Will water of uniform temperature with perfect insulation stratify?

[Ken Fabian]

In another thread I made this comment -

I don't expect water of uniform temperature with perfect insulation to stratify - but am not so sure of that to claim it cannot. But I do expect (by reason) that heat conduction within still water will tend to maintain temperature homogeneity.

My own reasoning says that without any heat exchange - without any cooling or heating affecting it - the temperature will remain uniform. I also expect that any such heating or cooling will have to be below a threshold - be too weak to cause an overturning circulation that would break up any stratification - to become stratified; with an overturning circulation the contents should get well mixed and be (close to) homogeneous in temperature.

I expect the transition between slow convection that makes stratification and convection strong enough to break up stratification and get homogeneity could get complex, so will begin with looking at those two states

I am interested in whether this is true ie, am I missing something?

 

[fresh_42]

Knowing what you mean by water, containment or basin, and environmental conditions would be helpful. Natural water in a lake is certainly completely different from pure $H_2O$ in a bottle, shielded from any electromagnetic radiation.

 

[russ_watters]

By definition the answer is no, unless you throw in a confounding factor like a temperature distribution not contradicting your "uniform temperature" assumption.

 

[256bits]

In another thread I made this comment -

Leaving aside your comment,

it might be better to study stratification, and easier to understand, with two separate fluids, rather than water of homogenous chemical content.
Immiscible - oil/water
Semi-immiscible - plain water/salt water
Miscible - alcohol/water

For the immiscible, you can consider that the density of the fluids is a constant, and never will the little packets of each combine, but rather appreciate the fact that that the lighter packets will always rise through the more dense packets.
For semi-immiscible, the interface between the two layers is distinct, but mixable. Consider the melting of icebergs and river flow of water into salt sea water. One fluid is solvent/solute; the other pure fluid.
Miscible - here we have a solute/ solvent.

For experiment, add a dye of different colour to each.

Note that the depth of each layer, and width, in the container, can determine the turbulence produced in each by heating the bottom fluid, preferably at a side wall, acting as a plane of symmetry, assuming a fictitious same volume on the other side of the wall.

Maybe this helps. I don't know. But these would be/are real world problems and perhaps better luck finding solutions that the limited water/water problem.

 

[Baluncore]

My own reasoning says that without any heat exchange - without any cooling or heating affecting it - the temperature will remain uniform.

I will take a different approach.

In the presence of gravity, and given that every molecule in the water has a slightly different velocity, I would expect a gradual migration of momentarily-slower molecules, towards the bottom, while momentarily-faster molecules, migrate towards the top. That will generate a small but continuous thermal gradient.

The process is driven by the faster molecules having a greater volume, so lower density, by virtue of their velocity, and so greater pressure on their immediate neighbours.

The gradient will increase, until the temperature difference between the top and the bottom, reaches equilibrium with the thermal conductivity of water.

 

[jbriggs444]

The process is driven by the faster molecules having a greater volume

I think that you are mixing models here. The continuum model of fluids where the concept of buoyancy exists associates greater volume with higher temperature. The tiny particle model where particles have velocities does not associate volumes with particles based on their speed.

The continuum model does have the concept of an adiabatic lapse rate. But, for liquids, this is quite tiny.

 

[Baluncore]

I think that you are mixing models here.

Yes, I am mixing models, because I believe reality lies somewhere in between.

The assumption that no heating or cooling takes place, ignores the fact that the fluid has a statistical spread of parameters at the molecular level, and that energy exchange is continuous between the molecules of the fluid. I expect it will be a small effect, that can usually be ignored if there is any external heating or cooling, which in this case there is not.

 

[Ken Fabian]

I'm not reading anything that makes me think it will stratify but I hadn't considered lapse rates.

Russ, should I give you an upvote for agreeing with me? Not necessarily the best reason but I do think you are correct.

I don't think my basic understanding of convection and how temperature differentiation (ultimately stratification) arises is flawed. I made it about water and perfect insulation but any fluid with perfect insulation should do.

I did wonder something similar to Balencore's suggestion might arise - statistically unlikely hot or cold spots big enough to persist, with subsequent convection - but thinking about it I think jbriggs444 has the right of it.

I am not aware of that occurring and am inclined to think the scales at which Brownian motion are working will be extremely unlikely to cause hot or cold spots that can persist. The extent to which heat transfers by other means than Brownian motion - IR emissions and absorption inside the insulated container - seem likely to work to homogenise temperature.

The continuum model does have the concept of an adiabatic lapse rate.

Thanks, that does add a factor I hadn't considered. I wouldn't expect any convection to arise within a fluid at equilibrium in a column but if starting with homogenous temperature top to bottom it will not be at equilibrium? I'll stir that possibility in and see if it rises to the top or settles to the bottom.

 

[Dullard]

My dog just looked over my shoulder. He mumbled something about Entropy in a closed system.

 

[Herman Trivilino]

The process is driven by the faster molecules having a greater volume

Faster molecules don't have a greater volume. The spacing between the molecules is larger, so the same number of molecules will occupy a larger volume.

 

[olivermsun]

I will take a different approach.

In the presence of gravity, and given that every molecule in the water has a slightly different velocity, I would expect a gradual migration of momentarily-slower molecules, towards the bottom, while momentarily-faster molecules, migrate towards the top. That will generate a small but continuous thermal gradient.

The process is driven by the faster molecules having a greater volume, so lower density, by virtue of their velocity, and so greater pressure on their immediate neighbours.

The gradient will increase, until the temperature difference between the top and the bottom, reaches equilibrium with the thermal conductivity of water.

Are you envisioning that gravity imposes a different acceleration on faster particles than on slower particles?

 

[olivermsun]

Thanks, that does add a factor I hadn't considered. I wouldn't expect any convection to arise within a fluid at equilibrium in a column but if starting with homogenous temperature top to bottom it will not be at equilibrium? I'll stir that possibility in and see if it rises to the top or settles to the bottom.

The atmosphere is typically temperature-stratified, so it can be said to have a lapse rate. The atmosphere's boundary conditions and the properties of "air" help determine what this lapse rate actually is at any given location and time.

Your question is whether an isothermal "ocean" that is insulated will stratify in the first place. Without any interesting boundary conditions like those of the atmosphere, what would create a stratification and hence a lapse rate?

Maybe it would be interesting to ask, what kinds of boundary conditions (or other forcing) are sufficient to cause an isothermal, but otherwise realistic, ocean to stratify?

 

[Baluncore]

Are you envisioning that gravity imposes a different acceleration on faster particles than on slower particles?

No.

"Will it, or will it not, stratify" ?
If you look sufficiently closely, it will stratify.
If you step back, you can ignore that stratification.