Espresso puck physics: how water moves through the bed

A bed of coffee as a porous medium

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Water gets through a packed bed by way of the gaps between the particles. The standard description of such flow is Darcy's law: the flow rate equals the bed's permeability, times its area, times the pressure difference across it, divided by the liquid's viscosity and the bed's depth. Permeability is the single number that says how easily a given packing lets liquid through. A deeper bed, a more viscous liquid or a less permeable packing all slow the flow for the same pressure.

One group, at a British university and a coffee company, measured flow against pressure through packed beds of roast and ground coffee and fitted Darcy's law to the result. It was not done on an espresso machine. A cell 37 millimetres across held 7 to 9.5 grams; water at 80 degrees was run through for ten minutes, until the coffee was fully extracted and the bed had stopped settling; and only then was the flow measured, at pressures from half a bar to four and a half. The permeabilities came out between roughly 3 × 10⁻¹³ and 3 × 10⁻¹⁴ square metres across four grinds and three packing densities, a spread the authors put at seventeenfold. The permeability predicted from the dry particle sizes by a standard formula did not match what was measured, and the authors suggest that the way a bed consolidates changes its packing more than the simple loss of pore space would imply. They watched it consolidate: under flow the beds shrank by anything from nothing to 31 per cent of their depth, mostly within the first minute, and the finer grinds shrank most. They also point out that a real shot is over within the unsteady first minute that their method waits out.

Permeability is not one number for a whole puck either. A group that scanned capsules of ground coffee by X-ray tomography and simulated flow through small cubes of the scanned structure, in a paper published in 2023, found that the permeability worked out at different places in the same bed varied widely, and more so the coarser the grind, even though the average rose steadily with coarseness. The capsules came from an Italian coffee company, where one of the authors works. A bed is uneven before any water arrives.

Where the pressure goes: a model of the path

CoffeeHQ explanation

A model of the water's path, drawn from the description of a cafe machine in one study that put a second pressure sensor under the basket. It is a way of seeing why the figure on a machine's gauge is not the pressure on the coffee.

More pressure does not mean proportionally more flow

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Darcy's law with a fixed permeability says that doubling the pressure doubles the flow. A group at the University of Warsaw tested that on a cafe machine with one coffee, an 18.5 gram dose in a 58 millimetre basket, a needle tool and an automatic tamper, at basket pressures from 1 to 12 bar. What they compared was the steady flow about 100 seconds after the pump started, long after a normal shot would have been stopped and after nearly all the soluble material had gone, in 60 brews spread over eleven pressures. Below about 5 bar that flow rose with pressure, in what the authors call a Darcy-like, linear response. Above that it stopped rising: across the pressures normally used for espresso, more pressure bought no extra flow at that late stage. Read from the paper's own chart, the highest flow was at about four and a half bar, and from there to 12 bar it drifted down by roughly a fifth; the points below 5 bar also climb more steeply than a straight line through zero would. With the traces lined up at the moment five grams had reached the cup, the cup filled fastest at about 5 bar. In the traces of flow against time, the first half minute, the part a drinker receives, shows the flow still climbing at every pressure but the lowest.

Their explanation is that the bed is elastic. The water pressing through it squeezes the particles together, most of all at the bottom, the pores narrow, and the permeability falls as the pressure rises. A model built on that idea, of the kind used for soils and rock, reproduced a straight line at low pressure and a plateau. It does not produce the slow fall in flow at the highest pressures, and its curve runs above the measured points at the lowest ones. They cite the bed measurements described above as showing Darcy-like behaviour at comparable pressures. That earlier study went no higher than four and a half bar, so it does not show where the straight line ends.

