# A violation of the second law of coffee dynamics?February 21, 2010 2:35 PM   Subscribe

What phenomenon of coffee physics or fluid dynamics is going on here?

This is a tall glass mug of hot coffee, about five minutes after adding a glug of skim milk. I didn't stir it. I could understand it if the milk were distributed uniformly around the coffee, or if there were a smooth gradient of milk density. But instead there are four distinct bands with sharp transitions between them, going from milkiest at the bottom to least milky at the top. I've now seen this happen three times, always at Steep and Brew. Of course this phenomenon could only be observed in a transparent container; but I don't believe I've seen it happen in a pint glass. Does the striation have something to do with the curvature of the mug? What could possibly be maintaining the sharp boundaries between the different layers?
posted by escabeche to science & nature (14 answers total) 13 users marked this as a favorite

I'm not sure, but I think it will probably be the same effect that allows your hot water service to keep delivering hot water until it's very nearly refilled with cold.

Hot coffee is less dense than cold milk. So in the absence of turbulent mixing (and perhaps the shape of the glass contributes to this absence during a pour) the natural tendency of any cooler region of fluid is to sink, and any warmer region to rise. If something vaguely approaching a boundary layer forms by accident, stuff warmer than the boundary will rise away from it, and stuff cooler than the boundary will sink away from it, all of which makes the boundary tend to sharpen up over time.

It would be interesting to experiment with your milk and coffee and vary your initial pouring technique to see whether you could generate different numbers of boundary layers with the same coffee, milk and glass. I'd expect that you would be able to.
posted by flabdablet at 2:46 PM on February 21, 2010

You can see the 2nd law of coffee dynamics in action by observing that the bands disappear over time as the temperature becomes uniform throughout.
posted by mpls2 at 3:23 PM on February 21, 2010

That effect doesn't have to be a function of temperature. I've seen White Russians served as separator drinks, with Kahlua on the bottom, cream in the middle, and vodka on top. All of them are cold; the difference is physical density.
posted by Chocolate Pickle at 3:36 PM on February 21, 2010

right, but when you pour separator drinks (like a black & tan), you generally want to pour in a spray, rather than a column, right? that's why you use the funny spoon thing.
posted by toodleydoodley at 3:58 PM on February 21, 2010

It's the Buoyancy effect. You can (not so) easily calcualte the density of water at different temperatures with the IAPWS-IF97 (PDF) equations.
posted by Confess, Fletch at 3:59 PM on February 21, 2010

Most of these answers seem to be missing the point. Yes; liquids of different temperature have different densities. Adding cold milk to hot coffee, you might expect the milk to sink to the bottom and form a layer. Why, however, is this system forming not two, but four, layers?

I dunno. Perhaps the milk is separating? Maybe you're seeing convection cells?
posted by mr_roboto at 5:02 PM on February 21, 2010

I'm with mr_roboto. Here's a few sentences from a colleague of mine in fluid dynamics, emphasizing that the 4 bands are harder to explain than 2 bands would be.

"Sharp interfaces are common in "stratified" (usually miscible, of slightly different density) fluids: they arise because as long as the flow is mostly laminar (not turbulent), mixing through molecular diffusion is very slow and therefore the lighter fluid floats above the heavier one (after some mixing). But the fact that you have 4 bands is a puzzle. My guess is that maybe you are mixing hot coffee and cold milk and that various combinations of temperature and mixing occur and then make bands. Try pouring milk more slowly and faster and you should see different things."

I wonder: if I poured the milk in really slowly, would it tend to make just 2 bands? And: if I left the coffee to sit for a long time without drinking it, would the milk indeed equidistribute as mpls2 says?
posted by escabeche at 5:24 PM on February 21, 2010

Pure speculation (but I use fancy words, so it's OK for AskMe, right?), but could the milk be undergoing some kind of phase separation? This would be in addition to the simple temperature/density effect.

Two possibilities occur to me: one is that the milk solids are getting denatured by the heat of the coffee and are settling out into their own layer, and the other is that the homogenized milk is somehow getting dehomogenized (by heat?) and a higher-fat layer is floating over the lower-fat layer.

Maybe some combination of density and phase separation is what's giving 4 layers rather than 2.

