Hydrodynamics: Meniscus Height in Thin and Wide Cylinders

[mkrems]

If I have some water in a thin (on the order of micrometer or nanometer even) cylinder, a
meniscus will form due to hydrodynamics and surface tension effects. There will be some characteristic height of the meniscus above the surface of the "bulk" water. Let's call this height "h". If I make the cylinder wider, say, to a macroscopic dimension, will this height "h"
remain the same or change? Please offer a reference if possible!

Thanks!

 

[Andy Resnick]

I don't understand your question- a cylinder is not an equilibrium fluid shape, unless there is contact line pinning (and no bouyancy).

In any case, the surface of the fluid is not physically distinct from the bulk- the surface can be endowed with properties that result in discontinuous bulk properties (jump conditions), but the meniscus does not exist at some height off of the bulk.

Can you expand your question a little more?

 

[atyy]

I am now looking at my "macroscopically sized" glass of water. It looks pretty flat - no obvious meniscus.

 

[Andy Resnick]

Oh- I think I understand what the poster is referring to.

The fluid-fluid interface is curved in the vicinity of the contact line due to the balance of the wetting force and bouyancy (Laplace equation). The height of the meniscus, as compared to the fluid height of the reserviour (http://www.ce.utexas.edu/prof/kinnas/319LAB/Book/CH1/PROPS/caprisegif.html) will depend on the radius of the tube because of the mass of fluid that has to be pulled up. But, the small amount of curvature in the immediate vicinity of the contact line is independent of the geometry and will always be present.

http://www.up.ac.za/academic/civil/divisions/geotechnical/pgcourses/sgm782/themes/theme3/objectives3.html

(section 3.1 is of relevance)

 

[Andy Resnick]

Oh- I think I understand what the poster is referring to.

The fluid-fluid interface is curved in the vicinity of the contact line due to the balance of the wetting force and bouyancy (Laplace equation). The height of the meniscus, as compared to the fluid height of the reserviour (http://www.ce.utexas.edu/prof/kinnas/319LAB/Book/CH1/PROPS/caprisegif.html) will depend on the radius of the tube because of the mass of fluid that has to be pulled up. But, the small amount of curvature in the immediate vicinity of the contact line is independent of the geometry and will always be present.

http://www.up.ac.za/academic/civil/divisions/geotechnical/pgcourses/sgm782/themes/theme3/objectives3.html

(section 3.1 is of relevance)

And there is a lower limit to how small the tube can be- Laplace's equation again. It shows that the pressure required to drive fluid into a small void increases as the pore radius decreases. To get water into a nanometer sized tube requires extremely high pressures, or extremely low interfacial energies.

Edit- not sure why there was a pseudo double-post.