Molecular Diffusion Calculator

Molecular diffusion in geologic media can be represented by Fickian diffusion and is solved as an expression using the complimentary error function.  (Carslaw and Jaeger, Conduction of Heat in Solids, Oxford University Press, 1959):
    
where: 

    C  = concentration at z, 
    C_o = initial concentration,
    z   = distance from the source,
      = porosity,
    D   = coefficient of molecular diffusion,
      = tortuosity, and 
     t   = time.

Note that the coefficient of molecular diffusion is a function of viscosity and that the tortuosity may determined with Archie's Law:

where m is an empirical parameter [generally >2 in materials of low porosity (0.2).] Furthermore, diffusion is also thought to be scale dependent.

The distance is calculated as:

In this calculator, enter the normalized concentration and time, then click on "Calculate Diffusion " and the distance from source to the desired normalized concentration is calculated.