Koga Kenichiro, Indekeu Joseph O
Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan.
Institute for Theoretical Physics, KU Leuven, BE-3001 Leuven, Belgium.
J Chem Phys. 2019 Apr 28;150(16):164701. doi: 10.1063/1.5091599.
A mean-field density-functional model for three-phase equilibria in fluids (or other soft condensed matter) with two spatially varying densities is analyzed analytically and numerically. The interfacial tension between any two out of three thermodynamically coexisting phases is found to be captured by a surprisingly simple analytic expression that has a geometric interpretation in the space of the two densities. The analytic expression is based on arguments involving symmetries and invariances. It is supported by numerical computations of high precision, and it agrees with earlier conjectures obtained for special cases in the same model. An application is presented to three-phase equilibria in the vicinity of a tricritical point. Using the interfacial tension expression and employing the field variables compatible with tricritical point scaling, the expected mean-field critical exponent is derived for the vanishing of the critical interfacial tension as a function of the deviation of the noncritical interfacial tension from its limiting value, upon approach to a critical endpoint in the phase diagram. The analytic results are again confirmed by numerical computations of high precision.
对具有两个空间变化密度的流体（或其他软凝聚态物质）中的三相平衡的平均场密度泛函模型进行了分析和数值研究。发现三个热力学共存相中的任意两相之间的界面张力可以由一个惊人简单的解析表达式来描述，该表达式在两个密度的空间中具有几何解释。该解析表达式基于涉及对称性和不变性的论证。它得到了高精度数值计算的支持，并且与同一模型中特殊情况的早期猜想一致。给出了在三临界点附近三相平衡的一个应用。利用界面张力表达式并采用与三临界点标度兼容的场变量，推导了在接近相图中的临界端点时，作为非临界界面张力与其极限值偏差的函数，临界界面张力消失时预期的平均场临界指数。解析结果再次得到高精度数值计算的证实。
