# How does bouyancy work from a molecular point of view?

1. Jul 19, 2004

### alpha_wolf

Gas/liquid/solid in solid is irrelevant, liquid in gas is too dense to be bouyant, solid in liquid/gas and gas in liquid are easy. So I'm mostly interested in the liquid in liquid and gas in gas cases. Thanks.

2. Jul 19, 2004

### Didd

Bouyant force is associated with liquids. If you drop a liquid in to another liquid, it is the momentum which makes the other liquid to sink down. Don't make things complicated.
Bouyant force:It is a reaction force. When you immerse an object in to a liquid a bouyant force acts upon the object. So, bouyant force =weight of the fluid displaced by the object. Whatever kind of liquid you are using th bouyant force is still the same as the weight of the object.It is better if don't make complications.

Last edited: Jul 19, 2004
3. Jul 19, 2004

### Galileo

Not true, the buoyant force on the object is equal to the weight of the fluid displaced by the body. This is Archimedes' principle.

It comes from the fact that as you go 'deeper' in the fluid the pressure increases. So the pressure pushing down on the object is lower than the pressure pushing it up, there is a force upward which is the buoyant force. Pressure comes from the molecules. Even if the fluid as a whole is at rest, the molecules that make up the fluid are in motion and they collide with their surroundings. Their change in momentum is what causes a force resulting in pressure.

Im not sure, but Im guess the molecules have a higher velocity when you go deeper, becuase that's the only way to increase pressure when the fluid is incompressible (as with most liquids).

EDIT: But, you mentioned liquid in liquid or gas in gas. Sorry.
I think the same thing applies though. In equilibrium the kinetic energies molecules of the gases will have the same distribution. The molecules of a liquid whose molecules are heavier have more momentum, since E=p^2/(2m). So they exert a higher force. For equilibrium they will thus go to the bottom.

Last edited: Jul 19, 2004
4. Jul 19, 2004

### Didd

Sorry about that. I mean to say that. I will edit my post

5. Jul 20, 2004

### alpha_wolf

Didd, I'm not trying to make anything more complicated. And I'm familiar with Archimedes' principle. I'm trying to understand the underlying mechanism(s) that make this principle work.

Galileo, I highly doubt that molecules go faster the deeper you go. If that was the case, the liquid's temperature would have to rise with depth. AFAIK, that is certainly not the case. This site seems to confirm my claim. Regarding incompressibility, I think this is just an approximation. If you apply enough pressure, you can compress anything, even solid. Otherwise, how would you get neutron stars and black holes? And as for molecular weight, that has little to do with bouyancy, at least for gases, since it is not the only factor that determines density, and it is density that controls bouyancy.

6. Jul 21, 2004

### Galileo

That the molecules would move faster is just speculation. And Im not sure if temperature is only dependent on the speed of the molecules. I'm sure a statistical analysis could answer that.
Anyway, for liquids, molecular weight is exactly what determines density. Higher molecular wieght means higher weight of the liquid, which means the higher the weight of the displaced liquid, thus a greater buoyancy. (Im only talking about liquids).

Incompressibility is indeed an approximation, but a very good one. Youll need a tremendously huge amount of force to compress even 1 liter of water by 1 cubic cm.
Im not sure if incompressibility holds for the bottom of the ocean, but it certainly does in your average swimming pool.

7. Jul 21, 2004

### Staff: Mentor

Temperature is a measure of kinetic energy. Kinetic energy depends on mass and speed. So more speed = higher temperature.

For all but the most extreme cases, you can, indeed consider water incompressible. We do in the scuba classes I'm taking now...

The question in the title of the thread doesn't really apply - buoyancy is rarely, if ever, applied to just a handful of molecules.

8. Jul 21, 2004

### Staff: Mentor

pressure in a liquid

Perhaps what alpha_wolf is looking for is a better understanding of how pressure variation exists in a fluid. For liquids, the short answer is that they get compressed. As you go lower in a liquid, the pressure increases. The molecules get squashed together, electrostatic forces resist that compression, thus allowing the liquid to exert an increased pressure.

