Quantification of Fickian Transport

Fick s first law is typically used to describe the flux density of mass transport by turbulent diffusion, 

The parameter D is usually called a turbulent (or eddy) diffusion coefficient when it arises from fluid turbulence its value varies enormously from one situation to another, depending on the intensity of turbulence and on whether the environmental medium is air or water. The diagram in Fig. 1-6 shows the Fickian mass flux arising from a concentration gradient in a smoke plume. 

Fick s first law can also be expressed in three dimensions using vector notation, 

[1-4] the vector notation indicates that the direction of flux is in the direction of the steepest change in concentration with distance (the direction of the gradient vector), assuming that D is equal in all directions. For illustrative purposes, this book works mostly with the one-dimensional form of Fick s first law—Eq. [1-3] in practice, many environmental situations also can be modeled in one dimension. Note that in the most general case, not only may D be anisotropic (i.e., not equal in all directions), but also D may vary with time and location. 

Turbulent diffusion is an important mode of chemical transport in both surface water and air. In the subsurface environment, groundwater flow normally lacks the eddy effects that characterize surface water and air movements because typical groundwater velocities are so much lower. Nevertheless, groundwater must take myriad detours as it moves from one point to another, traveling over, under, and around soil particles, as shown in Fig. 1-7. These random detours cause mixing, thus the net transport of a chemical from 

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