The tomography group offers a second contribution. Its simulations found that at the pressure gradients of espresso the water moves fast enough through the pores for its inertia to matter, which makes a bed look less permeable at high pressure even if nothing in it moves. A paper published in 2026 comes to a more cautious answer by a different route. Its authors scanned small samples of two coffees at eleven grind settings, loose in a narrow tube and not tamped, computed the permeability of each scan, and fitted a formula that predicts permeability from the mean particle size and the share of connected pore space. Putting a typical recipe through it, about 40 grams in about 30 seconds from the fine end of their range of grinds, they find the flow laminar but close to the point where inertia begins to count, and say that grinding finer or packing tighter for the same flow could cross it. Neither group measured flow through a wet bed in a machine: both computed it on scans of dry coffee. Compaction and inertia are not rivals: both bend the line the same way.

The Warsaw paper also records where the usual figure comes from. Nine bar, it says, is often traced to the force achievable with the first lever machines of the late 1940s. That is a history, not a finding that nine is best, and the same paper's plateau is one reason a machine set to eight and a machine set to ten may behave more alike than the numbers suggest. Its authors are careful about reach: one coffee, one grind, one dose, and a systematic study of other conditions, they write, remains to be done.

The first seconds: wetting, swelling and gas

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The bed starts dry, with air and leftover carbon dioxide in its pores. One group put a modified home espresso machine in an X-ray scanner and made a tomogram every second as water entered a hand-tamped bed, one shot at a fine grind and one at a coarse. In the fine bed the water first spread across the top, hardly entering for two or three seconds, then moved down as a fairly level front and had wetted the whole bed by about seven seconds. In the coarse bed it went faster and less evenly, running ahead near the basket wall. A model of flow in a partly wet bed, with the pump's behaviour included and two quantities adjusted to fit, reproduced the fine-grind front; the authors did not attempt the coarse one.

The same model says something about the empty space above the coffee. Water pools there, the air trapped in it is squeezed, and the pressure on the bed builds as the space fills, so the bed is wetted under neither a steady pressure nor a steady flow. In the model the pump's delivery falls to about a fifth of its starting rate within the first second and then climbs again. Other authors have put that dip in flow down to swelling, escaping gas or the bed rearranging; this model produces it from the pump and the headspace alone, and its authors suggest the pump is at least part of the cause.

A mathematical model from some of the same authors, read in its summary and conclusion, treats that first passage in detail. Its conclusion is that a significant part of the dissolved material that ends up in the cup is extracted during infiltration, before steady flow is established, with the smallest particles supplying enough to saturate the first liquid. That is a model's result and has not been checked against measurement in anything read here, but it is a reason to doubt accounts that treat the wetting stage as a mere preliminary.

The particles also swell as they take up water. A simulation by another group assumed a small swelling, about 3.6 per cent in size, and asked what difference it made. On a machine that fixes the flow rate, very little. On a machine that fixes the pressure, which is most of them, the swelling narrowed the gaps, slowed the water and raised the strength of the drink considerably, and more so for finer grinds. The Warsaw group's scans of a puck before and after brewing show what they describe as considerable swelling and a rearrangement of the structure.

What none of this establishes is what pre-infusion does to taste. Wetting the bed at low pressure before applying full pressure is a sensible-sounding way to let it swell and settle evenly. No study read for this page tested whether it makes a shot more even or better.

Fines: most of the particles, most of the surface

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Coffee ground for espresso has two populations of particle. A study that measured them by laser diffraction calls those above a tenth of a millimetre boulders and those below it fines. At one of its grind settings, 99 per cent of the particles by count were fines, and they carried 80 per cent of the surface area. Grinding finer made the boulders smaller and the fines more numerous, while the size of the fines stayed the same, which the authors take as a sign that fines are made at the fracture surface and are not simply small boulders.

Fines matter to flow because they fit in the gaps between larger particles, and it has long been proposed that they migrate with the water and block pores lower down. The Warsaw paper's assessment of that literature is that models with migrating fines explain some features of espresso flow, but with limited experimental validation, and it lists the migration of fines, jamming and the formation of preferred paths as things still to be measured.