Calling a liquid, such as water, incompressible is an excellent macroscopic approximation. But for the liquid to generate an increased pressure the molecules must be compressed together somewhat.

This is the same kind of thing that happens in a solid. Example: as I walk across the floor, the floor pushes me upwards. What allows it to do that is the fact that the molecules are crushed together. Of course, a solid has a rigid structure while a liquid is free to move about. Thus the pressure in a static liquid is exerted equally in all directions.

9. Jul 21, 2004

### alpha_wolf

Perhaps so, but all matter is composed of molecules (or atoms in the case of noble gases and most solids - and of course, the molecules are themselves composed of atoms). And as a result, all physical effects involving matter, even the ones copletely inapplicable on the mollecular scale, ultimately arise from certain molecular interactions, or combinations thereof (ok, some arise purely from sub-atomical processes, but that's not the point). What I'm trying to do with this thread, is get a better understanding of the molecular processes that give rise to bouyancy. So please, keep posting.

I completely agree. Here is another way of looking at it. A large pressure gives rise to a negligible amount of compression. This relationship can be described by an equasion. Reading the equasion in the opposite direction gives: a negligible amount of compression gives rise to a large pressure.

Last edited: Jul 21, 2004
10. Jul 21, 2004

### Staff: Mentor

Nothing about that requires compressibility though: stack some bricks on a scale and what the scale reads doesn't depend at all on how much the bricks compress each other, just what they weigh (mass). Similarly, buoyancy doesn't depend at all on compressibility from the standpoint of Archimedes principle. Yes, water at depth is denser than water at the surface - but Archimedes principle doesn't care: it only cares about mass (weight) displaced.

I see density variation/compressibility issues as a consequence of pressure, not a cause. Pressure at a point is simply the weight of the column of water (or air, for that matter) and the fact that the density varies greatly by altitude doesn't affect pressure measurements at a specific location with a known local density.

The reason that "as you go lower in a liquid, the pressure increases" is that it has more water above it, pushing down. Modeling the water as compressible with a variable density or incompressible (with the correct average density) gives precisely the same calculated pressure.

Last edited: Jul 21, 2004
11. Jul 21, 2004

### Staff: Mentor

Fair enough. Pressure is a result of molecules bouncing off of each other as stated. The precise force involved, in the case of buoyancy, (different from pressure in a sealed, rigid container) is exactly equal to the weight of the column of fluid.
....none of which has anything at all to do with buoyancy.

If your question is really about pressure, not buoyancy, fine - but please understand I'm just trying to keep you from confusing the two concepts.

If you want to relate pressure and buoyancy, consider cases where the object is fixed volume (and density) and the fluid isn't, and vice versa:

What happens to the buoyancy of a rock as altitude in air decreases?

What happens to the buoyancy of a balloon as you push it further and further under water?

In both cases, the pressure of the fluid is increasing, but...

Last edited: Jul 21, 2004
12. Jul 21, 2004

### alpha_wolf

Indeed (this is basically a rewording of Archimedes' principle). But what I don't understand is, how is that force relayed in such a way that the less dense fluid rises, especially considering that the two fludis can intermix? In ohter words, what are the molecular interactions/processes that result in a non-zero average velocity of the molecules of the less dense fluid (i.e. if you average out the vlocities of all those molecules)?
Yes, I see what you're getting at. The pressure issue simply became a kind of "sidenote discussion".. I often discuss two or more things in paralel, with little or no connection between them. Since you don't know me very well, I can't blame you for thinking I was getting confused.

13. Jul 21, 2004

### Staff: Mentor

My point was a trivial one. I'll try to restate it more clearly.
Right. But, looked at more closely, that bottom brick is different than the top brick--it is slightly compressed. It better be: it must exert a greater force to support the bricks on top of it. My point is that for the brick to exert a force, it must change (slightly). So must the scale (it depresses). And so must the floor "bend" as I walk across it.
Right. It's not buoyancy, but pressure that correlates to the fluid's microscopic compression.

Right. The pressure causes the water to compress more as the depth increases. This must happen, else no force can be generated.

Right.

