longitudinal dispersion in nonuniform isotropic porous media

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effective porosity as compared to the total porosity. As shown in
Table 4.4, no significant differences are detected between the two
porosity measurements. A possible explanation for the absence of an
early breakthrough may be that the amount of diffusion-limited pore
space in the column is small compared to the total pore space in the
column.
Now if the slope of DL/D versus Pee let number is one to one on the
log-log plot (Figure 5.3), then the dimensionless group DL/Vsd g is
constant, i.e. independent of the Peclet number. From the slopes
quoted in Figure 5.3, we see that the longitudinal dispersion
coefficient is practically independent of the value of the molecular
diffusion coefficient (i. e. DL a: D- O .044 for the nonuniform medium).
Consider the advective diffusion equation nondimensionalized by
t* = V tId
x * = x/d
s g g
where K is a constant. In this case, we would expect all breakthrough
curves at a given location to lie on top of one another, regardless of
the Peclet number. Figure 5.6 shows breakthrough curves at the third
(last) probe in the nonuniform medium at three Pee let numbers. The
majority of the breakthrough for the three curves does lie close to a
single line, but the tail shows significantly different behavior as a
function of the Pee let number. The tail is longer for higher Pee let