Advection, Dispersion, and Molecular Diffusion

At the scale of soil and rock pores, the two principal transport mechanisms are molecular diffusion and advection. At larger scales, transport is usually quantified in terms of an additional parameter, referred to as mechanical dispersion. 

Molecular diffusion is a process in which chemical species move from regions of high concentration to regions of low concentration by Brownian motion. The rate of movement is directly proportional to the concentration gradient, normal to the direction of movement. Distribution of chemicals in the near surface and subsurface is not uniform, so that molecular diffusion is an ever-present mechanism. 

In bulk water (free solution), the diffusive flux, given in units of mass per area per time, is related to the concentration by Pick s first law. 

In partially saturated media, the diffusion coefficient also is a function of the volumetric water content, 9. Calvet (1984) showed that the variation in soil water content influences the apparent diffusion coefficient for organic contaminants in two ways by changing the ratio of gas diffusion of volatilizable pollutants to liquid diffusion, because the air-filled porosity is affected, and by modifying pollutant 

From Eq. 10.1, together with the equation of continuity, we can derive Pick s second law, otherwise known simply as the diffusion equation in one-dimensional form, this is given by 

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