Dalton's law (And problems from it)

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#1: Post by rpavlis »

As a retired University chemistry professor, I hope it is in my power to provide some help understanding some problems that arise using machines such as the Europiccola and the like.

Around 1800 a man by the name of John Dalton stated his law of partial pressures. It says that when gases are mixed, the total pressure is equal to the sum of the partial pressures of each gas. Another principle of gas behaviour is the ideal gas law, PV=nRT. Modern students seem to call it "puvnert". P is pressure, V volume, n the number of moles, R a constant, and T the temperature in Kelvins. Still another is the principle of vapour pressure. Molecules in liquids and solids are held together by intermolecular forces of widely differing strength depending on molecular structure. Kelvin temperature is a linear measure of average molecular translational energy. Vapour pressure results from molecules in liquids (and sometimes solids) having sufficient energy to escape the intermolecular forces.

When we turn start a lever espresso machine it is a closed system. The space above the liquid is filled with air and a small amount of water vapour. Atmospheric pressure is usually around 100 kpa or 1 bar. The vapour pressure of water at room temperature is about 3 kpa. Inside the reservoir the air pressure is about 97 kpa and the water pressure is the vapour pressure, 3 kpa.

When we turn on the heat the temperature rises. The partial pressure of the air will raise by PV=nRT, and the water pressure will rise as its vapour pressure rises. Some of the air, however, is forced by the rising pressure into the upper part of the group above the piston which remains fairly cool because this air does not exchange with the reservoir. On machines with pressurestats the heating element is shut off when the total pressure inside reaches about 200 kpa. The air pressure at this point is a bit over 100 kpa and the water vapour pressure is a bit under. This results in a boiler temperature of around 100C. The group is not heated much, because the water vapour diffuses very slowly through the small passage to it. Some call the air pressure false pressure. Actually there is NOTHING false about this air pressure! We must get rid of this air, so we open the steam valve. Most of the air is quickly swept out.

If we touch the group at this point it is only slightly warm. While the air is being released we also need to raise the group lever about 3/4 of the way a couple of times to purge it of air too. It almost instantly becomes hot to the touch, hot enough to burn one's fingers. With the air gone the only gas in the system is now water vapour. The pressurestat turns off when the water vapour pressure reaches about 200kpa, around 120C.

Now we raise the lever and allow a few mL of water to pass through. The top of the group is already at 120 degrees, kept there by steam constantly condensing to keep it there. This heats the bottom. Now we put our filter basket in the portafilter and raise the handle. Air rushes through the porous coffee into the space below the portafilter. When we get the handle clear to the top the opening to the water inlet is exposed and very hot water enters inside the piston skirt. Some of it vaporises and mixes with the air--Mr. Dalton is at it again. There is a burst of pressure which forces much of the air downward through the coffee again, along with a lot of water vapour. As long as the coffee is not flooded with liquid water gases pass through it, and air is lost from the system. Once the coffee floods water is so viscous that the remaining air is trapped. If the piston skirt or cylinder wall be too cold not enough air will leave before this occurs and the pull will be spongy.

When we pull the handle down the pressure increases to about 1000 kpa. The vapour pressure of water is about 90 kpa at the 95 or so degrees of the waer, so 910 kPa is air. Gases are much more soluble at high pressure. Some of this high pressure air dissolves in the water. The high pressure also forces the water through the coffee. As it passes through the dissolved air forms bubbles as the pressure falls and air solubility decreases. This air interacting with surface active materials in the coffee form the foam which we call crema!
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#2: Post by ManualWorker »

This is very thorough indeed. Lots of food for thought, though as an absolute layman in physics I will need to read over a few times to get to grips with the formulas. Never thought of purging the air in the group when relieving the false pressure (I guess that's still what we call it...?). I tried it and it does make a difference for the group temperature. Thanks a lot!
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#3: Post by yakster »

Thank you for the post on Dalton's Law. I skimmed it this morning and just now re-read it. The first time I read it, I recognized some formulas but nothing much got through. The second time, I'm starting to see the application to espresso and it has increased my understanding of the process. I'll probably have to read it a few more times, though.

Again, thanks.

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#4: Post by yosetl »

One interesting point to me is the interaction of water vapor with the coffee puck.
I never aware of this phenomena.
Will this be another contributor factor to uniqueness of the shot resulted from lever machines?

Assuming that this mechanism work with dipper tube machine such us La Pavoni.
It makes me wondering , what happen with the HX lever design?
where there is not much vapour generated when fresh water pass through the HX tube.
As with most things in life, espresso journey is better when it is simpler and sensible.

