Buoyancy/Archimedes's Principle, how is it explained at the molecular level?

[Werg22]

I have looked for the answer but I haven't found it. Why does a fluid ends up being pushed upward in the presence of a higher density fluid? How is it explained at the molecular level?

 

[russ_watters]

If the fluids don't mix, then they work pretty much exactly like a solid in a fluid, and Archimedes principle can be applied directly at the macroscopic level. There is nothing relevant going on at the molecular level.

 

[cesiumfrog]

Buoyancy is explained by the difference in pressure between the upper and lower surfaces of some buoy (compared to its own weight).

The difference in pressure is calculated from the fact that pressure is constant everywhere at a particular depth (otherwise this would just have the fluid first rearrange itself until it is so), and away from the buoy the pressure difference is clearly given by the weight of the fluid suspended between those depths (again, otherwise the fluid there could not be in equilibrium).

From this it follows that an object floats if it has lower density than the fluid it is displacing.

The only thing to explain on the molecular level is "pressure". Looking at Bernoulli's equation, this clearly has to do with how much energy the fluid molecules have.

Perhaps someone else can explain precisely what distinguishes pressure from temperature on the molecular level?

 

[pivoxa15]

If the fluids don't mix, then they work pretty much exactly like a solid in a fluid, and Archimedes principle can be applied directly at the macroscopic level. There is nothing relevant going on at the molecular level.

You are saying it is like an emergent property?

Assume you have two mixtures of gases at different tempertures hence unlikely to mix because bonding forces is neglected. Also the hotter hence higher energetic molecules will not likely to mix with the cooler, lower energetic molecules (note: the molecular properties might need to come in here to explain this). However, when the temperture of the two reach equilibrium, than they will.

The hotter gas will be less concentrated than the cooler one because the hotter gas will move more frequently to more space. So when you look at a given volume of space, there will be more cooler molecules than hotter molecules. So in that volume, cooler molecules are more dense. Now you can apply Archimedes principle - just like you can with fluids.

However, I think that the molecular properties in explaining this principle for gases is more needed than if you are dealing with fluids or solids.

 

[russ_watters]

There are a bunch of different reasons why the density could be different, but it isn't really relevant to why density affects buoyancy. All that matters is that the density is different.

 

[billiards]

The hotter gas will be less concentrated than the cooler one because the hotter gas will move more frequently to more space. So when you look at a given volume of space, there will be more cooler molecules than hotter molecules. So in that volume, cooler molecules are more dense. Now you can apply Archimedes principle - just like you can with fluids.

No it doesn't work like that. The molecules themselves are not cool or hot, it is the combined effect of lots of molecules (and their kinetic energies) which makes a parcel of fluid cool or hot. The molecules in a hotter gas are spaced further apart on average which makes a parcel less dense - once again it is not the molecules themselves which are less dense (unless of course you are considering gases of different compositions in which case the molecules will have different densities - nothing to do with kinetic energy though).

You can apply Archimedes principle but you need not consider it at a molecular level, if the two fluids are immiscible (don't mix) then it's just plain common sense that the denser one will be more stable at the bottom whether you're considering molecules or not.

 

[pivoxa15]

No it doesn't work like that. The molecules themselves are not cool or hot, it is the combined effect of lots of molecules (and their kinetic energies) which makes a parcel of fluid cool or hot.

Okay. When I stated cool and hot, I was implicitly thinking about their kinetic energy which is the underlying reason for this emergent property.

The molecules in a hotter gas are spaced further apart on average which makes a parcel less dense - once again it is not the molecules themselves which are less dense (unless of course you are considering gases of different compositions in which case the molecules will have different densities - nothing to do with kinetic energy though).

Agree. Pretty much what I said.

it's just plain common sense that the denser one will be more stable at the bottom whether you're considering molecules or not.

Maybe it's this common sense you are talking about that is what the OP was asking.

 

[pivoxa15]

it isn't really relevant to why density affects buoyancy.

