0

It is known that raises to a certain height based on the parameters of surface tension, the radius of the tube, etc. Given by the formula $$h=\frac{2S\cos \theta}{\rho Rg}$$

When the capillary tube is of insufficient height I'm told the water does not overflow and read other answers which prove this using energy.

But why can't water be pulled by the surface tension on the interface outside of the tube? Resulting in all the liquid emptying out like a siphon.

enter image description here

Linkin
  • 2,093
  • That would set up a perpetual motion machine. – Deep Dec 03 '20 at 13:22
  • Perpetual motion isn't allowed. There is no "free lunch". – Deep Dec 04 '20 at 05:04
  • No perpetual motion is the same as proving it using energy like the other answers. @JustJohan You need to explain why the other answers don't explain your dilemma. – sammy gerbil Dec 04 '20 at 17:00
  • 4
    Does this answer your question? Capillary tube of insufficient length – sammy gerbil Dec 04 '20 at 17:02
  • @sammygerbil Sir that answer says It will not happen due to energy conservation, My question is why surface tension on the outside of the capillary tube is not enough to pull the water out. I never wished to bring in perpetual motion. – Linkin Dec 05 '20 at 01:58
  • @JustJohan Surface tension from the outside of the capillary is pushing the water inside the capillary downwards not pulling it upwards. Just the same as when the water starts to bulge above the top of the tube but has not yet overflowed, as described in the linked answers. This forces the water back down not up inside the tube, stopping the overflow not increasing it. – sammy gerbil Dec 06 '20 at 01:43

1 Answers1

1

We can think of capillary rise in terms of minimization of energy of a system. A fluid rises inside a tube because increasing the contact area between the tube and the fluid, while decreasing the contact area between tube and air, reduces the surface energy of the entire system (here is a nice explanation). But then you may expect that the fluid will continue to rise forever in a tube of infinite length. However, that is not what happens - the fluid rises to a certain height and stops. This is because, while fluid rising in the tube decreases surface energy, the potential energy of the system increases. The total energy therefore first decreases,reaches a minima and then increases (with increase in the height of the water column). The capillary rise stops exactly at the height where the total energy of the system is a minimum.

The same reasoning explains why the fluid would not flow over the outside surface of a shorter tube. While it is true that this would increase the contact area between fluid and tube, it also increases contact area between fluid and air (this factor did not come into play when the fluid was rising inside the tube), which increases the total energy of the system. The fluid therefore stops right at the top of the tube because that is the minimum energy state.

Deep
  • 6,504