Lin Chang-You, Widom Michael, Sekerka Robert F
Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012117. doi: 10.1103/PhysRevE.88.012117. Epub 2013 Jul 15.
We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [Phys. Rev. E 85, 011120 (2012)], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear functions that vanish at edges and vertices of the small triangle, yielding potentials in the form of quartic polynomials. We find that a subset of such potentials has simple analytic far-field solutions and is a linear transformation of our original potential. By scaling, we can relate their solutions to those of our original potential. For special cases, the lengths of the sides of the small triangle are proportional to the corresponding interfacial tensions. For the case of equal interfacial tensions, we calculate a line tension that is proportional to the area of the small triangle.
我们研究了三相接触线平均场密度泛函理论的广义势。与我们之前文章[《物理评论E》85, 011120 (2012)]中引入的对称势相比，这些势的三个极小值形成一个位于吉布斯三角形内任意位置的小三角形，这对于三元流体系统更现实。我们将在小三角形的边和顶点处消失的线性函数相乘，得到四次多项式形式的势。我们发现这类势的一个子集具有简单的解析远场解，并且是我们原始势的线性变换。通过缩放，我们可以将它们的解与原始势的解联系起来。对于特殊情况，小三角形边的长度与相应的界面张力成正比。对于界面张力相等的情况，我们计算出与小三角形面积成正比的线张力。
