94.4k views
1 vote
Show that there is always an excess pressure on the concave side of the meniscus of a liquid. obtain an expression for the excess pressure inside

a liquid drop

User Serge C
by
7.6k points

1 Answer

6 votes

Final answer:

There is always excess pressure on the concave side of the meniscus due to surface tension; for a liquid drop, the excess pressure can be described by the Laplace law, ΔP = 2σ/R, where ΔP is the pressure difference, σ is the surface tension, and R is the radius of the drop.

Step-by-step explanation:

The phenomenon of surface tension describes the property of the surface of a liquid that allows it to resist an external force. It is a result of the cohesive forces among liquid molecules. Surface tension is the reason why the meniscus of a liquid in a container is curved, and it leads to excess pressure on the concave side of the meniscus.

To obtain an expression for the excess pressure inside a liquid drop, we can employ the Young-Laplace equation which relates the pressure difference to the surface tension (σ) and the radii of curvature of the surface. For a spherical liquid drop, which has only one radius of curvature (R), the pressure difference (ΔP) inside the drop compared to outside is given by:

ΔP = 2σ/R

This equation is known as the Laplace law. The factor of 2 comes from the fact that a drop has an inner and outer surface, both contributing to the pressure difference. This internal pressure is higher than the ambient atmospheric pressure, a consequence of surface tension working to minimize the surface area of the drop.

User Dli
by
8.5k points