How long do these layers last? If you let the coffee sit there until it's cold, do the layers persist? How quickly do they form? You said the photo was taken 5 minutes after the milk was added, but when did you first notice the layers?
posted by Quietgal at 5:29 PM on February 21, 2010

one is that the milk solids are getting denatured by the heat of the coffee and are settling out into their own layer, and the other is that the homogenized milk is somehow getting dehomogenized (by heat?) and a higher-fat layer is floating over the lower-fat layer.

But wouldn't I notice the milk solids when I drank the coffee? Also, the milk is skim, so I don't think there could be much of a high fat layer. As for how long the layers last, I don't know, because I drink the coffee! I took the picture as soon as I noticed the layers, but as I recall they form pretty quickly, within a minute or so.
posted by escabeche at 5:40 PM on February 21, 2010

I think you're going to have to buy yourself two coffees tomorrow and only drink one of them. Then see what happens as the other one cools.
posted by lapsangsouchong at 6:00 PM on February 21, 2010

Yes, I think you'll have to sacrifice a coffee to SCIENCE! and let us know what happens to the layers as it cools.

Concerning denatured milk solids, you won't necessarily get cheese curds when the protein molecules denature.

(Brief digression into protein structure: proteins are long chains of amino acids, but these chains are normally tightly folded up into compact blobs. However, when you denature a protein, you unfold these tidy structures and now you have long chains waving around. These chains can get tangled up with other chains if you have a high concentration of protein, like in milk. The tangled clusters bang into other tangled clusters and stick together, then the clumps get big enough to form curds, and cheese happens.)

When milk is diluted into coffee, the protein gets too dilute for widespread chain entanglement, so it doesn't form curds. A few molecules clumped together can form a particle that's heavy enough to settle out of liquid suspension, but not big enough for you to sense as a curd on your tongue.

How long the layers persist is probably more informative than how fast they form, since everything we've speculated out here is pretty quick (heating, convection, denaturation, etc). But I think convection cells would be unstable as the coffee cools (that's a total WAG, though). Please come back tomorrow with another report!
posted by Quietgal at 6:47 PM on February 21, 2010

They are not convection cells. Convection cells are vertical and will run the entire height of the glass. It's extremely rare to see multiple convecting layers stacked on top of each other. Here is a self-link to a video of coffee convecting. Your coffee is probably not convecting at all, since convection would mix the layers fairly rapidly. This "see how long it lasts" test will probably just test how long it takes convection to set in, if it starts up at all. And this is merely a test of how much of a temperature differential your mug can form, which is in turn set by how quickly the coffee on the top can cool. Which is why blowing gently on the top can help convection to start.

Ok, in terms of basic fluid physics, I don't know, so I'm going to make some guesses about somebody else's field: fats or proteins in the milk are interacting with the phenols, oils or sugars in the coffee.
posted by kiltedtaco at 8:38 PM on February 21, 2010

Skim milk is a colloidal suspension of "casein micelles":

The largest structures in the fluid portion of the milk are casein protein micelles: aggregates of several thousand protein molecules, bonded with the help of nanometer-scale particles of calcium phosphate. Each micelle is roughly spherical and about a tenth of a micrometer across.

What you're seeing in that picture is layers in the distribution of colloidal particles, and because the instantaneous velocities of the particles of the colloid are so much less than the instantaneous velocities of the molecules of the liquid, mixing by diffusion of the colloid will be much slower even than molecular diffusion would be.

In whole milk, the lower density imparted by fat globules would tend to make the milk rich layer at the bottom rise to the top as the temperature equalized, and that would lead to a lot of mixing, but it's my guess that the casein micelles, by contrast, will actually make that layer the densest at constant temperature.

Therefore, that layering might turn out to be pretty stable.

So in order to get those four layers, I'd say that all you would need would be to produce four zones of turbulent mixing as you 'glugged' in the milk. I am visualizing the cold, dense milk going down the middle of the glass, generating four roughly donut shaped circulating cells of coffee; then when the milk hit the bottom of the glass, it would reflect off the bottom and come back up on the sides. Most of it would sucked in by the bottom cell, but some would continue up the sides and so on through four cells.
posted by jamjam at 11:34 PM on February 21, 2010 [1 favorite]

Skim milk.
posted by jamjam at 11:36 PM on February 21, 2010

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