where \(h_f\) is the head loss, \(f\) is the friction factor, \(L\) is the length of the coffee bed, \(D\) is the diameter of the coffee particles, \(v\) is the velocity of the water flow, and \(g\) is the acceleration due to gravity.
Mass transfer is the process by which the flavors and oils are extracted from the coffee beans into the water. The rate of mass transfer depends on the surface area of the coffee particles, the concentration gradient of the desired compounds, and the diffusivity of the compounds. The Physics Of Filter Coffee Pdf
\[J = -D rac{dc}{dx}\]
As the water flows through the coffee grounds, it encounters resistance due to the friction between the water and the coffee particles. This resistance causes the water to slow down and lose energy, which is described by the Darcy-Weisbach equation: where \(h_f\) is the head loss, \(f\) is
\[Q = hA(T_s - T_f)\]
where \(J\) is the mass flux, \(D\) is the diffusivity, \(dc\) is the concentration gradient, and \(dx\) is the distance over which the diffusion occurs. \[J = -D rac{dc}{dx}\] As the water flows