749.5ml of water, what was the mass of the water? Or did you add by volume, and if so at what temperature?
At what temperature is the 775ml taken, also at what time? It makes a difference (3-4% error in the volume of the water/coffee). Also, it may make a difference depending on when during the brewing you take the total brew volume.
When I did this I treated 1g=1ml for water (at 15-17°C) which isn't quite right so I correct for that here. It's a small correction though.
First I filled the flask with 775 g of water at about 15°C and marked the meniscus level halfway up the (~1.5 cm diameter) neck. Then I added ~300 ml of hot water to 34.5 g of coffee and let it brew. I transferred it along with ~300 ml cold water to the flask and allowed it to cool. I topped it up to the marked line with cold water and weighed it. The temperature of the liquid was about 17°C.
Net weight: 784 ± 1 g Coffee weight: 34.5 ± 0.1g Flask volume: 775.7 ± 1.0 ml Temperature: 17°C
So water weight = 784-34.5 = 749.5 g and water volume @17°C = 749.5 g ÷ 0.9987 g/ml = 750.5 ml
The coffee (grounds, dissolved solids, oils) displaces a volume of 775.7-750.5 = 25.2 ml and that implies an overall coffee solids density of 1.37 g/ml
I repeated this with cold water and observed many suspended bubbles in the mixture. After about an hour these bubbles were largely gone and I measured a coffee solids density of 1.3 g/ml.
Netphilosopher Said:
I was trying to come up with an equation to predict brew volume so I wouldn't overflow. I use bloom suppression to eliminate the primary variable - excessive bloom - that displaces significant volume.
At the end of the brewing/extraction, though, the "mass" of the grounds is about 20% less.
At the beginning the equation that has worked for me is:
(brew water ÷ 0.965) + (coffee grounds ÷ 0.9) = estimated brew volume. This seems to predict (for me, YMMV) the stabilized brew volume at bloom dissipation and subsiding grounds during an immersion brew.
At the end of the extraction, but prior to separation the brew mass is still a solution of:
(coffee solution mass [brew water mass, minus evaporation, plus dissolved coffee solids] ÷ [similar density to water]) + (spent grounds ÷ spent grounds density) = slightly less than brew volume (based on observation).
That's pretty much what I saw in my experiments too. The initial volume implied a coffee grounds density of roughly 0.9 g/ml. But what I observed was that there was a lot of air in the system, either as small bubbles or foamy grounds. It took tens of minutes for this to fully dissipate. With the air/foam removed the density of the solids (dissolved+undissolved) was significantly higher.
This "sans air" density may not be a particularly useful metric. Even in an espresso machine there will be gas coexisting with the grounds as hot water is forced through. So "volume displaced by the coffee" probably makes more sense if one includes the gas. This makes it, like so many things in the coffee world, less predictable.
Sorry, jp, just thinking about this again over lunch.
You mention the brew mass density at 20 and 25 minutes being 1.0g/ml after you re-topped the system off (to 264ml) - so this implies that your added water made the total mass ~264g.
At 45 minutes: 18g coffee + 250g water = 268g total brew mass. Density=1.0g/ml (T=47°C) The volume displaced by the coffee = 264ml - water volume. Water volume= 250g ÷ 0.989g/ml = 253ml. So volume displaced = 11ml. Density of solids (dissolved+undissolved) = 18/11 = 1.6g/ml.
The evaporation rate was so slow that I neglected to keep track of it! I realized my error later, repeated the experiment, and observed an evaporation of only 2±1g in 81 minutes. This surprised me. I suspect the cap of grounds and foam inhibited evaporation.
End result is that I calculated the solids (dissolved+undissolved) density to be 1.2-1.3 g/ml.
I have very little confidence in these numbers. A volume difference of only 5 ml (about 2 mm of height in the AP) would change the result completely. How do I know that I'm topping the Aeropress back up to the same top? And how can I be certain that the plunger hasn't shifted? When I did my second run I put the plunger in exactly the same place (so I thought) but the total volume changed by 4 ml.
