Liquid–gas Interface Under
Hydrostatic Pressure
Author(s)
A. Gajewski
Abstract
The surface-tension forces and the pressure force at a gas–liquid interface were
balanced. This was done at a differential control surface under hydrostatic
pressure. As a result, three quadratic and two linear equations were derived
representing the conditions for equilibrium at the interface. These equations have
eight roots describing eleven different equilibrium states. The most important is
the Young-Laplace formula under hydrostatic pressure which is denoted in the
spherical coordinate system. Hence, it is a quadratic equation. The first root of
this equation describes a pendant drop, drop or bubble, while the second one
circumscribes a sessile drop. There are two solutions for the uniform pressure,
where one of them is the Young-Laplace formula. It is concluded that the surface
existence depends on the pressure difference between both bulk phases. A plane
is formed when the surface-tension forces equilibrate themselves. Under uniform
pressure the interface is a sphere and its other shapes need a pressure gradient.
To form a drop or a bubble the pressure difference must be higher than its border
value. A sessile drop exists if the gauge pressure is negative, while a pendant
drop requires a positive value. A comparison with experimental results is done
for the bubble.
Keywords: Young-Laplace equation in spherical coordinates, static equilibrium,
drop, bubble.
1 Introduction
To describe the force balance on the liquid–gas interface, the Young-Laplace
equation is usually applied. The equation must be solved for each point
separately. Hence, it is computationally difficult to balance the surface-tension
Keywords
Young-Laplace equation in spherical coordinates, static equilibrium,
drop, bubble.
Related Book
Other papers in this volume
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