Clouds in my coffee
March 18, 2010 4:45 AM   Subscribe

Today I poured cream into my coffee whilst standing up. As the cream 'billowed' through the coffee, I happened to rotate my body but kept my eyes on the coffee, and I noticed that the cream 'clouds' seemed to remain in the same place while the mug turned around them, i.e. the turning motion of the mug had no effect on the 'absolute' position of the goings-on inside it. I think this is kinda cool, and I'm just curious: what principle of physics is this based on? Can someone explain to me how/why this works?
posted by Brentusfirmus to Science & Nature (20 answers total) 9 users marked this as a favorite
I'm going to assume for both my sanity and yours that while unstated, you were holding the cup. The principle you're looking for is rotational inertia.
posted by phrontist at 4:47 AM on March 18, 2010 [6 favorites]

Phrontist has one half of the answer, the other half is that coffee doesn't have much viscosity.

The rotating mug doesn't exert much torque on the liquid inside, since the liquid isn't very sticky, so the milk keeps on doing its thing while the mug turns around it.
posted by Dr Dracator at 4:57 AM on March 18, 2010 [5 favorites]

If I understand your question then you turning turned the mug but the coffee being a liquid did not move in sync. I would expect you might see more movement in the liquid at the edge of the mug than in the center.
posted by Fiery Jack at 5:02 AM on March 18, 2010

Viscosity is the short answer.

I'm not a chemist, but I'll give this a shot: The long answer is that all matter is made out of atoms. These atoms are tiny indivisible particles which are always in some sort of motion -- this motion is related to the temperature.

You can think of atoms (or molecules, to some extent) as really tiny hard spheres, like really tiny billiard balls (this is the Van Der Waals picture of matter). Now these atoms are going to interact in a bunch of different ways, which is something we call 'bonding'. Some atoms (or molecules) are going to hold on to each other really tightly. If you push on one atom, all the other atoms are going to want to come along, because they're bonded to tightly to each other. If something is solid, like your coffee cup, this is what happens: You turn part of the coffee cup, the rest of the coffee cup turns with it, because the atoms like to hang out with each other so much that they come along for the ride.

Now in a liquid, like coffee, the molecules don't need to do that. This is because the molecules of the liquid don't hold on to each other as tightly, so in a liquid they're not packed together as tightly (which is why solids are generally more dense than liquids). Let's say I push on a molecule of a liquid. It's not holding on to it's neighbors really tightly, like in a solid, so it moves a bit, maybe hits another liquid molecule, and transmits force that way. So it's kind of indirect. If something isn't very viscous, the liquid molecules aren't holding on to each other very tightly at all, so you can be putting force on the molecules at the edge of a liquid (which is what you're doing when you're turning your coffee cup), and the molecules at the center of the coffee cup are being kind of all, "Eh, not today."
posted by Comrade_robot at 5:35 AM on March 18, 2010 [3 favorites]

FYI, the same phenomina can be observed with ice cubes floating in a glass of liquid

posted by DavidandConquer at 5:42 AM on March 18, 2010

Could this same principle be applied to people (or I guess, things, including smoke or air) moving in an elevator, or people swimming in a pool on a boat, etc.? The idea is that what's going on in the elevator, mug, pool, Earth relatively trumps what's going on outside it, right? (And for the things that don't have free will, it's their inertia that's doing the trumping?)

Also, I think this post title is about me.
posted by iamkimiam at 6:06 AM on March 18, 2010 [1 favorite]

Your "absolute position" reference does indeed have a long physics lineage. You should look at Newton's Bucket argument. You're actually bringing up a pretty complicated question in physics, but in short, there is not absolute position for the liquid (coffee or cream). The motion of the liquid is based on gravity, centrifugal force, and the force exerted by the container to keep the liquid contained.

It turns out that all motion is relative, and the liquid is already "moving" so to speak, because the force of gravity causes it to have a kind of inertia (like you have inertia, like I have inertia) that it responds to by filling the bottom of the container to reach equilibrium. Your turn was not enough to change this equilibrium. If, on the other hand, you got some rope and a bucket, you could replicate Newton's experiment and observe that if you rotate the container enough, the surface of the water becomes concave--its equilibrium position changes.