If you get into the 'why' than you will need molecular explanations? If so than that is what the OP was asking isn't it?

 

[Werg22]

Yeah, I'm interested in the "why".

 

[russ_watters]

What are you asking - why density affects buoyancy or what happens on a molecular level? Like I said, molecular interactions causing density changes are not relevant and buoyancy itself is not a molecular process. The classical explanation of buoyancy is simply Archimedes Principle and it works just fine on its own, considering fluids to be continuous media. Are you asking for an explanation of Archimedes Principle?

 

[Werg22]

Yes, I'd be interesting into knowing the cause of Archimedes principle.

 

[pivoxa15]

Yes, I'd be interesting into knowing the cause of Archimedes principle.

In Post 4, I gave a rough account (I didn't derive it from physical laws) of what was happening behind the Archimedes principles. What do you think?

Although I think QM is not necessary so thermodynamics might be more relevant because usually lots of molecules (too many for QM) are involved when applying Archimedes principle.

 

[Werg22]

pivoxa15, I have to say I find your explanation to be porous. First, Archimedes principle applies to fluids of the same temperature also. Second, solubility is not affected by small temperature changes. The kinetic theory of gas shows us qualitatively that pressure is proportionate to density. That said, I am confused on how to use that information in order to deduce that the lower density gas will go on top.

 

[pivoxa15]

pivoxa15, I have to say I find your explanation to be porous. First, Archimedes principle applies to fluids of the same temperature also. Second, solubility is not affected by small temperature changes. The kinetic theory of gas shows us qualitatively that pressure is proportionate to density. That said, I am confused on how to use that information in order to deduce that the lower density gas will go on top.

Note when I made post 4, I was thinking too much my other thread about why warm air rises. Sorry about that.
So you are saying at a fixed temperture and number of particles, pressure is inversely proportional to density. That makes sense.

I realized that the key to Archimede's principle is the immiscibility of the particles and the ability of entities to move through each other. Once you accept that than it follows straight away that the denser substance will be down the bottom and the lighter on top - due to gravity. That is why it applies so well to at least one substance being a liquid. If there were all solids, than it wouldn't work because they can't move through one another. And if they were all gases, they are not immiscible, unless ofcourse as I pointed out in post 4, they are at different tempertures. That is why warm air rises - or rather cold air displaces the warm air.

 

[Werg22]

Ok, it's clearer now. Also, a minor correction, pressure is directly proportional to density, not inversely.

 

[pivoxa15]

Also, a minor correction, pressure is directly proportional to density, not inversely.

So assuming fixed T and n (number of moles of the gas)

PV=nRT
P=nRT/V
P=(RT/M)nM/V
P=aD

a=RT/M
D = density = mass/volume
M=molar mass

Hence yes you are correct, its directly proportional.

 

[codec9]

why is the buoyant force exactly equal to the weight of the fluid displaced?

 

[russ_watters]

I'm not sure how to answer that - that's simply what buoyancy is. Imagine if you submerge a weightless vessel: The weight difference between the vessel if it is empty and if it is full is the volume of water displaced (times its density).

Is there more that you don't understand or another effect that you think should be included?

 

[Doc Al]

why is the buoyant force exactly equal to the weight of the fluid displaced?

One way to see that this must be the case is to imagine a fluid at rest. Would you agree that every "piece" of the fluid is in equilibrium--that the net force on it must be zero? (I hope so!) Now take a parcel of the fluid and picture an imaginary boundary around it. There are two forces acting on that fluid parcel that must be equal and opposite: The weight of the fluid within the boundary, and the force of the fluid outside the boundary pushing on the parcel. That last force is the buoyant force and it must be an upward force exactly equal to the weight of the fluid within the boundary.

Now replace that imaginary parcel with an object with the same shape, submerged in the fluid. The force from the surrounding water--the buoyant force--is the same as before. So the buoyant force on any object equals the weight of the displaced fluid.

Make sense?