longitudinal dispersion in nonuniform isotropic porous media

185
For a finite medium of length L, an appropriate boundary condition
for the exit of the porous medium must be developed. Dankwerts (1953)
again used a flux boundary condition
- dCvc(L
,t) - DL ax (L ,t) t > °
where c e 1S the exit concentration, and L- refers to the exit interface
(x = L) as approached from x < L. Dankwerts (1953) argued, however,
that c(L-,t) must equal c ,or the solute concentration within the bed
e
would have to pass through a maximum or minimum. The exit boundary
condition is then,
o t > ° (B.13)
Brenner (1962) gives the solution to equation (B.5) with equations
(B.8), (B.14) and the initial condition
to be
C
-=
C o
2exp [t (2X - T) ] x
2/2
X exp (-A k T 4P )
c(x,O) = °
° < x < L
(B.14)