My point is that there is a microscopic correlate to increased pressure: the molecular bonds are compressed. (I thought that this might have been what alpha_wolf was puzzling over.)

14. Jul 21, 2004

### Staff: Mentor

Now I'm confused. How can pressure be a side issue in a discussion of buoyancy? Fluid pressure on an object is what causes the buoyant force. Since the pressure is greater on parts of the object immersed more deeply, there is a net upward force.

15. Jul 22, 2004

### alpha_wolf

Yes, Indeed. A small correction and clarification to hopefully relevieve the confusion: the issue of pressure *as related to compressibility* was the side discussion. However, in this case this side discussion still relates to the main discussion, and is not completely detached (I'll detail my thoughts later).

With the help of the various replies in this thread, I think I've figured out the mechanism last night. I will post the details later.

Last edited: Jul 22, 2004
16. Jul 23, 2004

### alpha_wolf

A possible mechanism

As promised, here is my take on the problem.

Suppose we have two fluids A and B, with densities D1 and D2 respecitvely. D1 < D2. For the moment, let's assume we have less of fluid A. For a column of fluid B of heigt h, the weight of the column is w = D2*h*g, where g is the graviational acceleration, and assumming a negligible variation in Di and g. For a column of fluid of the same height, where a fraction f of that height is fluid A (and the rest is fluid B), the weight would be w' = f*D1*h*g + (1-f)*D2*h*g. Obviously, since D1 < D2, we get that w' < w. The same applies if Di and g do vary significantly, except that the weight formulas would be more complex.

Now, let's see what happens near a bubble of fluid A, immersed in fluid B. Let's look at some depth h, which is slightly deeper than the bottom edge of the bubble. Every spot that is under the bubble, is under a column of fluid that weights w'. Every other spot is under a column that weights w. The weight of a column of fluid causes the fluid under that column to compress a little (even if the fluid is an "incompressible" liquid). From a molecular point of view, the heavier the column of fluid, the harder the molucules need to push in order to "hold it up". But they can only push so hard. So the column pushes them down, until they are sufficiently close to nearby molecules for the electrostatic repulsion beween them to be strong enough to hold the column up. Once the fluid under a column has been compressed, the compression results in a higher hydrostatical pressure. In other words, the motion of the molecules distributes the downward force of the column in all directions. But since w' < w, the resulting pressure under the bubble is lower than the surrounding pressure. So the surrounding molecules will move under the bubble, strivng to equalize the pressure. In doing so, they will raise the pressure under the bubble such that it is more than it should be according to w'. In other words, the pressure under the bubble will rise enough to overcome the weight of the fluid above that area. As a result, all the columns of fluid that contain fluid A, will be pusshed upwards. And since fluid flows downhill, some of the fluid in those columns will flow sidewards to reduce the column's height as necessary. All that happens simultaneouly and continuously until the bubble can rise no further.

If we have a bubble of fluid B inside fluid A, it will sink by a similar process - the pressure under the bubble will initially be higher then the surrounding pressure; it will be reduced, and will no longer be capable of holding the bubble up. If we have equal amounts of the fluids, then both processes will occur.

I'm not sure how this accounts for the apparent higher bouyancy at larger depths, but then I'm not entirely sure how this works macroscopically either, or whether this effect even applies to the cases of fluid in fluid (i.e. when the immersed "object's" volume is not necessarily constant)...

Intermixing:
Often, the two fluids can intermix, and desolve in one another. As long the solubility limit is not reached, the fluids will desolve in one another. This means that the molecules of the desolved fluid will be separated from the other molecules of that fluid. As a consequence, one cannot talk about the density of the desolved fluid (since you need multiple molecules to define density), and so bouyancy will not occur. Once the solubility limit is reached, bubbles will start to form, and then the above analysis can be applied to those bubbles. If there are no impurities that would allow bubbles to nucleate, we would get a supersaturated solution, and again no bouyancy would occur. This suggests that if the mutual solubility is perfect (100% solubility), and the two fluids have been thouroughly mixed, neither fluid will experience bouyancy. In addition, the easier the two fluids intermix, the less well defined the borders of the bubbles would be, if they do form.