Extraction Uniformity and Channeling

For a while now I’ve been trying to understand the details of channeling in pour over coffee, and I found it very difficult to find a convincing description of why channeling (and thus astringency) happens suddenly when we grind a bit too fine, even if the surface of the coffee bed looks flat at the end of a brew.

Yesterday I finally found a scientific paper about percolation in non-uniform porous media that I think may be the missing piece to how we think about channeling.

Before I get into it, I’d like to briefly try to explain why a Google search for percolation returns a lot of stuff not obviously related to water penetrating a porous medium. It happens that the maths which are useful to describe water traversing a porous medium are also very useful to describe many other systems in physics. This edifice of mathematics called “percolation theory” turns out to be extremely useful in describing large statistical systems like those often encountered in quantum physics, and therefore most of what you’ll tend to find online is specifically centered around quantum or particle physics rather than brewing coffee.

So, back to the scientific paper above – the authors used a computer simulation to model the details of how a fluid flows in a disordered set of obstacles, which is exactly what happens when we brew coffee. Water flows around our coffee particles, and because they have variable shapes and sizes, the voids between them (which we can loosey call “pores”) are also very disordered. Water will flow faster where the voids are larger, and slower where the voids are small.

This is a consequence of two things: the “no-slip boundary condition” that states the layer of water immediately touching a solid surface must have zero velocity; and the fact that water is viscous means that subsequent layers of water can’t easily have extremely large differences in velocity. The no-slip boundary condition is a consequence of the adhesion between water molecules and solids being larger than the cohesion of water molecules within themselves; it is true in most typical real-life conditions, and coffee brewing is one of those.

In other words, if you imagine a small “tube” of spacing between coffee particles with water flowing in it, the thin layer of water on the sides of the tube that touches a coffee particle is not moving, and the layer immediatey on top of it (toward the center of the tube) can only move slowly. The next layer of water on top of all that can move a bit faster than the last one, and this trend goes on until you reach the layer in the center of the tube. You can imagine that a wider tube will have a larger central flow, and therefore also a larger average flow.

Here’s what this looks like in a computer simulation:

You can see how the flow of water is not very uniform, and some clumps of particles tend to be isolated from most of the flow (in the blue regions). In the context of coffee brewing, these particles will get under extracted. But now let’s see what happens if we pump up the flow of water, by applying more pressure on it:

If you look carefully at the second image, you’ll notice that there are now much less clumps of particles that are isolated from the flow of water, which is now overall a bit more uniform than before (although it is still not perfectly uniform). The authors decided to characterize this global flow uniformity in an objective way – this is great for us, because it directly impacts the uniformity of extraction. To do this, they simply measured the standard deviation or water’s kinetic energy (its energy of motion) across the pixels in the simulations, and they called the inverse of that quantity π. Larger values of π mean that the flow is more uniform, and smaller values mean that it’s very non-uniform, or “localized” in only a few paths as they call it. A perfectly uniform flow would have π = 1 (this can’t happen even with perfectly uniform spherical particles, because water still has to get around them), and an extremely non-uniform flow would have π close to zero. The authors parametrized the flow velocity in terms of the “Reynolds number” (Re), which we don’t need to get into here; we just need to realize that a higher Reynolds number corresponds to a faster overall flow.

As you can see, very slow dripping rates correspond to a “flat” regime with very poor uniformity that doesn’t depend much on overall flow rate, but above the threshold of Re ~ 0.6 (or log Re ~ -0.25) you start getting more uniformity as you have more overall flow. Now the question is: what Reynolds numbers correspond to realistic V60 preparations ? Are we in the regime where flow has an effect on uniformity or not ?

To answer this, I used the geometry of Hario’s plastic V60 with my typical 22 grams dose of coffee and the properties of water at a typical V60 slurry temperature of 90°C (194°F – this corresponds to a kettle set to boiling) to translate this into a V60 dripping rate instead, in grams per second. The threshold below which flow has very little effect on uniformity (Re ~ 0.6) corresponds to a V60 dripping rate of ~ 0.2 g/s, which is extremely slow. If we transform the x-axis of the figure above to talk about V60 dripping rate, and plot it in linear rather than log space, we get this:

I removed a few data points in the “low flow” regime for visibility because they were very crowded.