The one direct experiment read is reassuring about fines. A Swiss group sieved fines out of ground coffee and, at three of its six grind settings, swapped one, two or four grams of a 20 gram dose for them. More fines made the bed less permeable and the shot slower, which is the paper's main finding. But extraction yield plotted against shot time fell on a single curve, with or without added fines, and the flow of a coarser grind with fines added was not markedly different from that of a finer grind. Their one taster, who was experienced but neither blind nor part of a panel, found no penalty for a higher share of fines. That is a single coffee and a single palate; it is also the only test found.

The experiment the argument turns on

Accounts differ

In 2020 a group of physicists, chemists and baristas published a model of espresso and a set of shots made in a cafe to test it. The model assumed that water flows evenly through the bed. On that assumption, grinding finer should always extract more: more surface, shorter distances inside each particle, a slower shot.

The shots did not behave that way. With 20 grams in and 40 grams out at 6 bar, shot time rose in a straight line as the grind was made finer, but extraction yield rose only to a point and then fell. The same yield, 22 per cent, was reached at two quite different settings, one fine and slow and one coarse and fast. The authors chose 6 bar because at 9 the finest settings clogged.

Their explanation is that below a critical grind the flow stops being even. Parts of the bed are partly clogged and under-extracted while the rest is extracted further than the average suggests. By comparing the model with the measurements, and assuming the extreme case in which the clogged regions receive no flow at all, they report a gap between predicted and measured yield of about 13, 6 and 3 per cent at their three finest settings, which on that assumption is the share of the bed the water never reached. They add that the truth is more likely a spread of partly extracted regions, which a single reading cannot resolve.

A second paper, from one of the same authors with others, tested a different mechanism. It built the simplest model that could show uneven flow, with two pathways that start slightly different, and found the same peak in yield. But in that model the unevenness is present at every grind; the peak appears when one pathway has given up all of its soluble material. Its authors say their model does not support the idea that the onset of clogging causes the turnover, and they note that one of its parameters was chosen so that the behaviour would appear.

So there is one experiment and two accounts of it, and they agree on the point that matters most to a reader: a single extraction figure for a shot is an average over a bed that was not extracted evenly, and at fine grinds it may be a poor guide to what is in the cup. Neither group looked inside a bed while it brewed.

Channelling: five things one word is used for

Accounts differ

Channelling is used for at least five different things. They are worth keeping apart, because the evidence for each is different, and because a shot can taste wrong for reasons that have nothing to do with any of them.

Something you can see

A jet, a spurt or a pale streak under a bottomless portafilter, or a hole in the spent puck. This is an observation of the outside of the bed. No study read for this page connects what is visible from below with a measurement of uneven extraction, in either direction.

A path of higher flow inside the bed

A region more permeable than its surroundings, through which more water passes. The tomography work found permeability varying widely within one bed before brewing. A simulation by the same group of water wearing away coffee grains produced unevenness across the bed as well as along it, on the assumption that grains not fully wetted stay brittle, and their scans of two capsules after brewing showed more pore space near the outlet than near the inlet, which they take as support for it. That such paths exist is well supported; what they look like in a real basket during a real shot has not been observed in anything read.

Uneven extraction

Some coffee extracted much more than other coffee in the same basket. This is what the 2020 experiment infers from the fall in yield at fine grinds. It is an inference from an average, and the two published explanations of it differ.

A defect in how the bed was built

A crack, a gap at the wall, a clump, a tilted surface. These are the things distribution and tamping are meant to prevent. They are plausible causes of a high-flow path, and no controlled trial of any of them was found.

An effect of the container

Flow that is uneven because of the shape of the bed and not because of a flaw in it. A modelling study found that flow through a cylindrical bed of coffee is close to one-dimensional, while a bed shaped like a truncated cone has markedly uneven flow and a wide spread of local extraction. That was a study of packed beds in general. Nothing read examines espresso baskets or their hole patterns; the one study of the space above the coffee is described under the first seconds.

Dose, depth and the basket

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In the 2020 model the bed is assumed to pack to the same density whatever the dose, so its depth is proportional to the dose. A smaller dose is a shallower bed, which resists less. The model predicted higher extraction from less coffee for the same weight of drink: its curves for doses of 16 to 24 grams sit one above the other, lowest dose highest.

