by another_jim on Mon Sep 05, 2011 1:58 pm
I'm not a chemical engineer; but I am a mathematician of sorts -- You need to avoid being mathematically overdetermined here. The "average rate of rise" is the overall roast temeperature minus room temperature divided by the roast time. Slower and faster roasts can make a difference, so can darker or lighter roasts, without this being caused as an independent variable by the rate of rise. The rate of rise is entirely determined by these other factors
You could make the roast non-monotonic, sending the temperature up and down, and then the rate changes would be independent of the average roast times or temperatures. But in that case, the cause of any taste changes might be the falling temperatures themselves creating a new cascade of reactions (having the chemicals created at higher temperatures available as feedstocks)
Back in the 80s, I worked my way through Ilya Prigogine's (the so called poet of thermodynamics) book on self organizing chemical reactions. The rate at which any chemical is produced depends on a reaction constant and the density of its precursors (what I called feed stocks here). The reaction constant depends on free energy as well as catalysts. The reactions themselves release or absorb free energy. Free energy is an instantaneous quantity, and therefore not dependent on rates of change. Any reaction system, as a whole, can be written as a coupled set of differential equations with one equation for each chemical's rate of production.
If no reaction is autocatalytic (the presence of chemical A creates more chemical A) or in an autocatalytic cycle (e.g. A makes B; B makes A), the equations are linear, well behaved, and easily solved. If some reactions are auto-catalytic, some of the reaction equations become polynomials; and there are no general closed form solutions. Instead, the system has to be solved piecewise. This is where they can become interestingly periodic over time and patterned over space (self-organizing).
Coffee roasting Maiilard reactions have autocatalytic cycles, but aren't self organizing, since a bean is a closed system and eventually runs out of amino acids, sugars and water (the basic reaction feedstocks). This allows a measure of control -- allocating the raw materials to one phase of the reaction or another. But it laos means that it is possible to get indistinguishable roasts from different roasters using different roast times, since while the rate of rise varies, the reactions rates are all equally slowed or accelerated. For instance, I've had slow HG/DB roast that tasted identical to fast air roasts.
My feeling is that it is the proportion of time spent in each phase of the roast that is more important that the overall time. If I use a 3/3/3 profile (warmup, ramp to first, and roast finish) on my air roaster, and a 4/4/4 on my drum, the results are usually very much the same.
As a completely irrelevant but interesting aside -- Prigogine proved that all episodes of self organization are detectable from the outside as a spike in entropy production -- a garbage explosion. That pretty well describes my episodes of trying to organize my roasting more efficiently. But sadly, while all self organization produces extra garbage, the reverse is not true; an explosion of garbage does not always mean a rise to a higher level of organization.