If you want to measure your V60 dripping rate you need to use a brew stand and weigh your beverage rather than the total water, and see how fast it goes up with time during your brew. To do this I use two Acaia scales (a Pearl and a Lunar) and a Hario brew stand (make sure your server is not too tall; I use the 400 mL Hario Olivewood one; apparently it’s only on Canadian Amazon) which allow me to build detailed brewprints like this one:

If you focus on the dark purple dashed line, you’ll see that my flow rate went from ~ 3 g/s when the V60 had the most water in it, down to ~ 1 g/s when it was almost empty, placing me right in the regime where flow rate affects flow uniformity, and therefore extraction uniformity, quite a lot.

Here’s why I think this is really interesting: this could explain why brews suddenly become astringent when we grind too fine, even if no channels were physically dug into the coffee bed by the flow of water. I think it would be confusing to call this effect of low-velocity non-uniform flow “channeling”, and I’d rather keep this word for situations where the coffee bed is eroded by water and coffee particles are pushed away to form a channel. Rather, I’d prefer to speak about this as “flow uniformity”, or its direct consequence “extraction uniformity”.

Speaking of which, there is one major limitation to the computer simulation these authors made: it treats the bed of coffee as a fixed and immovable object. Therefore, no bed erosion can occur, and no channels can be dug by water. This is why their simulation tells us that “the fastest flow is always best”, which may have you want to apply 150 bars of pressure on your pour over. If you did this however, you’d find that your coffee bed would quickly erode and channel pretty badly, resulting in a super astringent brew (and probably an exploded coffee server). Espresso brewing often faces this challenge: you don’t want flow to clog, but you also don’t want to destroy your coffee puck by eroding it with a very large flow and pressure. This is partly why puck preparation became very important in espresso brewing, as a way to make the coffee bed structurally more robust against erosion.

That’s a lot of information, so I think it would be good to remind ourselves of all the possible sources of non-uniform flow can be:  

• Classical channels, i.e. water pushed away coffee particles to form a void space. Those channels will appear more easily if coffee particles are lighter (therefore smaller), and may be visible from the formation of hollows at the surface of the coffee bed. This will also happen more easily if the global flow of water is too intense by applying a lot of pressure on it, and can be mitigated by compressing the coffee bed with puck preparation like we do when pulling espresso shots.
• The uniformity of your grinder’s particle size distribution will directly affect flow uniformity because it governs the uniformity of void spaces between the particles.
• A flow that is too slow, either from filter clogging or a coffee bed resistance that is too high, will make the flow of water less uniform even in the absence of classical channels.
• Clogging your filter will also likely not happen everywhere at once on the filter, causing the flow to be even less uniform because it will only pass where the filter wasn’t clogged.
• Poor blooming that leaves dry spots in your coffee bed will also make your flow less uniform, because the coffee bed will have more resistance in these dry spots (dry coffee is more hydrophobic than wet coffee).

This realization made me think that maintaining a more stable flow of water through the coffee bed is crucial to get a good, uniform extraction. Here are a few predictions I think I can make based on the considerations above:

• Applying a gentle pressure (or suction) on a pour over would allow us to grind a little bit finer without astringency, and therefore reach higher extraction yields, more particle size uniformity and better brews overall. I think this is only true up to a point, because if you apply too much pressure or grind too fine, then you need to care about puck preparation like for espresso.
• Using James Hoffman’s continuous pour method rather than the two-pour method might produce more evenly extracted brews, because it eliminates a moment of slow water flow between the two pours where less water in the V60 is providing downward pressure. This is completely independent of temperature stability.
• Using a warmer slurry temperature will make water less viscous, which will make it flow faster and therefore more uniformly.
• Using too much water and cutting off the brew at the desired beverage mass may allow us to eliminate that final moment of slow water flow, and further improve extraction uniformity.
• Using many pours will produce a less uniform extraction unless you compensate with a coarser grind setting. This is doubly true not only because less water in the V60 will be pressing down on the coffee bed, but also because the slurry temperature will be lower and water will be more viscous.

As you can imagine, I’ll now definitely try James Hoffman’s pour over method, and I will also investigate whether cutting off a brew produces a better coffee ! I’ll also pay a lot more attention to my V60 dripping rate and the coffee bed resistance that I calculate for my brews.