That's why I used a volumetric flask instead of an Aeropress.
---- Details: (Run #1) Aeropress volume measured with 264 ± 1 g of water @15°C 18 ± 1 g coffee 18 ± 1 g water @ 50°C 213 ± 1 g water @ 96°C T = 88°C
@20 minutes: 10 ± 1 g of water added to top up T = 67°C
@45 minutes: 9 ± 1 g of water added to top up T = 47°C 3 g evaporation loss (estimate based on second run)
total mass = 265 g (includes evap estimate) total water = 247 g
(Run #2) Aeropress volume measured with 260 ± 1 g of water @15°C 18.0 ± 0.1 g coffee 18 ± 1 g water @ 50°C 212 ± 1 g water @ 96°C
@81 minutes -2 ± 1 g evaporation +16 ± 1 g water to top up T = 36°C V = 260 ml total water = 244 g total mass = 262 g
Netphilosopher Said:
At any step of the system, the solution can be modeled as a closed form:
(solution ÷ density) + (solids ÷ density) = volume. It also has a total brew mass at any given point.
Initially, hot, it looks something like:
231g @ 0.97 + 18 @ 0.7 = 264ml, with a total brew mass of 249g. Unless I'm missing something, the brew mass density is 0.94. (this includes the foamy floating grounds).
231g @ 0.97 + 18g @ 1.3 + 12ml = 264ml. It's that 12ml of gas that dissipates over time that makes the difference.
I wasn't trying to determine exactly where the coffee was in the brew. Dissolved or undissolved, I was assuming that it would still occupy the same volume. This may not be strictly true but at the concentration I doubt it is an important factor.
I think I understand better. We're probably looking at slightly different things. Your statement that the "sans air" density may not be particularly useful is pretty true.
I just thought it was interesting that great minds think alike - I needed to figure out how to make coffee at an acceptable extraction (at least 18% or so) at maximum amount from an Aeropress, so your equation or my equation is close enough - and the difference between accounting for bloom dissipation or not.
The way I brew with the AP also periodically tops off as the bloom dissipates, and then I measure the final brew mass just before pressing, so my estimates seem to match the method I use for brewing.
Regarding using cold water, Cold brewing off-gasses SO slowly that it's really hard to figure out a real grounds density. In this case, the grounds really float around (especially on fresh coffee) even after agitation. Lots of bubbles, so my estimate for useful density cold would be closer to the 0.7 or even 0.6 g/ml.
I basically align the plane of the plunger (bottom? when inverted, "top" when reverted...) with the plane of the cylinder plus a bit. I've done it so many times that I actually have a small mark now in the cylinder - this is 110mm from the filter end of the tube. In my case this is so close to 280ml, and I can repeat this within 1% quite reliably, that I call it 280ml for all practical purposes. I wonder sometimes that the heat expansion of the plastic also partially compensates for the expansion of liquid...
It may seem like not much of a difference when it comes to volume, but the difference between hot water and cold water is pretty noticeable. The region from 0°C to 50°C is only about 1.25%, but the difference between 50°C and 95°C is 3%. This is noticeable especially if you have a decent measurement device. Even on the AP, the difference between full at 95°C and 30°C an hour later (covered to prevent evaporation) is about 2-3mm.
I think at the 45 minute mark, you can no longer count dissolved and undissolved solids as one thing - the "density" of dissolved solids is really a misnomer.
Think of salt water - (making me remember my old chem classes decades ago now! LOL ).
NaCL is around 2 g/ml as a solid. (Table salt crystals, however, are just a bit more than 1.1 g/ml based on DRY volume and crystal size)
Going by memory, Aquarium water is like 3.5% salinity - 35g salt / liter of water.
Add a 35g chunk of solid NaCl (large salt crystal or two, about 17.5 ml of displaced volume) to 1 liter of 4°C water, and the overall density of the mass is 1035g/1017.5ml, or about 1.017g/ml.
