There have been interesting discussions on Decent Diaspora (the Decent Espresso forum) recently, attempting to quantify puck resistance. The idea of puck resistance comes from the analogy between electricity and hydraulic fluids: voltage<->pressure, current<->flow, and
resistance R = V / I <-> R = P / F or sometimes R = P / F^2.

Puck resistance may be a useful measure of how the puck erodes. Here is an example:


In the above graph, I have plotted pressure (green) and flow (dark blue) data from a spring lever profile extraction on my DE1+. Puck resistance (both P/F and P/F^2) is displayed. Resistance increases as the puck saturates and pressure rises to 9 bar, then declines as the extraction continues.

Another example with a flat 9 bar pressure profile:

RapidCoffee wrote:...or sometimes R = P / F^2.

Why F^2?

I've seen this subject discussed in Illy as well as a paper on moka pots. In both cases the relationship was given as linear between P and F -- Darcy's Law. It seems likely that the resistance is itself a function of the pressure and I'm guessing that in that forum the relationship is being determined empirically. But looking at the graphs I can't see why F^2 is better than F. What am I missing?

Just curious.

jpender wrote:Why F^2?

Good question! As I understand it, this helps account for the observation that small changes in flow can lead to large changes in pressure. Some systems apparently are best modeled with a squared relationship ("laminar flow through a single hole in a plate"). So I decided to plot it both ways.

There isn't consensus yet on how to compute puck resistance (other formulas are also being explored). The puck changes throughout the extraction: swelling as the grounds saturate, compressing as pressure builds, losing mass as the shot progresses. This might even require a dynamic model (particularly for puck compression), which would complicate matters further.

On a more practical note: is this useful? Does a change in puck resistance tell us anything new about the extraction?

BaristaBoy E61 wrote:Is this not excessive navel-gazing; how many angels can dance on the head of a pin?

Oh no, we'd never do that on H-B.

BaristaBoy E61 wrote:What's the goal here, to come up with a kind of 'Ohm's Law' for coffee pucks?

Something like that. Until now, exploring the well-known analogy between electricity and hydraulic flow in espresso has not been readily available. It's possible that the pressure-flow ratio tells us something useful about puck erosion.... which in turn might provide insight into when the puck is fully extracted.

RapidCoffee wrote:Good question! As I understand it, this helps account for the observation that small changes in flow can lead to large changes in pressure. Some systems apparently are best modeled with a squared relationship ("laminar flow through a single hole in a plate"). So I decided to plot it both ways.

How does it help? The curves you posted using F and F^2 look very similar in character.

I agree that H-B is as good a place as any for geekery or navel gazing or whatever. Both Illy and Navarini took the trouble to discuss this subject. Illy only seems to have examined the first part, where the resistance increases. They came to the conclusion that particle migration was responsible for the pressure increase. Navarini looked at the whole brew cycle and in his experiments the resistance never decreased. Granted, a moka pot is not an espresso machine. But how would you explain that with a model of puck erosion?

It seems almost as if the rate of drop in the puck resistance might be a more telling indicator of puck extraction rather than the resistance itself.

Puck resistance is something we briefly discussed back in the ramble, and it seems that there is a limit to the analogy:

Some smart person wrote: For practical purposes it can be approximated that such ''supercompactible'' filter cakes with n > 1 yield the same flow rate independently of the pressure applied: increasing pressure only increases the compressed layer adjacent to the filter cloth...
...The filter resistance often is concentrated in a thin, compressed layer facing the filter medium, the rest of the cake being very porous and wet.

Cheers!

- Jake

Jake_G wrote:It seems almost as if the rate of drop in the puck resistance might be a more telling indicator of puck extraction rather than the resistance itself. Puck resistance is something we briefly discussed back inthe ramble...

Sorry, forgot about this interesting discussion from a couple of years ago.

jpender wrote:How does it help? The curves you posted using F and F^2 look very similar in character.

Agreed: standardizing the definition of puck resistance would be good. (Being a practical guy, I'd opt for most useful rather than most theoretically accurate.)

jpender wrote:I agree that H-B is as good a place as any for geekery or navel gazing or whatever. Both Illy and Navarini took the trouble to discuss this subject. Illy only seems to have examined the first part, where the resistance increases. They came to the conclusion that particle migration was responsible for the pressure increase. Navarini looked at the whole brew cycle and in his experiments the resistance never decreased. Granted, a moka pot is not an espresso machine. But how would you explain that with a model of puck erosion?

With all due respect to Illy et al, I cannot explain their results. Common sense and visual observation suggest that puck resistance does decrease during extraction, and particle migration is not the only (or even the primary) mechanism for resistance increase.

When the extraction begins ("preinfusion" stage), flow is high and pressure is near zero. At the end of preinfusion, the puck is saturated, coffee grinds have expanded, and the first drops begin to appear at the bottom of the basket. Puck resistance now increases sharply, the flow rate drops, and pressure rises sharply (to ~9 bar in a traditional espresso shot). As the extraction progresses, the puck erodes: soluble material washes out of the grinds into the cup, and small insoluble particles (fines) migrate downward. Puck resistance to flow eventually decreases, and flow rate correspondingly increases if you maintain constant pressure. Eventually most of the soluble material extracts from the puck, most of the particle migration finishes, and both puck resistance and flow rate level off to steady state values.

As far as utility goes: when do you end an extraction? You can use brew ratio to compute a predetermined espresso weight in the cup, or monitor the extraction color (look for shot blonding). But as Jake notes, monitoring puck resistance could help determine the level of puck extraction. This might be useful for identifying over/under extraction issues.

jpender wrote:Navarini looked at the whole brew cycle and in his experiments the resistance never decreased. Granted, a moka pot is not an espresso machine. But how would you explain that with a model of puck erosion?

RapidCoffee wrote:...As the extraction progresses, the puck erodes: soluble material washes out of the grinds into the cup, and small insoluble particles (fines) migrate downward. Puck resistance to flow eventually decreases...

How does that explain a case where the resistance fails to decline?

jpender wrote:How does that explain a case where the resistance fails to decline?

While I've seen situations where more pressure alters the puck resistance to a point where no more flow comes out, I'm not sure I've ever seen a shot where the puck resistance fails to decline.

Do you have an example aside from Navarani and the Moka pot experiments? Obviously a pressurized portafilter would be a good example of a perceived or forced steady puck resistance, but I think the puck eroding is a very real thing that happens in a very predictable manner when you are literally removing 15-25% of the mass from the cake in dissolved solids.

I also theorize (from filter cake analysis) that increased puck resistance during so called "preinfusion" is caused not just from fines and other solids migration, but from actual hydraulic compression of the coffee particles which form the cake. Preinfusion lessens this compression because when water fills the voids it applies pressure in all directions, but when a dry coffee cake is supporting wetted layers above it, all the pressure is downwards towards the bottom of the basket. Thus a shot that wets the basket before ramping up to full pressure saves the lower layers of the puck from having to support the full brunt of the pump pressure.

Also, the linear range of puck resistance is actually quite narrow as can be seen as both models (F and F²) spike to about the the same level at the point of saturation. This is the point where 8, 9 or 20 bar will likely flow the same because the compacted cake can only flow "so much", regardless of the pressure applied. I really do think that the rate of change is the thing to look at in terms of extraction. A shot isn't complete when P/F² hits some certain point, it's far more likely that the shot is complete when the rate of change of puck resistance hits zero...

Cheers!

- Jake