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#5: Post by rpavlis (original poster) »

It is interesting to notice that if the vaporisation of the first water to enter the group did not raise the internal pressure and displace a large portion of the air, it would be impossible to get more than a trace of water into the group at all! The absolute pressure in the reservoir is near 200 kPa. The air partial pressure has to be not much less than 100 kPa, and the vapour pressure of water at 95C or so is about 90 kPa. After just a few mL would get into the area below the piston the pressure there would be 200 kPa like the reservoir and no more water would come in! (Remember the atmospheric pressure is about 100 kPa.)

As one lifts the handle one can actually feel that suddenly the force required to lift it falls dramatically as the first bit of water enters and vaporises forming water vapour. Sometimes there is even a faint audible sound. After that one no longer has to provide force to keep the handle from coming back down.

It is apparent that the turbulence in the liquid water during the filling process most facilitate dissolution of the air that leads to crema because it allows more water to contact the liquid water-vapour interface.

The way that the La Pavoni machines are designed so that the water enters against the piston skirt rather than sprays directly into the space below the piston must help delay "flooding" of the coffee and help purge more air from the space so more water can get in.

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#6: Post by hbuchtel »

Fantastic! Posts like this are one of the things that makes this forum great.
...if the vaporisation of the first water to enter the group did not raise the internal pressure and displace a large portion of the air, it would be impossible to get more than a trace of water into the group at all!
This is the first time I've seen an explanation of this phenomenon! And I've been asking for a while...

Many thanks. I'm off to make an espresso now. :)

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#7: Post by jonny »

Nice post. I'd like to add something slightly different but related all the same that might be of interest as well. I have a machine without a vacuum breaker. Every morning I would experience a phenomenon in which shortly after the power switch was flipped, a disturbing explosive sound come from the machine. The whole thing sounded like it was trembling on the brink of eruption. It startled me several times, especially since I built it myself! I learned though that opening the steam wand would halt the sound immediately. I was puzzled and never did find an answer despite lots of HB and google searches. Not until chemistry 222 this past term did I finally discover what was happening. Eureka! Here is the low down.
1. Open the boiler cap, fill with water. Replace the cap. At this point I have filled the boiler with water but also air from the room entered to fill the space above the water. simple.
2. Turn on the machine to begin heating. When the pressurestat reads it's max set pressure, it switches off. However, this pressure is created by the air in the boiler from the start plus some vapor from the heated water. The sum of the pressure from the water vapor and air equal the total pressure. The pstat doesn't know the difference, pressure is pressure. This is "false" pressure as we know it. Proper pressure, improper temperature. It should be called false temperature.
3. The steam wand is opened which expells the air which drops the boiler pressure and allows it to continue heating to full pressure with a saturated headspace of water vapor. Once the pstat clicks off again, the machine is "ready"
4. When coffee is had, and evening is nearing, the machine gets turned off. The boiler cools and the water vapor present in the headspace returns back to the water, now at room temperature.
The twist happens here! The headspace in the boiler is left utterly empty! It used to be occupied by water vapor but now that that is gone, nothing exists there. No air to fill the void because the boiler is sealed. This here is a vacuum!
5. Now we have a closed boiler at room temp (25 c) and near zero atmospheric pressure. If we refer to the phase diagram for water (water is special if you are into this stuff :wink: ) we see water at 1 atm boils at 100c, but can boil at different temperatures at different atmospheric pressures (hence different boiling points at different altitudes and hence why boiler water temps are unaffected by elevation).

http://www.askamathematician.com/2009/1 ... -of-space/ (also some insight into this very topic... did not even mean to link to this subject!)
Here is the kicker, in a vacuum, or near vacuum, water boils at drastically lower temperatures (why our blood boils in space). Once all of this hit me I knew exactly what was happening. When the heating element kicks on in the water at this low pressure, it almost instantly causes the water to rapidly boil which was the cause of all the disturbance. After I realized this, I let the machine do this and continue to heat to full pressure. The noise slowly diminished over the entire duration of heating and when the element clicked off, the machine was at full pressure and temperature, no bleeding of air because there was none! but that noise sure was not pleasant. Anyone who has a machine with no vacuum breaker may experience the same occurence.

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#8: Post by sorrentinacoffee »

Thanks so much! MY PV Lusso does exactly this- if I turn it on after it has cooled down- starts deep rumbling. I knew it was related somehow to the 'false pressure' as bleeding it off always stops the rumbling completely.

Only odd thing is I think as my machine has gotten older it seems to rumble more. I don't like the sound of the rumbling- I was worried it might damage the element.

Thanks to the OP for this description of the process. I have wondered about the physics of 'false temperature'- ad I have noted the phenomena (now explained) when water does not want to go into the group head...

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#9: Post by peacecup »

This is all very interesting. And one good reason to have a open boiler machine, such as the magic Caravel, on hand at all times (which I don't due to a lack of PF!).

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#10: Post by allon »

I'd wondered how the air in the cylinder affected things - now I see that it is expelled. Neat!

So, how does this work in an open boiler lever machine, where the water isn't flash boiling on entry to the cylinder?
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