Capillary Action: Physically Possible Forms

In summary, the question is asking which of the three cases of a simple, straight capillary with perfect wetting are physically possible. The height of the fluid in case c is higher than in the other cases, so it is possible.
  • #1
khuysent
3
0

Homework Statement



(see figure) Three forms of capillaries are given, and the question is simple : which of these are physically possible?

There are no data given (such as densities or dimensions of the capillaries), so it is just the form that is of importance here. The three cases stand on their own, so the fact that the height of the fluid in case c is higher than in the other cases is irrelevant. The fluid has a contact angle of 0 (perfect wetting)

Homework Equations



*The equation for the height of the fluid in a simple, straight capillary with perfect wetting (contact angle = 0) :
h = (2.sigma) / ( (Rhl - Rha) . g . Rcap)

sigma = surface tension
Rhl = density of liquid
Rha = density of air
g = 9.81 N/kg
Rcap = radius of capillary

*The Young-Laplace equiation
Pi - Po = sigma (1/R1 + 1/R2)

Pi = pressure inside
Po = pressure outside
sigma = surface tension
R1 and R2 are the principal radii of curvature at the interface
(see also wikipedia : young-laplace equation)

The Attempt at a Solution



Case a : is possible, I think. One can imagine a fluid for which the height in a capillary with the thickest radius would be higher than the point where the radius gets smaller. In this case, the fluid would keep rising in the smaller radius (because smaller radius means higher fluid) with the result as given in the figure.
I think the height in this case would be
h = (2.sigma) / ( (Rhl - Rha) . g . Rcap) with Rcap the smallest of the two radii, because the pressure at a point in the fluid is (Rhl - Rha) . g . h with h the distance to the surface, and the pressure difference given by young-laplace is (2.sigma) / Rcap

Case b and c : I'm not sure about these ones, I would say they are possible too, with the same explanation as above, but then I don't really get the point of the question, if they are all possible. Or am I missing something? I was thinking about a situation where laplace-young would predict the pressure to rise when you go up the capillary, which would be impossible?

Can someone please help with this one? I am thinking about it for quite some time now...

Thanks,

Kristof
 

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  • #2
Do not multiple-post questions across forums. I'm leaving this post here in Advanced Physics for now, and I deleted the duplicate post in Intro Physics.
 
  • #3
ok, that's fine, I didn't really now where to put it
 
  • #4
anyone to help, please?
 

1. What is capillary action?

Capillary action is a phenomenon where liquids are able to move against the force of gravity in narrow spaces or tubes. This is due to the combined forces of adhesion, which is the attraction between the liquid and the surface of the tube, and cohesion, which is the attraction between the molecules of the liquid itself.

2. What are some examples of capillary action?

Some common examples of capillary action include water rising up through the roots and stems of plants, ink being drawn up into a fountain pen, and liquid being soaked up by a paper towel or sponge. It can also be observed in a thin glass tube placed in a cup of water, where the water level inside the tube will be higher than the water level outside the tube.

3. How does the shape of the capillary tube affect the rate of capillary action?

The rate of capillary action is affected by the diameter of the capillary tube. A narrower tube will have a faster rate of capillary action, as the surface tension of the liquid increases with decreasing diameter. This means that a smaller amount of liquid is needed to overcome the force of gravity and rise up the tube.

4. Can any liquid exhibit capillary action?

Yes, any liquid can exhibit capillary action as long as it has cohesive and adhesive forces. However, the degree of capillary action may vary depending on the surface tension and viscosity of the liquid.

5. How does temperature affect capillary action?

Temperature can affect capillary action in two ways. Firstly, as temperature increases, the surface tension of the liquid decreases, resulting in a slower rate of capillary action. Secondly, as temperature increases, the viscosity of the liquid decreases, allowing it to flow more easily and thus increasing the rate of capillary action.

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