Discerning between bulk diffusion and surface crossing in diffusion measurements

We point out a method for experimentally discerning between impurity bulk diffusion and surface crossing by a systematic study of diffusion in bulk samples of varying dimensions: varying thickness for the case of plane-parallel plates and varying radii for spheres and long cylinders. When a miscibility limit exhibits, the time t_0.7 of reaching 70% average of the miscibility limit, starting from zero, is given by t_0.7/L=(0.6/s)+(0.1/D)L for the plane-parallel plate of thickness L, surface-crossing velocity s, and a diffusion-constant D. It is given by t_0.7/R=(0.6/s)+(0.145/D)R for a long cylinder of radius R, and by t_0.7/R=(0.4/s)+(0.0745/D)R for a sphere. For example, in the plane-parallel plates case, plotting experimental t_0.7/L results as function of L would show a straight line, with ordinate intercept yielding s, and slope yielding D. Making use of this method should allow the experimental study, hence a chemo/physical modeling, of both D and s as functions of external system conditions such as temperature and pressure.