# If I replace water molecules with microscopic solid spheres, will they still reach the same height in communicating vessels?

I'm having an hard time understanding why liquids take the shape of the container or why they reach the same height in communicating vessels.
I'm wondering if I try to simulate their behaviour in ordinary life using really little balls will they approxitamate the behaviour of liquid molecules?
If they don't, what factors that I'm not considering determine the difference in behaviour?
If they do, is behaviour's approximation a function of the radius of the spheres?

UPDATE: Seems that answers show different opinions and point of views. I don't have the experience to decide which one is the most accurate. I'm waiting for extra details or for the community to pick one. I will go on with my reaserches in the meantime.

• It should work if you model them having little friction. I do not see any limitation due to specific interaction as for communicating vessels work for any liquid, water and mercury, oils and paraffins, etc. The crucial point is that the particle should be so slipping onto each other that no forces different from tge hydrostatic one can be sustained. I think so, not totally sure tough. Jan 12, 2018 at 13:40

One aspect that has been touched on in other answers is that an attribute of liquids that differentiates them from gases is that there's an intermolecular attractive force. If you release a quantity of liquid is a zero-gravity environment, it sort of sticks together in a blob, occupying a more-or-less constant volume. Release a gas and it expands without limit as the molecules fly off in every direction, bouncing off their neighbors but otherwise ignoring each other. A bunch of marbles released into outer space thus make a decent model of a gas, but a terrible model of a liquid.

However, a swimming pool full of marbles certainly does not seem to behave like a gas. Why not? Obviously, because gravity stops the marbles from flying away. Why does gravity not stop gas molecules from flying away? Because they have thermal velocities of hundreds of meters per second. They are flying around so fast that they don't care much about gravity or about the attractive forces of other molecules.

In liquids, the molecules are close enough together that, even though they're jiggling pretty violently, they still feel the attraction of their neighbors, but not so much that they glom onto any particular ones which much tenacity. They still jiggle free all the time and cozy up to some other neighbors. They don't like to leave and go off into empty space because that means overcoming all the forces from other molecules pulling them back, but they're happy to rearrange, so macroscopically they flow to take the shape of their container.

In solids, the attractive forces between molecules are strong enough to lock them in place, despite their energetic jiggling. They fall into some energetically favored lattice and don't tend to wander off. From this perspective, a swimming pool full of marbles is much more like a solid. Gravity creates a pressure that tends to squeeze all the marbles together. They tend to find ways to eliminate empty space, and if you look through you will probably find regions where there are several marbles packed together in an organized fashion--perhaps hexagonally close-packed, which is the densest way to arrange spheres. A marble in the middle of one of these organized patches is fairly well locked in place, allowing the whole structure of marbles to support some amount of shear without deforming.

The thermal velocity that prevents the molecules of liquids and gases from dropping into lock step goes inversely as the square root of the mass of the molecule. For marbles, whose mass is greater by a factor of $10^{20}$ or more, the thermal velocity is vanishingly small, and won't cause a marble to jiggle free from its spot.

So: in free space, marbles act like a gas. Under the influence of gravity or another source of pressure, they act like a solid.

Gas molecules (especially in a sufficiently dilute gas) are frequently viewed as behaving like hard spheres. This is used in collision term of the Boltzmann equation; lots of literature is published.

However, if the gas is very dense and even more in liquids, you cannot view the molecules as spherical balls. This is due to the intermolecular attraction between the molecules. Water has Dipole-Dipole interactions as intermolecular attraction forces; the dipoles are formed by Oxygen (negatively charged) and hydrogen (positively charged).

The closer water molecules (or in General liquid molecules) are, the higher is this intermolecular attraction strength. On very high temperatures, kinetic energy of molecules is more than at lower temperature; thus, the molecules can travel far apart from each other more easy; the intermolecular interaction becomes less relevant.

But always relevant is the Repulsion between molecules due to the electron hull. If the molecular structure Looks like a ball, the molecules can be assumed to behave like a ball bouncing off other balls.

To the title of your question: If the molecules would be like balls, in General, no. The fact that the same height is reached in vessels relies also on the surface Tension of molecules which has also the origin in intermolecular interactions. The surface Tension makes the liquid surface tending to be at a Minimum.

I'm wondering if I try to simulate their behaviour in ordinary life using really little balls will they approximate the behaviour of liquid molecules?

Sure. That's exactly what smoothed particle hydrodynamics does. Care is needed in such a simulation to make the physics be closer to that of a liquid as opposed to a bunch of solid granular particles.

If the little balls can sustain a shear stress without moving then they cannot approximate the behavior of a liquid.

The answer is a solid sphere does not have the same behavior as a liquid (unless solid to solid is friction-less).

• But, the question is not about "a solid sphere", it is about a collection of millions of tiny spheres, and there are real-world examples where a collection of tiny, solid particles can behave like a fluid. en.wikipedia.org/wiki/Fluidized_bed Jan 11, 2018 at 15:48
• @jameslarge I sure read solid in the title. For sure I do not read fluidized bed. Jan 11, 2018 at 15:52
• The title asks about replacing water molecules with solid spheres. A water molecule does not behave like a liquid either. Jan 11, 2018 at 15:58
• @jameslarge Not going to argue with you. Jan 11, 2018 at 15:59

I'm wondering if I try to simulate their behaviour in ordinary life using really little balls will they approxitamate the behaviour of liquid molecules?

No. We can proceed in a similar way of finding the limit of a function in calculus. Starting with coarse sand, we can replacing it with finer grains, until it is a kind of dry mud. It makes any difference? I don't think so.

Suppose that the grains are not only really small but also perfectly spherical and without friction. If they are poured over one side of an U-tube, what force would make them climb the other side? There is only gravity and the wall reaction. Nothing would drive them upwards.

The explanation are based on the kinetic theory of the molecules as the microscopic cause for pressure and temperature. Pressure relates to momentum that are randomly distributed in all directions. The force that make them go upwards is the change of momentum after kicking the bottom of the tube. That is the translation to statistical mechanics of saying that pressure is the reason for that.