Hydrodynamics across a fluctuating interface

Intrinsic Stress Field for Liquid Surfaces

The microscopic stress field inhomogeneity in the interfacial region adjacent to the liquid surface is the fundamental origin of the liquid surface tension, but because of broadening due to capillary fluctuations, a detailed molecular level understanding of the stress field remains elusive. In this work, we deconvolute the capillary fluctuations to reveal the intrinsic stress field and show that the atomic-level contributions to the surface tension are similar in functional form across a variety of monatomic systems. These contributions are confined to an interfacial region approximately 1.5±0.1 times the particle diameter for all systems studied. In addition, the intrinsic density and stress profiles show a strong spatial correlation that should be useful in the development of a statistical mechanical theory for the prediction of surface stress and surface tension.

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

The Intrinsic Fragility of the Liquid-Vapor Interface: A Stress Network Perspective

The evolution of the liquid-vapor interface of a Lennard-Jones fluid is examined with molecular dynamics simulations using the intrinsic sampling method. Results suggest clear damping of the intrinsic profiles with increasing temperature. Investigating the surface stress distribution, we have identified a linear variation of the space-filling nature (fractal dimension) of the stress clusters at the intrinsic surface with increasing surface tension or, equivalently, with decreasing temperature. A percolation analysis of these stress networks indicates that the stress field is more disjointed at higher temperatures. This leads to more fragile (or poorly connected) interfaces which result in a reduction in surface tension.

Local stress tensor calculation by the method-of-plane in microscopic systems with macroscopic flow: A formulation based on the velocity distribution function

In this work, we developed a calculation method of local stress tensor applicable to non-equilibrium molecular dynamics (NEMD) systems, which evaluates the macroscopic momentum advection and the kinetic term of the stress in the framework of the Method-of-Plane (MoP), in a consistent way to guarantee the mass and momentum conservation. From the relation between the macroscopic velocity distribution function and the microscopic molecular passage across a fixed control plane, we derived a method to calculate the basic properties of the macroscopic momentum conservation law including the density, the velocity, the momentum flux, and the two terms of the stress tensor, i.e., the interaction and the kinetic terms, defined on a surface with a finite area. Any component of the streaming velocity can be obtained on a control surface, which enables the separation of the kinetic momentum flux into the advection and stress terms in the framework of MoP, and this enables strict satisfaction of the mass and momentum conservation for an arbitrary closed control volume (CV) set in NEMD systems. We validated the present method through the extraction of the density, velocity, and stress distributions in a quasi-one-dimensional steady-state Couette flow system and in a quasi-2D steady-state NEMD system with a moving contact line. We showed that with the present MoP, in contrast to the volume average method, the conservation law was satisfied even for a CV set around the moving contact line, which was located in a strongly inhomogeneous region.