longitudinal dispersion in nonuniform isotropic porous media
longitudinal dispersion in nonuniform isotropic porous media
longitudinal dispersion in nonuniform isotropic porous media
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motion of a s<strong>in</strong>gle particle. Hence the residence time for a particle<br />
<strong>in</strong> a capillary tube (without shear) is governed by the follow<strong>in</strong>g<br />
equation<br />
where u 1S the mean velocity <strong>in</strong> the pore and s is the local axial<br />
63<br />
(3.20)<br />
coord<strong>in</strong>ate. The boundary conditions imposed on equation (3.20) reflect<br />
the def<strong>in</strong>ition of residence time to be used. For example, if we<br />
consider an <strong>in</strong>f<strong>in</strong>ite doma<strong>in</strong> with a po<strong>in</strong>t source at s = 0 we know the<br />
solution 1S<br />
1<br />
c(s,t ) = -----s<br />
/41TDt s<br />
For an observation po<strong>in</strong>t, sl' the residence time distribution is<br />
c(sl,t s )' where residence time means the duration between ts = 0 and<br />
the first time the particle has a position s > sl for all subsequent<br />
times. Alternatively, we could have the boundary conditions<br />
Lim<br />
s-+ -
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