Savchenko Problem 4.6.16
Physics · mechanics · fluid-mechanics
Problem
With what force are two parallel square plates with side a partially immersed in a liquid attracted to each other if they are not wetted by the liquid? The density of the liquid , the distance between the plates , the surface tension of the liquid .Intuitive explanation
When liquid doesn't wet the plates, it forms a curved meniscus at the edges—curving away from the solid surfaces. This curvature creates a pressure difference across the liquid-air interface (via the Young-Laplace equation), which pulls the liquid inward and creates a net inward force on each plate. The key is recognizing that surface tension acts along the perimeter where the meniscus meets the plates, and this tension has a component perpendicular to the plates that draws them together.
Intuitive explanation
When liquid doesn't wet the plates, it forms a curved meniscus at the edges—curving away from the solid surfaces. This curvature creates a pressure difference across the liquid-air interface (via the Young-Laplace equation), which pulls the liquid inward and creates a net inward force on each plate. The key is recognizing that surface tension acts along the perimeter where the meniscus meets the plates, and this tension has a component perpendicular to the plates that draws them together.