IANYP (I am not your physicist. Nor am I a physicist of any kind, actually).
posted by _cave at 6:09 AM on March 18, 2010

There is "no" absolute position. I need to stop coming here before I finish my morning coffee.
posted by _cave at 6:09 AM on March 18, 2010

The first two answers have it exactly: rotational inertia of the fluids and low viscosity/low friction with the cup walls (coffee doesn't stick to the cup). Try this with honey and the honey will rotate with the cup rather than staying still.
posted by bonehead at 6:33 AM on March 18, 2010

low viscosity/low friction with the cup walls (coffee doesn't stick to the cup)

Well ... low viscosity is different from low friction. And the coffee at the very edge of the cup can be thought of as moving along with the cup. See:

No-slip boundary condition. Or as another example, this is why
posted by Comrade_robot at 6:48 AM on March 18, 2010

Well ... low viscosity is different from low friction.

Not really particularly different. Viscosity is the fluid analog of friction. It's a result of intermolecular forces and it converts kinetic energy to thermal energy.
posted by mr_roboto at 7:00 AM on March 18, 2010

Simplified, you can think of this as an example of Newton's first law of motion, that is, an object at rest will stay at rest until a force acts upon it.

Simplifying the model, you can consider the coffee and milk as roughly a singular object, with the rotational force applied to the cup. As coffee's thin (low viscosity), and the walls of the mug are smooth, there's a low amount of frictional force to move the coffee with the mug. So essentially, you're seeing the coffee "stay" in place while the mug moves around it.
posted by explosion at 7:04 AM on March 18, 2010

low viscosity is different from low friction.

You are, of course, correct, but in the example described, with very low torque, this implies very poor coupling between the vessel wall and the liquid, most probably some form of shear-thinning. Laminar regions are much broader for high viscosity fluids, so, for high-friction, low-viscosity behaviour, a strongly non-Newtonian fluid would be necessary. Those aren't very common in everyday life.
posted by bonehead at 7:10 AM on March 18, 2010

The coffee is at rest with respect to the room. When you rotate the cup, the cup walls are exerting a torque -- a force that causes a change in the state of rotation -- about the center of the cup. But not much of a torque, because mostly the walls of the cup are slipping by the coffee inside rather than pulling the coffee along with it. So the coffee remains mostly at rest.
This is an example of Newton's first law applied to rotation: An object that is not rotating remains not rotating, unless acted on by an external torque.
The analogue for translation (movement of the center of mass) is: An object at rest remains at rest, unless acted on by an external force. Here's Newton's first law for translation. Cool! The coffee is what's on the table, the coffee cup is the cloth, you play the part of the motorcycle.
posted by Killick at 7:47 AM on March 18, 2010

You are, of course, correct, but in the example described, with very low torque, this implies very poor coupling between the vessel wall and the liquid, most probably some form of shear-thinning.

Probably not. I think coffee is pretty newtonian and that the wall is no-slip. It's just not viscous enough to rotate the entire body of fluid. I don't think it's necessary to invoke any nonideal fluid properties here.
posted by mr_roboto at 7:54 AM on March 18, 2010

I think we're agreeing but talking past each other. Sorry, not being clear before coffee myself:

Coffee, or rather water, is quite Newtonian in behaviour. While there is coupling to the cup walls, coffee is of low enough viscosity that the bulk fluid in the cup rotates on a bearing of a thin layer of liquid undergoing laminar flow. Even at quite low rates of rotation, this shear layer is very thin and almost invisible to the naked eye.

In a similarly Newtonian high-viscosity fluid, the laminar layer cannot establish because the cup is too small and/or is not spinning fast enough (scaling as the Reynolds number, of course). Thus a high viscosity, Newtonian fluid will rotate with the cup because of coupling. Put honey in an industrial size vat and similar bulk rotations can be observed.

In order for no coupling to occur, in such a small vessel, a high viscosity fluid would have to be (very) shear-thinning non-Newtonian.

Assuming in all cases, no-slip, high friction walls (which is a pretty safe bet with a ceramic coffee cup).
posted by bonehead at 8:55 AM on March 18, 2010

See also: the last bits of cereal floating in a bowl of milk.
posted by lohmannn at 9:10 AM on March 18, 2010

Fluid Mechanics is the portion of continuum mechanics (which is the portion of mechanics which is a portion of physics) that deals with things like this.
posted by Brian Puccio at 10:50 AM on March 18, 2010

Related: A violation of the second law of coffee dynamics? about a month ago.
posted by madcaptenor at 11:23 AM on March 18, 2010

Because the cream weighs more than the coffee..?
posted by marimeko at 5:21 PM on March 18, 2010

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