When the salt (finally) dissolves, it will occupy more like 1005ml (salt aquarium water is about 2.5-3% more dense than freshwater, again by memory - since the mass is the same at 1035, but we know that salt water density is 1.025-1.03 that of freshwater, we know what the volume of the 3.5% salt solution will be). At that point when 100% of the salt has dissolved, it's impossible to say that the density of the salt "solid" is now much more than the original 2g/ml because we think that the water is still 1000g of the total mass and still occupies 1000ml.
Example of backcalculating: (1000g ÷ 1.0) + (35g ÷ ?) = 1005 ml (a measured volume)
In this case, we would (incorrectly) assume the water still occupies 1000ml, leaving only 5ml for the salt - yielding a density of 7g/ml. We know this can't be correct - as Aluminum is 2.7, steel/iron is around 7.9... When a solid has "dissolved", it becomes part of the solution and therefore doesn't hugely increase the VOLUME. It's probably why I'm having a hard time getting much of a change in density in brewed coffee vs water - the solution is only 1.2% concentration, to start. Coffee solids aren't that heavy - I have some that I recovered from dehydration, so when they go into solution they don't increase volume and they don't make THAT much of a mass difference.
All interesting stuff... can make you think if you're not careful. ;^D
------------------------------------------ ----------------------------------------- Le café doit être noir comme le diable, chaud comme l'enfer, pur comme un ange, et doux comme l'amour.
"There is no right answer with coffee. There is only the elixir in your cup at the moment you partake."
"...I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;..." - Lord Kelvin RECIPES thread => http://www.coffeegeek.com/forums/coffee/machines/585708
I think at the 45 minute mark, you can no longer count dissolved and undissolved solids as one thing - the "density" of dissolved solids is really a misnomer.
Think of salt water - (making me remember my old chem classes decades ago now! LOL ).
NaCL is around 2 g/ml as a solid. (Table salt crystals, however, are just a bit more than 1.1 g/ml based on DRY volume and crystal size)
Going by memory, Aquarium water is like 3.5% salinity - 35g salt / liter of water.
Add a 35g chunk of solid NaCl (large salt crystal or two, about 17.5 ml of displaced volume) to 1 liter of 4°C water, and the overall density of the mass is 1035g/1017.5ml, or about 1.017g/ml.
When the salt (finally) dissolves, it will occupy more like 1005ml (salt aquarium water is about 2.5-3% more dense than freshwater, again by memory - since the mass is the same at 1035, but we know that salt water density is 1.025-1.03 that of freshwater, we know what the volume of the 3.5% salt solution will be). At that point when 100% of the salt has dissolved, it's impossible to say that the density of the salt "solid" is now much more than the original 2g/ml because we think that the water is still 1000g of the total mass and still occupies 1000ml.
I understand that that solutions and solutes don't generally mix ideally and I agree this is one possible explanation. In addition, the densities of the soluble and insoluble fractions may be different.
The main reason I counted the dissolved and undissolved fractions as one thing was simply because my initial simple experiment could not distinguish between the two. But I was probably too eager to jump to the conclusion that there was no reason to do another experiment to be sure.
Well, now you did it... I added "initial" pour mass to my recording. LOL
Knowing that my AP normal (not maximized) volume is 280ml, this morning's initial pour was only 256g (on 22.1g of Kenya AA with 21g cool pre-soak). Final pour was around 275g brew mass.
The estimate is really only important if you are trying to achieve a certain brew ratio AND are close to the maximum capacity of the device.
For example, if you are targeting a brew ratio of 18.75% (ragged edge of extraction with preheating in an AeroPress), and you know your max volume is about 300ml:
(X ÷ 0.965) + ((X * 0.1875) ÷ 0.9) = 300, solve for X (the brew water) at 241g (and getting the coffee mass at 45.2).
throw some Western Michigan windage into it and you get 240g water with 45g coffee at 18.75% brew ratio, should take up about 300ml give or take near the end of brewing.
