# Gravity “sorting” and French Press coffee

I have read about the Earth's sorting of different-sized grains of sand and such. Larger particles are supposed to fall through water faster. I've seen it demonstrated before and have full faith. But this morning, on emptying my French press carafe, I was puzzled on seeing that the finer (smaller) coffee grounds had settled, and always do seem to settle (each morning) beneath the coarser (larger) grounds. So,

1. can someone refresh me on gravity's sorting mechanism? I know it has to do with air- or fluid- resistance, surface-area-to-volume ratio, but I'm pretty rusty on the specifics. How would one account for all possible particle shapes? Or do we just assume perfect spheres?

2. Does anyone else use a French press? If so, have you noticed similar? If so, how do you fit that into this picture?

• This is just a hunch, but maybe grounds trap air inside of them, so larger coffee grounds are more buoyant? – user140323 May 17 at 14:44

This made me go and have a coffee, and I also saw the sorting. Indeed, I have spent a little bit too much time thinking about the physics of French presses (mainly how to avoid percolation breakthroughs and the rate of diffusion of taste compounds from non-spherical grains).

A spherical grain will be subject to a gravity/buoyancy force of magnitude $$F_{g}=-gV(\rho_{grain}-\rho_{water})$$ and a drag force $$F_{drag}=6\pi\eta r v$$ (Stokes drag for sphere). That gives a terminal velocity $$v=\frac{gV(\rho_{grain}-\rho_{water})}{6\pi\eta r} = \frac{2 g r^2 (\rho_{grain}-\rho_{water})}{9\eta} .$$ Notice how it scales as $$\propto r^2$$: larger particles fall or float faster.

In the case of coffee there is a blooming as air (and CO$$_2$$ from roasting) inside the grains expands out, and this makes larger grains extra quick to rise since it boosts their effective radius. Stirring with a spoon after adding just some water reduces this effect, but will not stop the sorting.

Ground shapes likely have only minor effects: this is a qualitative analysis, after all.

• As well as the blooming of large grains, I suspect that the small grains lose their gas content & become water-logged faster, which increases their density. – PM 2Ring May 17 at 15:25

You are correct that, intuitively, one might expect the heavier particles to settle out faster. That's only the case, however, if there is no other agitation of the grains. In granular convection, for example, one may observe the larger particles move to the top (the "Brazil nut effect") under agitation. The simplest way to think about it is that the bigger particles bounce around and leave spaces that the smaller particles can fall through. The smaller particles move around and leave spaces, too, but those spaces aren't big enough for the larger particles to get through.

The motion of the grounds in a French press may be complicated by the initial flow of the hot water (both from pouring and stirring), from thermal convective flows in the coffee as it cools slightly at the top, and by the agitation of the coffee by the screen during the press.

It would be interesting to do some experiments to characterize the actual amount of sorting of the grains, and some modeling of the flows and their effects on the sorting.