Young equation gravity effect

It is well known that when liquid droplets form on a flat substrate they adopt spherical cap shapes (neglecting gravity effects) with a contact angle 6. This angle depends solely on the interfacial energies as described by the Young s equation ... 

Utilizing the above expression for E in Eq. 9, one can arrive at a more generalized form of the Young equation incorporating gravity effects, as... 

The Laplace equation of capillarity and the Young equation are two principal equations in contact angle measurements. In essence, the shape of a liquid drop is determined by a combination of surface tension and gravity effects. Surface forces tend to make drops spherical, whereas gravity tends to elongate a pendant drop or flatten a sessile drop. The shape of the drop is governed by the Laplace equation of capillarity, as follows ... 

Provided that the droplet is very small the effects of gravity can be neglected and the droplet may be assumed to be spherical with radius r. If so, the Young-Laplace equation becomes... 

Pendant or Sessile Drop Method The surface tension can be easily measured by analyzing the shape of a drop. This is often done by optical means. Assuming that the drop is axially symmetric and in equilibrium (no viscous and inertial effects), the only effective forces are gravity and surface or interfacial forces. In this case, the Young-Laplace equation relates the shape of the droplet to the pressure jump across the interface. Surface tension is, then, measured by fitting the drop shape to the Young-Laplace equation. Either a pendant or a sessile drop can be used for surface tension measurement. The pendant drop approach is often more accurate than the sessile drop approach since it is easier to satisfy the axisymmetric assumption. Similar techniques can be used for measuring surface tension in a bubble. 

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