In the middle of the last century, the German physiologist Fick
applied the principles of heat conduction to various examples
of diffusion in animals. He observed that the velocity at which
a substance diffused through a given cross sectional area, its
diffusive flux (J), was related to the concentration
gradient of that substance (dC/dX), in the following
manner:
where D is the Diffusion coefficient (in cm2 per
sec) and the negative sign convention indicates diffusion occurs
from regions of higher C to those of lower C. Integrating
this expression for diffusion from a region of high concentration
to one of lower concentration, produces the following relationship:
Thus, in the cgs system, a deltaC measured in M (mol per
l or mmol per cm3) over a distance of 1 cm, with a Diffusion Coefficient
of cm2 per sec, would produce a flux with units of (mol per cm2)
per sec. Redefining the terms and solving for the substance's
velocity (V) of diffusion produces:
where P is the Permeability Coefficient of the substance
being measured (the Diffusion Coefficient per unit X),
and A is the effective cross-sectional area of the region
over which diffusion occurs.