Simulation of Fick’s verification of the 2nd law

Abstract

Adolph Fick’s original diffusion experiments used two vessels containing water and salt to establish a steady-state concentration gradient that demonstrated the validity of what is now called Fick’s second law of diffusion. The first vessel had a cylindrical shape creating a linear gradient. The second vessel was shaped like a funnel having a correspondent variable flow area. Using Fick’s second law, general solutions for any shape of the vessel are developed for steady diffusion in two and three dimensions, respectively. Two dimensional random walks were performed via computer simulations, and the numerical results are compared to continuum theory. Provided that a sufficiently large number of steps are simulated to allow the random walkers to traverse the total diffusion path, good agreement is achieved between discrete “molecular” motions (random walk) and the classical continuum description provided by scalar field theory (partial differential equations).