That is the basis of the paper's best-known proposal, to use 15 grams where a cafe used 20 and to grind coarser, reaching the same extraction with a quarter less coffee. The authors report putting it into practice in one cafe; the dose curves themselves are the model's. It is a statement about yield. A shallower bed in a basket made for more coffee also leaves more space above it. The tomography study of the first seconds shows that this space fills with water and governs how the pressure on the bed builds. No study read varies it to see what a larger or smaller space does to the shot.

The same is true of the basket. Hole size, hole pattern, wall angle and the fit of the tamper are the subject of confident trade advice. No study of any of them was found. The pages on this site that describe baskets describe what they are, not what they have been shown to do.

Tamping: two short statements of evidence

Accounts differ

The instruction to tamp with a particular force, often given as thirty pounds, is among the most repeated in espresso. The evidence on tamping force that CoffeeHQ could find in peer-reviewed papers amounts to two short statements. The authors of the 2020 study write that they explored a range of tamp pressures and did not observe an appreciable variation in shot time or extraction yield, and so standardised on an automatic tamper pressing at 98 newtons, about ten kilograms. They add that flavour differences were noted but not quantified. And a 2017 paper from a German university, which followed how fast caffeine and a second compound left espresso made on a commercial machine at different grinds and tamping pressures, says in its summary that particle size significantly affected the extraction and that tamping pressure had no detectable effect. That paper is not open and only that summary was read, so the forces it compared are not known to CoffeeHQ. Roasters and enthusiasts have published their own comparisons of tamping force online; those are not peer-reviewed and are not drawn on here.

Other papers use a fixed tamp as a control and not as a finding: 20 kilograms by machine in both the Swiss and the Warsaw studies. A review by two authors at an Italian coffee company gives the range in practice as a few kilograms, where a plate on the grinder is pushed up against the basket, to about 20 with a hand tamper.

There is a physical reason to expect force to matter less than it is given credit for, and it follows from the Warsaw model, though that paper does not draw the conclusion itself. Twenty kilograms spread over a 58 millimetre basket is a pressure of about three quarters of a bar. Once water is flowing, the pressure difference across the bed is carried by the particles, and at the bottom of the bed the load on them approaches the full brewing pressure: several bar, or the equivalent of well over a hundred kilograms on the same area. The water compacts the bed far harder than a hand does. This is CoffeeHQ's arithmetic on that paper's model and basket area, and a model's implication is not a measurement.

What tamping plainly does is make the surface level and the bed coherent, which the 2020 paper gives as its purpose: coffee must be tamped to level the bed. A level tamp repeated the same way is supported by the reasoning above. A particular number of pounds is not supported by anything read.

Distribution and needle tools

Accounts differ

Stirring the grounds in the basket with fine needles before tamping, usually called the Weiss distribution technique, is now routine among enthusiasts and in several of the papers cited here. The Warsaw group used a needle tool on every shot and describes removing clumps as necessary for good reproducibility. That is a practitioner's statement inside a physics paper. They did not compare shots made with and without it.

One group has tested an arrangement of the bed, and the test is theirs to benefit from. An Italian group built pucks in three layers, the same 15 grams ground one notch coarser at the bottom, at the usual setting in the middle and one notch finer on top, and compared them with ordinary pucks over several hundred shots. Shot-to-shot variation in flow was lower with the layered puck in four of five batches of one coffee. When the coffee was changed without touching the grinder, the layered puck's flow stayed within 15 per cent of the target for two brands whose ordinary pucks ran 25 and 35 per cent fast. The reverse order, coarse on top, extracted badly and its figures are not reported. Nobody tasted any of it, and the paper's starting point, that the best flow is one gram per second, is asserted and not tested. The method is patented and the authors are its inventors, as the paper states.

So the position is this. That clumps and uneven density make an uneven bed follows from everything above. That any particular tool or motion reduces unevenness in the cup has not been shown in a controlled comparison that CoffeeHQ could find, and a reader can test it more easily than most claims on this page.

