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I recently realized that if I turned my coffee cup downward, all the liquid spills out easily. This amazement prompted me to wonder about the impacts of surface tension for a situation in which the radius is much smaller than my cup. I might bring it up to my professor soon though she is not covering this topic for another few weeks.

If I have a system that has a capillary tube that has a much smaller diameter than my cup filled with a fluid of constant density and viscosity in which it is static at the moment in which my coffee cannot move in this container, I am wondering if it would have two meniscus at each end, the first at the top to correspond with my pressure of coffee vapor and the bottom to represent contact with the room pressure and if they would be the same shape.

I ran into this diagram online investigating the issue which I thought could be useful.

enter image description here

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  • $\begingroup$ Check out good references like Mechanics of fluids by Massey. $\endgroup$
    – Solar Mike
    Feb 9, 2023 at 11:15
  • $\begingroup$ Please clarify. Is the fluid inside the capillary different from the fluid outside (surrounding) the capillary? Essentially, you have taken the capillary full of one fluid and put it into (immersed it into) a different fluid? $\endgroup$ Feb 11, 2023 at 15:23

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You are very perceptive. It would indeed possess two free surfaces (meniscii). The customary action of gravity on liquids is strongly interfered with when the scale lengths get small i.e., for water inside a glass tube with an inside diameter of less than a quarter inch. This is where capillarity effects must be taken into account.

Where capillarity effects (that is, surface tension forces) are dominant, gravity will not pull the water out the open end of a tube, and air and water cannot squeeze past each other within the tube either. Inside a capillarity-dominant (small) tube like this, water and air ball up into separate blobs along the length of the tube

There is a special dimensionless number which is called a similitude parameter which you can calculate to determine where one set of effects (for example, gravity effects) give way to another set of effects (for example, surface tension). These numbers are very useful in the study of physical systems and have been given names (Mach number, Reynolds number, Nusselt number, Froude number, etc.) and guess what! There is a nondimensional group pertaining to fluid dynamic behavior in tubes which for a given surface tension, tube diameter and fluid density and gravity strength allows you to predict whether or not two meniscii will form in a tube and thereby trap the fluid inside the tube.

But alas, I cannot remember its name (it's been 15 years since I was an active practitioner in the field of microfluidics)- but it does exist!

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