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

Abstract

In this work, we showed a calculation method of local stress tensor applicable to nonequilibrium MD systems based on the Method of Plane (MoP). 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, the interaction and kinetic terms of the stress tensor 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.We verified the present method through the extraction of the density, velocity and stress distributions in a quasi-1D steady-state Couette flow system and in a quasi-2D steady-state system with a moving contact line. In our method, as opposed to volume average method, the density, mass and momentum fluxes are defined on a surface, which is essential to be consistent with the mass and momentum conservation laws in dynamic systems.

Maximizing friction by liquid flow clogging in confinement

“…Therefore, liquid molecules in Couette flow show a caterpillar-like motion (Fig. 3 c) [ 30 ]. Figure 3 d also shows that large relative velocity only appears in the vicinity of the contact line and on the vapor–liquid interface.…”

Flujo de mezclas agua-metanol en nanotubos de grafeno

“…Otros enfoques para el cálculo de la presión implican su estimación a partir de las tensiones sobre planos generados por las fuerzas sobre los átomos. Al momento de la redacción de este texto estamos evaluando una variación del método de planos para dinámicas fuera de equilibrio (Kusudo et al, 2021). Con el mismo se tiene aviso de la componente de momento lineal del flujo producido por la aplicación de una fuerza al momento de calcular la tensión normal sobre el plano de evaluación.…”

(Invited) Nanoscale Wetting and Its Connection with Macroscopic Young's Equation

“…[4] mentioned above as well, the relative SL interfacial tension 𝛾 − 𝛾 is obtained from Eqs. [13][14][15].…”

“…In this case, 〈𝜕𝐻/𝜕𝜆〉 in Eq. [13] is equal to −Φ (Γ, 0), and can be easily calculated. Note that some care must be taken for system at 𝜆 = 1 because it might result in numerically instability or even singularity depending on the parameter coupling, and a robust approach is to use extrapolation from nearby data points.…”

“…Molecular dynamics (MD) analysis is a powerful tool to investigate and predict wetting from a microscopic point of view, with which various combinations of liquid and solid surface can be tested in silico. We have carried out MD simulations on the liquid behavior especially around the solid surface including static wetting (2)(3)(4)(5)(6)(7)(8)(9)(10)(11), dynamic wetting (12,13), liquid diffusivity (14-16) around the solid, and solid-liquid friction (17)(18)(19)(20)(21)(22)(23), where the fluid-solid pairs ranged from Lennard-Jones fluid to water, methanol, iso-propyl-alcohol and their mixture as fluids and from simple fcc crystal to OH-terminated Silica as the solid surfaces. In this series of studies, we have developed and adopted several methods for the calculation of the solid-related interfacial tensions from mechanical and thermodynamic viewpoints.…”