longitudinal dispersion in nonuniform isotropic porous media

like D L , is a function of the flow and medium characteristics.
Similarly, its value may be orders of magnitude greater than the
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coefficient of molecular diffusion. Experimental investigations of DT
have used a steady-state dispersion pattern developed from coflowing
streams (List and Brooks, 1967). For steady-state dispersion in two
dimensions, as in Figure 1.4, equation (1.6) reduces to
The longitudinal dispersive flux is considered negligible for a
continuous source when advection dominates longitudinal transport or
V x
s
DL
» 1
where x is the longitudinal distance from the source. Therefore,
sufficiently far from the source, the transport equation may be
approximated by
v de
S dX
and the appropriate boundary conditions are (neglecting boundary
effects in Figure 1.4)
H(y) is a step function, defined by
H(y) = 1 y < 0
H(y) = 0 y > 0