Liquid in a vertical pipe open at the lower end and closed at the top

[anders_r_r]

Consider a vertical pipe partially filled with liquid. The pipe is open at the lower end and closed at the top. See the attached picture. Will the liquid fall out or not?

In a small diameter pipe a stable meniscus will form due to surface tension and prevent the water from falling out. In a larger diameter pipe the liquid will fall out of the pipe. What is the exact criterion that determines wether or not the water will fall out? Where/how do I find the answer? Can someone point me in the right direction?

/Anders

 

[Dr Lots-o'watts]

I suppose it depends on what liquid. Perhaps its viscosity, but maybe also other properties it may have.

 

[anders_r_r]

Thanks for your input, Dr Lots-o'watts.

I suppose that the answer is closely related to the stability of the meniscus. In a large pipe the surface tension may not be strong enough to create a stable meniscus.

 

[anders_r_r]

After a few days of searching I found the answer :-)

In the large diameter tube long wavelength capillary waves on the interface between the gas and liquid causes the interface to be unstable and the liquid will fall out. This phenomena is called the Rayleigh-Taylor instability.

When the diameter of the tube is sufficiently small, the longest possible wavelength of the capillary waves is not long enough to cause instablity, thus the liquid will stay in the tube.

If the gas is air and the liquid is water, the critical diameter of the tube is 8.5 mm.

The theory is very well explained in the textbook: "Physics of continuous matter" by B. Lautrup.

 

[PJC01]

The exact criterion that determines whether or not the liquid will fall out of the vertical pipe is the balance between the gravitational force pulling the liquid downward and the surface tension force keeping the liquid from falling out. This balance is known as the capillary action.

To find the answer, you can look into the equations for capillary action and the parameters that affect it, such as the surface tension of the liquid, the diameter of the pipe, and the density of the liquid. Additionally, you can also conduct experiments to observe the behavior of liquids in different pipe sizes and conditions.

Some helpful resources for understanding capillary action and its criteria include textbooks on fluid mechanics and surface tension, as well as scientific articles and research papers on the topic. You can also consult with experts in the field of fluid mechanics or conduct further research through online databases or scientific organizations.