流体在不可渗透壁面上的统计力学
Statistical mechanics of fluids at an impermeable wall
摘要：
研究了流体/力场边界处的表面效应问题。考虑了一个经典的简单流体与局部引入的场模拟固体。对于一个硬核场的情况下，刚性的，指数的，现实的，宏观上光滑的边界进行检查。两种方法来解决这个问题进行了分析。具有一定程度的任意性，它们可以被称为“吸附”与“表面张力“或“团簇膨胀”与“压力张量”。“吸附”方法用于获得γ放射性的幂级数。对于迈耶型展开的Ursell函数的积分包含的因素，取决于粒子/壁相互作用势。在硬墙的情况下，该系列的系数减少到第一时刻的Ursell功能在某些地区。“表面张力“的方法是用来扩展的Kirkwood-Buff公式的伽玛的任意局部化的分割面。“表面张力系数“分为与亨利常数成比例的项（取决于划分表面的位置）和通用的非线性表面系数。它示出的压力张量的切向分量相对于化学势的导数与平均在过渡区域上的近表面数密度一致，这有两个后果。首先，它证明了“张力”和“吸附”方法在它们存在的领域中的完全同一性。其次，给出了近表面维里展开式，它确定了近边界“二维”流体的精确状态方程。过渡区平均压力张量的切向分量起压力的作用，平均数密度起数密度的作用。
英文摘要：
The problem of surface effects at a fluid/force field boundary is investigated. A classical simple fluid with a locally introduced field simulating a solid is considered. For the case of a hard-core field, rigid, exponential, realistic, and macroscopically smooth boundaries are examined. Two approaches to this problem are analyzed. With some degree of arbitrariness, they can be referred to as "adsorption" vs "surface tension" or "cluster expansion" vs "pressure tensor". The "adsorption" approach is used to obtain a series in powers of the activity for gamma. For Mayer-type expansion the integrals of the Ursell functions contain factors which depend on the particle/wall interaction potential. In the case of a hard wall, the coefficients of the series reduce to the first moments of the Ursell functions taken over certain regions. The "surface tension" approach is used to expand the Kirkwood-Buff formula for gamma to the arbitrary localization of the dividing surface. "The surface tension coefficient" breaks up into the term proportional to the Henry constant, depending on the dividing surface position, and universal nonlinear surface coefficient. It is shown that the derivative of the tangential component of the pressure tensor with respect to the chemical potential coincides with the near-surface number density on average over the transition region, that has two consequences. Firstly, it proves complete identity between "tension" and "adsorption" approaches in the domain of their existence. Secondly, it gives the near-surface virial expansion, which determines the exact equation of state of near boundary "two-dimensional" fluid. The tangential component of the pressure tensor averaged over the transition region plays the role of pressure, and the average number density - the role of number density.
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