ECE532 Biomedical Optics ©1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute  
Chapter 5 Course Home  Fick's 1st law of diffusion 
Diffusion occurs in response to a concentration gradient expressed as the change in concentration due to a change in position, . The local rule for movement or flux J is given by Fick's 1st law of diffusion:
in which the flux J [cm^{2} s^{1}] is proportional to the diffusivity [cm^{2}/s] and the negative gradient of concentration, [cm^{3} cm^{1}] or [cm^{4}]. The negative sign indicates that J is positive when movement is down the gradient, i.e., the negative sign cancels the negative gradient along the direction of positive flux.
Examplearbitrary units  Consider a local concentration of 10^{6} units per cm^{3} which drops by 10% over a distance of 1 cm. Then the gradient is 10^{5} [units cm^{4}]. Assume the diffusivity is 10^{3} [cm^{2}/s]. Then the flux J equals: 
For light, the diffusivity is proportional to the diffusion length D [cm] and the speed of light c:
where D = 1/(3 µ_{s}(1g)). The units of velocity [cm/s] times the units of length [cm] yield the units of diffusivity [cm^{2}/s]. The following example describes the local diffusion of red light in milk.
Exampleoptical energy  Consider a local fluence rate F of 1 W/cm^{2} in milk (n = 1.33, µ_{s}(1g) = 10 cm^{1}).

For optical diffusion, Fick's 1st law is expressed as the energy flux J [W cm^{2}] proportional to the diffusion constant D [cm] and the negative fluence gradient dF/dx:
which was obtained by substituting cD for and substituting F/c for C. The factors c and 1/c cancel to yield the above equation.