capillary action

khuysent

1. The problem statement, all variables and given/known data

(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)

2. Relevant 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)

3. 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

Attached Thumbnails

 

berkeman

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.

khuysent

ok, that's fine, I didn't really now where to put it

khuysent

anyone to help, please?