Fick's Law
Roasted Beans |
Fick's law describes a concept called flux. Flux is the rate at which something accumulates. It is measured in units of volume per unit of time * unit of area. For example. Suppose you you had a bathtub a drain one inch by one inch square. Now, suppose, you add one gallon of water to the tub water and then opened the drain. If it takes 1 minute to empty 1 gallon of water through the drain, then the flux of water is one gallon per minute, per inch square drain. We are going to use Fick's law to perform a measurement to find the rate of accumulation of caffeine in brewing coffee. Along the way, we will discover why it is important to grind coffee beans before you brew them. Other concepts we need to find flux are discussed below. |
w J is the variable we will use to represent flux. We will be finding J in the examples below.
w DAB is a constant that describes how quickly a substance, A, diffuses into another substance, B. For the brewing of coffee, these two substances are caffeine and water. DAB for caffeine and water is 1.14 * 10-4 m2/sec
w Csat is the maximum concentration of caffeine that may be contained in water. For water at the brewing temperature of coffee, Csat is 1.77 mol caffeine / mol water. We will find this concentration of caffeine right next to the coffee ground. The farther from the surface of the ground, the more the caffeine will diffuse into the surrounding coffee, and the concentration will decrease.
w Cbulk is the average concentration of caffeine in the final product, a cup of coffee. Cbulk is 0.538 mol caffeine / mol water.
w l is the distance between the surface of the coffee ground and the bulk coffee at concentration Cbulk. This is a stagnant layer of liquid next to the surface of the coffee ground. We can estimate the distance it takes for the caffeine to diffuse to Cbulk to diffuse to be 0.00001 m.
We now have all of the concepts necessary to use Fick's Law to find the flux of caffeine in coffee brewing.