Dispersion in Chromatography Columns - Dispersion Processes that take Place in an LC Column > Longitudinal Diffusion > The Diffusion Process > Page 18

Thus, if , the solution of the equation is a Gaussian function, and, for that equation,                             (7)

Ordinary diffusion is the result of random molecular movement in first one direction and then another and thus, resembles the Random Walk Model. Uhlenbeck and Ornstein (8), derived the following  expression for the overall standard deviation (s) arising from diffusion process,


     where (t) is the time period over which the process occurs,

         and Dm is the Diffusivity of the solute in the mobile phase.

Actually, (t) is the time the solute spends in the moving phase and thus, is given by,  , where (l) and (u) is the length of the column and the linear mobile phase velocity respectively.