Assessment of the free shear boundary condition in a capillary meniscus via molecular dynamics

Abstract

Computational fluid dynamics models often employ the free shear boundary condition at free surfaces, a result from the continuity of the stress and the large viscosity contrast at liquid–gas interfaces. This study leverages nonequilibrium molecular dynamics simulations to investigate the validity of the free shear boundary condition on the exposed surface of a liquid meniscus at the nanoscale. The primary objective is elucidating the fundamental mechanisms and behavior of fluid interactions within a capillary meniscus formed between two carbon nanotubes (CNTs) in shear-driven flow. Shear-driven flow simulations were conducted by varying the velocity of a solid slab to induce different shear rates in the adjacent water molecules. The results demonstrate, for the first time, negligible shear at the free surface, supporting the free shear assumption from the nanoscale point of view. A force balance analysis reveals that capillary and surface tension forces dominate within the meniscus, dictating its shape and stability. Meniscus deformation was observed and primarily attributed to interatomic interactions between water molecules and CNTs, driven by a combination of short-range repulsive forces and van der Waals attractions. The minimal contribution from shear forces suggests that interatomic forces, rather than applied shear stress, are the primary drivers of the meniscus deformation. These findings offer valuable insights into fluid behavior and a sound fundamental analysis of the free shear boundary condition at the nanoscale.