If I take the heavier density (your formula, ->> (X ÷ 0.97) + ((X * 0.1875) ÷ 1.33) = 300) knowing I have 300ml to play with, I would have predicted 256 brew water and 48g of coffee - and would have run into a problem of overflow in trying to get all the water in.
(all the trouble just to get around the limitation of a single cup brewer! ROFLOL... talk about obsessed!)
------------------------------------------ ----------------------------------------- Le café doit être noir comme le diable, chaud comme l'enfer, pur comme un ange, et doux comme l'amour.
"There is no right answer with coffee. There is only the elixir in your cup at the moment you partake."
"...I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;..." - Lord Kelvin RECIPES thread => http://www.coffeegeek.com/forums/coffee/machines/585708
If I take the heavier density (your formula, ->> (X ÷ 0.97) + ((X * 0.1875) ÷ 1.33) = 300) knowing I have 300ml to play with, I would have predicted 256 brew water and 48g of coffee - and would have run into a problem of overflow in trying to get all the water in.
That would be analogous to using the density of NaCl to figure out what mass of granulated salt will fit in your salt shaker. Starting with the chemical density you'd have to study the size/shape of your salt granules and calculate a range of packing densities.
Or just measure it in your shaker, like you did with your Aeropress.
I could have set up my moka pot to measure the volume displaced and that's what I'm going to do eventually. It's more complicated than measuring the volume in an Aeropress which is why I was hoping to get at it indirectly. And then I became curious about the nature of coffee just for the sake of curiosity.
Spent grounds sink, why is that? Oven dehydrated spent grounds seem resistant to sinking. Finely ground coffee sinks more readily than coarsely ground. If it sinks it can't be less dense than water but sometimes it doesn't. Why? Gas? Change in composition during brewing?
I repeated that flask experiment and this time filtered the coffee and dehydrated the grounds. Hot brewed, cooled with ice, and then allowed to sit overnight, the extraction was 25.1%. The liquid coffee (1.3% strength) had a density of 1.00 g/ml. I calculated a density of 1.2 g/ml for the dissolved coffee, but the uncertainty was so large that the number is almost worthless. I started another batch with a lot more coffee to decrease the uncertainty. On the other hand, the spent grounds displaced enough volume to determine that density to be about 1.4 g/ml.
That would be analogous to using the density of NaCl to figure out what mass of granulated salt will fit in your salt shaker. Starting with the chemical density you'd have to study the size/shape of your salt granules and calculate a range of packing densities.
Or just measure it in your shaker, like you did with your Aeropress.
I could have set up my moka pot to measure the volume displaced and that's what I'm going to do eventually. It's more complicated than measuring the volume in an Aeropress which is why I was hoping to get at it indirectly. And then I became curious about the nature of coffee just for the sake of curiosity.
Spent grounds sink, why is that? Oven dehydrated spent grounds seem resistant to sinking. Finely ground coffee sinks more readily than coarsely ground. If it sinks it can't be less dense than water but sometimes it doesn't. Why? Gas? Change in composition during brewing?
I repeated that flask experiment and this time filtered the coffee and dehydrated the grounds. Hot brewed, cooled with ice, and then allowed to sit overnight, the extraction was 25.1%. The liquid coffee (1.3% strength) had a density of 1.00 g/ml. I calculated a density of 1.2 g/ml for the dissolved coffee, but the uncertainty was so large that the number is almost worthless. I started another batch with a lot more coffee to decrease the uncertainty. On the other hand, the spent grounds displaced enough volume to determine that density to be about 1.4 g/ml.
In one way, this is true - but the analogy breaks down because granules of NaCL are pretty much solid. The interstitial water in granular table salt quickly gets between the grains. Initially, salt granules act more like sand - bulk density dry is only 1.2, but pour sand into a pail of water and you'll displace only half of that volume.
