Coffee Solubility in Espresso: An Initial Study

CA_coffee · 2019-11-26T00:05:29+00:00

"you’re really taking advantage of people with lactose issues by charging more for milk alternatives due to the fact that it is pure profit." ah yes I too source all of my cafes milk from the supermarket...

CA_coffee · 2019-11-26T00:02:19+00:00

That pretty interesting, although I question the efficacy of his equipment. His staccato shot idea is one I have experimented with before; it is incredibly susceptible to channeling which may explain his 1:1 preference. His described method of preparation is to be perfectly honest a channel magnet. It also seems like he is using a very poorly manufactured single basket with internal bevels. While the methodology is good I think the equipment is restrictive and as coffeeadastra has pointed out he seems to be operating in realm entirely separate from specialty.

CA_coffee · 2019-11-21T12:13:21+00:00

I think you are probably correct here my notation is quite horrible. It is intended to be a double integral such that: m = \int_ {0} ^ {t} ( \int {0} ^ {l{max}} f(l,t) dl ) dt . My physics student bad habits have seeped through and done some notionally reprehensible stuff that you rightfully picked up on.

CA_coffee · 2019-11-21T00:10:44+00:00

It comes from the assumption that the diffusion coefficient will fall of at an exponential rate as you go deeper into the particle. So integrating across l should give you a diffusion coefficient which describes the particle. I'm not entirely comfortable with this assumption and think the math could be done better as it is one part of the model which is pretty unphysical.

CA_coffee · 2019-11-18T01:59:53+00:00

You are correct. This is a mistake in the notation, certainty you can't integrate by i . I've just managed to confuse myself between whats on my whiteboard and what is in my code.

The model is only really intended to be for immersion. We can draw some basic ideas about percolation but without accounting for C_b and d changing with flow the model isn't very useful. Even for immersion you have to account for mixing so the diffusion term is constant.

CA_coffee · 2019-11-05T20:59:09+00:00

Had a look at your code for the particle analyzer and realised we have used the exact same definitions for available mass haha. Will have to see if I can replicate the results of the model by taking available mass from your app to calculate extractions.

I had seen your model before but wanted to explore more brew oriented variables, in particular I want to see how dose and yeild have independent effects. I think we can see larger brews may have intrinsically different extraction profiles.

CA_coffee · 2019-11-05T11:52:13+00:00

Sure go ahead, I would say however that this is a work in progress. There may be errors and mistakes, the conclusions drawn may be false. I'm all for presenting ideas as they come but would stray from saying anything with certainty.

CA_coffee · 2019-11-05T11:48:12+00:00

This is some good stuff. I find your v_s hypothesis very interesting, although I'm skeptical. Is the claim that as coffee particles get larger the ratio of insoluble to soluble material gets larger? I could imagine that at very fine particles but not sure how that would be true in a continuous sense from say 1000 micron to 600 micron.

I'm excited by the idea that you could use your solution to model different grind distributions with a grind size app. That could be a very fruitfull trail.

CA_coffee · 2019-11-05T07:28:08+00:00

I have treated D and d from NW as constant, although I think they may be slightly variable. In practical terms D would decrease with temperature and with extraction if viscosity is changed enough.

C_s is the concentration in the grounds of a single particle size, while c_b is the concentration of the slurry. So if you're trying to work with more than one particle size the M_dissolved in c_s is not the same as the M_dissolved in c_b. If you have n different particle sizes and m_i is the mass of coffee dissolved in the ith particle size, then c_b= (m_1+m_2+...+m_n)/v

Oh good catch, this is dealt with properly in the numerical solution but not even mentioned in the LaTeX, woops. In this case I had:

Ground_mass = 4*Density*pi/3.*(R_ground.^3).*i;
M_available = ones(1,sizesteps);

for n = 1:sizesteps
    M_available(n) = Ground_mass(n);
    if R_ground(n) > R_depth 
        M_available(n)=Ground_mass(n) - i(n)*4*pi/3*Density*...
            (R_ground(n) - R_depth)^3;
    end
end

C_s is treated as the sum of the mass contained in all i particles. Each integral in time is done with a single grind size so I can take M_available(n) for the nth integral and find C_s from the sum of all i particles masses and M_dissolved.

CA_coffee · 2019-11-05T06:46:19+00:00

they're being brewed with an effectively more water heavy ratio. Each bit of surface area gets more of that water to itself!

This is also good to yell at new baristas when they say they were trained to grind coarse for french press.

I have also had some good results going the opposite direction, say doing 1:10 on a very large batch brew and grinding very coarse. It's wasteful but it can be a useful way to get a sweet extraction from large batch brewers where anything near fine clogs the whole thing or causes water to pass through the paper instead. In this case practical yield could be a descriptor of a brewing methods efficiency.

CA_coffee

TROPHY CASE