Facultad de Minas, Universidad Nacional de Colombia, Medellin, Colombia.
Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain.
J Chem Phys. 2018 Feb 14;148(6):064107. doi: 10.1063/1.5010401.
Density Functional Theory (DFT) is a successful and well-established theory for the study of the structure of simple and complex fluids at equilibrium. The theory has been generalized to dynamical situations when the underlying dynamics is diffusive as in, for example, colloidal systems. However, there is no such a clear foundation for Dynamic DFT (DDFT) for the case of simple fluids in contact with solid walls. In this work, we derive DDFT for simple fluids by including not only the mass density field but also the momentum density field of the fluid. The standard projection operator method based on the Kawasaki-Gunton operator is used for deriving the equations for the average value of these fields. The solid is described as featureless under the assumption that all the internal degrees of freedom of the solid relax much faster than those of the fluid (solid elasticity is irrelevant). The fluid moves according to a set of non-local hydrodynamic equations that include explicitly the forces due to the solid. These forces are of two types, reversible forces emerging from the free energy density functional, and accounting for impenetrability of the solid, and irreversible forces that involve the velocity of both the fluid and the solid. These forces are localized in the vicinity of the solid surface. The resulting hydrodynamic equations should allow one to study dynamical regimes of simple fluids in contact with solid objects in isothermal situations.
密度泛函理论（DFT）是一种成功且成熟的理论，可用于研究简单和复杂流体在平衡状态下的结构。该理论已被推广到扩散主导的动力学情况，例如胶体系统。然而，对于与固体壁接触的简单流体，动态密度泛函理论（DDFT）并没有这样明确的基础。在这项工作中，我们通过包含流体的质量密度场和动量密度场来推导出简单流体的 DDFT。基于 Kawasaki-Gunton 算子的标准投影算子方法用于推导这些场的平均值的方程。假设固体的所有内部自由度比流体的自由度松弛得快得多（固体弹性可以忽略不计），因此将固体描述为无特征的。流体根据一组非局部流体力学方程移动，这些方程明确包含了由于固体而产生的力。这些力有两种类型，一种是源于自由能密度泛函的可逆力，用于说明固体的不可穿透性，另一种是涉及流体和固体速度的不可逆力。这些力集中在固体表面附近。所得的流体力学方程应该允许人们在等温情况下研究与固体物体接触的简单流体的动力学状态。