Coffee (the structure of the grounds) is more like waterlogging. Cellulose, for example, has a density of 1.5. But wood (with a high percentage of cellulose) floats. If you keep wood sealed, it will float indefinitely. Yet, in rivers around Muskegon, Ludington, Traverse City, Menominee, etc. there is old lumber at the bottom of some of these rivers because during the 19th century river drives a certain percentage of the logged lumber... sank. At some point, some of these logs become waterlogged and the density of the log becomes greater than the water, especially with really old very dense trees.
A grain of coffee is kinda like a small log - cellulose structure with dried or roast byproduct compounds and sugars and some lipids interspersed with it, along with some trapped pressurized CO2. When you put it in hot water, initially the grain will float - but the cellulose structure absorbs water, and releases the trapped gas as well as give up solubles into solution. Initially, the density is less than water (why when you take grounds and pour them into water, they float). They have an approximate dry unpacked bulk density of .32-.47 or so (similar to roasted coffee beans, actually - about 10g/2Tbl to 14g/2Tbl). As they soak up water, they transition to close to 1.0 density.
I have a couple of backcalcs with initial pour and final brew (just before press) density, using my 280ml setting on the AP:
All at 2:30 contact time, D+3 setting on the Bodum Bistro, and use a equal coffee mass cold pre-soak, and they all have an intital backcalculated density of around 0.4, and final backcalculated coffee density of around 0.85-0.95 (using the same estimate of water = 0.965). The initial density is, of course, lower if the bloom is not suppressed.
Example: The Kenya AA at 21.9g had an initial pour brew mass (to the top of the AP) of 240.2 (initial pour of brew water = 218.3, includes the presoak water). this had floating grounds and some small bloom. (218.3÷.965) + (21.9 ÷ X) = 280ml, X=0.37
After topping at 1/2 minute and again at 1:30, just before pressing: Total Brew Mass = 271.9, Brew Water total = 250.0g (250 ÷ .965) + (21.9 ÷ X) = 280ml, X = 0.84
At the end, 95%+ of the grounds were sunk, bloom was pretty much gone but maybe had a mm or so of light foam on the top just before cap application.
Remember, this was an initial predictor to determine the end volume of the brew volume, and I think it seems to work well at around 0.7-0.9 coffee grounds density for predicting the total volume if I am trying to achieve a particular brew ratio with a limited volume.
------------------------------------------ ----------------------------------------- Le café doit être noir comme le diable, chaud comme l'enfer, pur comme un ange, et doux comme l'amour.
"There is no right answer with coffee. There is only the elixir in your cup at the moment you partake."
"...I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;..." - Lord Kelvin RECIPES thread => http://www.coffeegeek.com/forums/coffee/machines/585708
Okay, you're right: coffee is more like wood than salt. The point is that bulk density tells you one thing while true density tells you something else. Though true density is more precise it isn't always easy to apply. And while an ad hoc approach is easier to use for a given situation it is harder to extend to new situations.
You've found a way to reliably estimate the volume of your Aeropress brews. But will those estimates still work if you brew in an AP differently? What about in an espresso machine or a moka pot? Since the main source of variability appears to be due to the presence of gas will a brew method that features flowing liquid change the equation significantly?
In those examples above, did you mean 285ml?
I finished my (hopefully last) flask experiment. In order to reduce the uncertainty I used a lot more coffee and also got my better scale into the picture when possible. I had never brewed at this high a ratio (21%) before and was surprised that the grounds retained almost half the water. It had a wonderful chocolatey aroma but was bitter as if overextracted. Because so much liquid remained in the grounds I think the normal calculation for extraction (12.3%) is misleading. But the point was to see if I could measure various densities, sans gas and foam. I need to double check these figures but, even though they may turn out to be of little practical use, here they are.
1.017 ± 0.005 g/ml - density of filtered coffee (4.8% strength) 1.37 ± 0.04 g/ml - effective density of total coffee solids (dissolved+grounds) 1.6 ± 0.1 g/ml - effective density of dissolved coffee solids 1.3 ± 0.1 g/ml - effective density of spent grounds
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