4
$\begingroup$

I am studying about fluids at the moment and I never been so massively confused since about some fluid related topics that I thought I was confident about like liquid pressure, velocity of particles, buoyancy. The more I research the more I realize that I don't think I understand what is the cause/source of liquid pressure, manner of liquid particle movement anymore. And after much time spent scouring the web, I realize the main source of this problem, which is that I have been visualizing liquid molecules like an ideal gas particle this whole time, which I realize now is not correct.

I obviously knew from basic physics chapters that liquid molecules are closer to each other (in terms of distance) than gas particle, but somehow I still visualized liquid molecules as constantly zipping off and colliding with each other and sides of container in full velocity like gas particles. I saw liquid particles are moving everywhere freely without much hindrance, from one extreme side of container to another, from bottom of container to top of liquid level just like how gas particles freely bounces from top of container to bottom of container like a ball . With this assumption, I then thought of fluid pressure as property arising from collision among particles and between particles and container, without significant influence from gravity (since gravity does not play much role in gas pressure, from what i know. I could be wrong though! Please correct me if this is also not correct) But I now realize that something is wrong in these assumptions because I am at loss to understand topics like fluid pressure, buoyancy, velocity

My main question then is that how is liquid particles organized around each other in a container? How do they move around each other? Are they free to move anywhere without much hindrance? Why does gravity play a significant role in liquid pressure but not ideal gas pressure? When i submerge a object in liquid, why don't the object simple sink in the bottom of container no matter how light or heavy it is, because individual liquid molecules are free to move right? So why don't they simple keep on moving to side, up, down and obviously raise liquid level while making space for the object? Why go through whole explanation of buoyancy force, floating, half submerged, full submerged head ache? If anyone can please explain this issue or point me to any direction, I would greatly appreciate it. Thanks.

$\endgroup$
1
4
+25
$\begingroup$

The key difference between a liquid and a gas is the presence of interactions between particles. In an ideal gas, the particles are far apart and don't interact, or in slightly more sophisticated theories have a hard core contact interaction. For this reason, in a gas, pressure is created by the momenta of individual particles striking the walls of a container, so it really just depends on the kinetic energy of individual particles (i.e. the temperature of the gas) and the density.

Liquids are different. Inter-particle interactions can't be ignored because the average spacing between particles is comparable to the distance scale of interactions. Since there are so many interactions, they may be much more complicated than a contact interaction like a gas gets treated... though frequently people use contact interactions because they are straightforward to physically model. However, water for example has attraction and repulsion between the poles of the individual molecules, an interaction which cannot be modeled as a contact interaction. The particles in a liquid are so close together that they are constantly scattering off of each other; the mean free path is very short. Liquid pressure is still created by particles colliding with the walls of the container, but because of inter-particle interactions, that may be more complicated than an elastic collision of a free particle like you have with a gas.

As to your question about gravity, it is worth noting that gas pressure is affected by gravity in the same way as liquids. The distance scale is pretty long, but you may have noticed that at high elevation, it's harder to breath because the density of the air is less. The reason this occurs for all fluids - both liquids and gases - is simply just that something has to hold the higher particles up in order to not have everything be sitting in a flat layer on the bottom of its container. For a given layer of particles in a liquid (at a fairly uniform temperature), on average the vertical force on the layer needs to be zero. Since gravity is pushing down, that means that there needs to be more force coming from inter-particle interactions from below than from above. If you then think about the next layer up, there still needs to be more force from below than above, but the force from below that layer is less so the force from above can also be less. So you see there will be a gradient with higher layers needing less force from below to maintain equilibrium, and the net force between layers divided by the cross sectional area is the pressure. When you put an object in the liquid, it feels that same force from above and below, so it feels some buoyancy because the force from below is greater. The question of whether it sinks or floats comes down to whether the force of gravity on the object is greater than the difference of the force from above and below.

I hope this helped, let me know if there's parts I could clarify or elaborate on

$\endgroup$
3
$\begingroup$

I think that the main difference with a gas is that in a liquid, each molecule is constantly in contact with other molecules. In a sense, their are free to move anywhere, but their paths might be much more erratic than if they were in a gas. Gravity plays a more significant role simply because the density is usually much higher in a liquid than in a gas

$\endgroup$
1
$\begingroup$

I will copy for you here one of my earlier answers on this topic:

Liquid molecules (taking water as an example) are constantly jostling about, bumping into, swapping places with, hitting head on, and squeezing past their neighbors like dancers in a mosh pit. They bounce off the walls and off of each other with equal force. At any given instant, some are moving really fast, others more slowly, but on average they are all in rapid motion, moving only a tiny bit between collisions while all jammed together shoulder-to-shoulder.

