Influence of gravitational forces and fluid flows on a shape of surfaces of a viscous fluid of capillary size

TL;DR

This paper formulates Navier-Stokes equations in curvilinear coordinates to analyze how gravity and fluid flows influence the shape of capillary-sized viscous fluid surfaces, aiding numerical studies.

Contribution

It introduces a curvilinear coordinate formulation of fluid dynamics equations for capillary surfaces considering gravity and flow effects, enabling detailed shape analysis.

Findings

Provides estimations of gravitational and flow effects on evaporating drops.

Establishes a basis for numerical simulations of fluid surface shapes.

Enhances understanding of capillary surface behavior under external influences.

Abstract

The Navier-Stokes equations and boundary conditions for viscous fluids of capillary size are formulated in curvilinear coordinates associated with a geometry of the fluid-gas interface. As a result, the fluid dynamics of drops and menisci can be described taking into account an influence of gravitational forces and flows on the surface shape. This gives a convenient basis for respective numerical studies. Estimations of the effects are presented for the case of an evaporating sessile drop.