Fast, coarse, lower-pressure shots

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The 2020 paper ends with advice that has travelled further than its evidence: use less coffee, grind coarser, and accept a shot that may run in under fifteen seconds. In the cafe where the authors tried it, shot times were routinely about fourteen seconds and a quarter less coffee was used. The claim made for these shots is that they are more reproducible and waste less. The authors say plainly that such a shot is weaker and has a different flavour, that extraction yield is not directly indicative of quality, and that the barista still has to taste.

They also say, without having run a tasting panel, that a shot at the same yield from the slow, partly clogged regime tastes more complex than the fast one, and suggest blending two shots to recover it. That is the authors' impression and is reported here as that.

The Swiss study of fines looked at the aroma above shots of different lengths with an instrument and found that it changes with shot time in a way that is not a straight line; fast shots, it suggests, have the potential to keep more of the most volatile compounds and taste fruitier. Its own taster, though, preferred that coffee at about thirty seconds and 19 to 20 per cent extraction, and the authors conclude that where a coffee tastes best depends on the green coffee and the roast, with too little information yet for general conclusions.

Fast shots are, then, a well-argued way to make espresso more repeatable, proposed from one experiment on one coffee. Whether they taste better is a question the papers leave to the drinker.

Figures in the studies, and whose they are

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None of these is a recommendation. Each is a figure one source reports, set down so that a reader can see how far the published conditions spread.

Each row comes from a different coffee, grinder, basket and machine, and three of the seven are figures a source quotes from elsewhere. They cannot be combined into a recipe.

Three comparisons a reader can run

CoffeeHQ explanation

Each changes one thing and holds the rest. The fuller protocols, with what to record and what the result cannot tell you, are on the page of experiments.

• Does your tamp force change the shot?

  Change

  Tamp three shots lightly and three as hard as you comfortably can, alternating, keeping the tamp level each time.

  Keep the same

  Coffee, dose to a tenth of a gram, grind setting, distribution, yield by weight and machine settings.

  What to notice

  Whether shot time differs between the two groups by more than it differs within each group. If it does not, force is not what is moving your shots.

• Does needle distribution make your shots more alike?

  Change

  Make five shots with the grounds stirred by needles and five without, alternating.

  Keep the same

  Coffee, dose, grind setting, tamp, yield by weight and machine settings.

  What to notice

  The spread of shot times within each group, not the average. A tool that works should narrow the spread.

• Where is the peak for your coffee?

  Change

  Step the grind coarser from your usual setting by small equal amounts across five or six shots.

  Keep the same

  Dose, yield by weight, tamp, distribution and machine settings.

  What to notice

  Taste each one. If you have a refractometer, note whether the reading keeps falling as you go coarser or rises first, as it did in the published experiment.

What this page does not claim

CoffeeHQ explanation

It gives no pressure, dose, tamping force, shot time or extraction yield as correct. It does not say that fast shots taste better or worse, that fines are harmless, or that any distribution tool works. It does not describe what a jet under a portafilter means, because nobody has measured it.

Most of what is firm here comes from a handful of experimental studies, each on one or two coffees, and none of them used a trained tasting panel. The rest is modelling. A model that reproduces a measurement shows that an explanation is possible, not that it is the right one, and two of the models here reproduce the same measurement in different ways.

One paper on tamping could be read only in its published summary. It is named in this page's sources so that a reader with access can go further than CoffeeHQ did.

What to do next

• Pressure and flow in espresso — What one study found when flow rate, grind and temperature were varied, and what profiling and pre-infusion are.
• Grinding and particle size — Why a grinder makes a distribution and not a size, and why a setting does not travel.
• Coffee experiments to run at home — Full protocols for the tamping, distribution and flow comparisons, with their limits.
• Channelling — The practical side: what to check in how the bed was prepared.
• Espresso dial-in assistant — Takes dose, yield, time and taste and suggests one change at a time.