Because their motion is random, as a group they don't go anywhere, but by slipping and sliding and squeezing about and swapping positions, each one will over time find itself drifting off away from its original position and in this manner the dance floor is well-mixed: none of them stick with their original dance partners for very long.

The dancers are not holding hands, which means that they do not support shear forces, so they can slide past each other without much resistance.

We drop a big balloon on top of the crowd, does it fall to the floor? No, there are dancers in the way, and they are denser than the balloon so gravity pulls the dancers down and the balloon floats on top.

We drop a sphere of solid lead on top of the crowd, does it float on top? No, it is denser than the dancers and pushes them all out of the way while falling to the floor, and the dancers float instead (not a perfect analogy, but I think you get the picture).

Finally: imagine we make a pyramid of the dancers on their hands and knees, with other dancers on top of them, and still more on top of them. They quiver and shake from the load and the ones on the bottom are bearing all the weight of each layer of dancers above them. But since they have nowhere to go sideways because of the walls of the dance hall, they just sit there getting squished. A dancer in the middle of the pile (with dancers above and below) is surrounded on all sides by squished dancers and because she too is constrained sideways, she feels a uniform pressure squeezing in from all sides.

A dancer on top of the pile feels no such pressure, just the sideways contact of their nearest surrounding neighbors.

Because the dancers are modern, they are so flexible and wiggly that any dancer at the bottom of the pile can still squeeze around and swap places with their nearest neighbors, but the pressure they feel doesn't "follow" them if they happen to wiggle up to the top of the pile- since it depends on how deep the dancer is in the pile.

So just think of water molecules as modern dancers in a mosh pit having a good rage and you'll be on the right track!

$\endgroup$
1
$\begingroup$

Adding to other answers, you actually can think of a liquid as a special case of a gas, for example, you can read about Lenard-jones fluid. This means that the force of each particle makes each other is dictated by a Lenard-jones potential https://en.wikipedia.org/wiki/Lennard-Jones_potential. With this, you can simulate solid, liquid, gas, or even 2 or 3 states coexisting of a substant if you put the right initial conditions. Normally the initial conditions are chosen with the temperature, that thermodynamically is $$ \begin{equation} T=\frac{1}{NK_bf}\sum_{i=1}^N\frac{1}{2}m_iV_i^2 \end{equation} $$ $K_b$ is k Boltzmann constant and f is the number of degrees of freedom of each particle. In a 3D fluid that cant rotate, imagine liquid argon, $f=3$. Also, using the viral theorem you can calculate the pressure $$ \begin{equation} P=\frac{2}{3Vol}<E_{kin}>+\frac{1}{3Vol}\sum_{i=1}^N\sum_{j=i+1}^N(x_i-x_j)F_{ij} \end{equation} $$ as you can see in this article http://mate.tue.nl/mate/pdfs/9267.pdf. Where $<E_{kin}>$ is the mean kinetic energy, $x_i$ is the position vector of particle i and $F_{ij}$ is the force that particle j does to particle i.

Answering your other question, the particles are free to move around but they can't go everywhere they want. They are bounded by the Maxwell-Boltzman energy distribution. For example, the x component of the velocity of all particles must distribute normal center in 0 with $\sigma=\sqrt{\frac{K_bT}{m}}$ assuming all particles have the same mass. This is true for solid, liquid, or gas, or even some plasmas if quantum effects are not significant if they are you have to use Fermi-Dirac energy distribution. This means that horizontal forces cancel each other and that's why an object sinks straight down if there's no turbulence in the fluid.

The reason we don't study fluids this way is that this microscopic approach is difficult to use in practice. If you take a course on statistical mechanics you can learn more about this. Fluid dynamics is a macroscopic approach, so thinking of a fluid as a bunch of particles is a bit miss leading.

Also, the role of gravity is to force the particles to come closer together, thus, converting something that should be a gas at $g=0$ in a fluid or a solid. This happens in the earth's core or in stars for example. The effect of gravity also increments pressure because particles are closer to each other, so the force between particles increases.

For your last question, the way the particles are organized is in a way that has the minimum energy. In the case of solids, for example, they tend to organize in crystalline structures. In the liquid, there's too much freedom to spot a particular structure but you can find some organized regions for a given instant.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.