An advection-diffusion-reaction model for coffee percolation

Advection-diffusion-reaction equations are largely exploited in applied science, for their ability to describe real-life phenomena where mass transport and diffusion, as well as chemical reactions, occur. Here, these models are used to describe the percolation phenomena arising in espresso coffee extraction. The resulting initial/boundary value problem is solved using the Crank-Nicolson scheme and a nested fixed-point iteration. Mass conservation and positivity of the solution are guaranteed. The reliability of the model together with the proposed solving strategy is assessed experimentally, by comparing the efficiency of real and simulated extractions conducted under different physico-chemical conditions.