Capillary Tube Rise: Does Water Reach Max Height & Stop?

[adiphysics]

Does the water approach the maximum height in a capillary tube with 0 velocity?I mean to say that does it go to the maximum height and just stop or perform simple harmonic motion ?Water is in equilibrium but velocity need not be 0 or is it(why?).The expression we derive for h should be for mean position then not for maximum height.

 

[sophiecentaur]

The losses involved would be very high and I should imagine that any oscillation would be highly damped. But I think you are right to assume that the 'restoring force' will be roughly proportional to displacement, which, in principle, produces SHM.
I wonder if there is, in fact, any combination of substances that exhibits this.

 

[Andy Resnick]

Does the water approach the maximum height in a capillary tube with 0 velocity?I mean to say that does it go to the maximum height and just stop or perform simple harmonic motion ?Water is in equilibrium but velocity need not be 0 or is it(why?).The expression we derive for h should be for mean position then not for maximum height.

It's actually an interesting problem:

http://capfluidicslit.mme.pdx.edu/reference/Capillary%20Flow%20and%20Wetting/Capillary%20rise/Zhmud_JCIS2000_DynamicsOfCapillaryRise.pdf

To summarize, the fundamental equation, assuming Poiseuille flow, is

ρ[zz'' + (z')^2] = (2γcosθ)/r - (8ηzz')/r^2 - ρgz,

where ρ, η is the fluid density and viscosity, z the column height, r the radius of the tube, and ' means time derivative. There are two asymptotic solutions; the Lucas-Washburn equation (steady state) and the low viscosity limit (Quere equation).

The Lucas-Washburn equation asymptotes as t→∞ to z(t) = Z(1-exp(-Kt)), where Z is the 'final' height Z = 2γcosθ/ρgr and K is another constant. The Quere equation asymptotes to z(t) = at + bt^2+..., with a = √(2γcosθ/ρr) and b = -g/6.

At equilibrium, perturbations to the height (Z + ε(t)) follow ε'' + g/Z ε = 0 (simple harmonic motion) in the Quere limit, and a more complicated function if the full fundamental equation is used.

 

[adiphysics]

Can water be transferred from high level to low level using a cotton wick ?

 

[Andy Resnick]

Sure- and as an alternate method, gravity works well for that.

 

[sophiecentaur]

But the wick is a 'self priming' syphon, which can be very handy.

 

[adiphysics]

then from low level to high level ? water rises in the wick then it should also fall down due to gravity

 

[sophiecentaur]

of course.
that's what I meant by syphon.
It can rise a short distance and fall as far as you like. Such a syphon is ideal for automatically getting rid of small rain puddles on seats etc.

 

[adiphysics]

are we not increasing the potential energy of water without doing any work ? is it not violation of law of conservation of energy ?

 

[sophiecentaur]

The energy for the process comes as thermal energy.
I suggest that it would be the water molecules with the highest KE that make it to a higher level. KE to PE conversion will reduce average KE (temperature).

 

[adiphysics]

I have never read that.If that is the case then at a large scale,energy can be generated by this method by some innovations.We can use the gravitaional P.E. of water for that.

 

[adiphysics]

I wanted to ask another thing.When water rises in a ct , if a hole is made, then water does not come out.Has it anything to do with this ?

 

[sophiecentaur]

I have never read that.If that is the case then at a large scale,energy can be generated by this method by some innovations.We can use the gravitaional P.E. of water for that.

How could you use this on a large scale? All that happens is that the water cools down in order to increase the PE of a minuscule fraction of its volume. There is not 'something for nothing' here, any more than in any other form of energy transfer. Before suggesting a 'large scale application, it is always worth while putting in some actual numbers of mass lifted and distance lifted.

The only example I have ever come across of wicking plus evaporation being used as a driving mechanism is the 'drinking bird' demonstration. In that case, the majority of energy comes from the evaporation - helped on by the wicking effect (surface tension).

 

[Andy Resnick]

are we not increasing the potential energy of water without doing any work ? is it not violation of law of conservation of energy ?

Hardly- wetting occurs if the water/substrate interfacial energy is lower than the air-substrate interfacial energy. The total energy is lower, and the force balance is between the weight of the water and the (difference) in interfacial energy (Young's equation).

 

[sophiecentaur]

So the temperature should rise? Or is that irrelevant?

 

[Andy Resnick]

So the temperature should rise? Or is that irrelevant?

Are you asking me, or the OP? In general, wetting is not accompanied by a change in temperature, although thermal gradients can change wetting behavior.

 

[adiphysics]

Please look at the picture.I wanted to ask if water from A will go to B then to C and so on..

 

[sophiecentaur]

Are you asking me, or the OP? In general, wetting is not accompanied by a change in temperature, although thermal gradients can change wetting behavior.

Yes, I was asking you, because, if the system is going to a lower PE state then Energy is conserved so is it reasonable to suggest that it would appear as a rise in KE / temperature? This is not what I thought originally but seems to make more sense.
OR is the energy just rearranged in Potential form - Electric to Gravitational, with no change in KE? From what you say, this is probably the right way to see it.

 

[Andy Resnick]

Yes, I was asking you, because, if the system is going to a lower PE state then Energy is conserved so is it reasonable to suggest that it would appear as a rise in KE / temperature? This is not what I thought originally but seems to make more sense.
OR is the energy just rearranged in Potential form - Electric to Gravitational, with no change in KE? From what you say, this is probably the right way to see it.

In the context of capillary rise, the gain in energy caused by raising a volume of fluid is equal to the loss of energy due to wetting. In the absence of gravity, a fluid column will not stop rising- alternatively, a perfectly wetting fluid will spread until the entire substrate is covered (as long as the continuum approximation is valid).

Does that help?

 

[sophiecentaur]

So it's: Work In = Work Out (and not thermal).
Fair enough, thanks.

 

[adiphysics]

in the context of capillary rise, the gain in energy caused by raising a volume of fluid is equal to the loss of energy due to wetting. In the absence of gravity, a fluid column will not stop rising- alternatively, a perfectly wetting fluid will spread until the entire substrate is covered (as long as the continuum approximation is valid).

Does that help?

thank you very much.