图。对于固定温度和混合物组成的封闭系统，液体分离发生在表面电势（或电荷密度）的有限“窗口”内。更高的电势或电荷密度会违反直觉地破坏界面，导致液体混合。这些结果通过提供关于液体在非均匀电场中行为的易于测试的预测，为实验提供了有价值的指导。
