longitudinal dispersion in nonuniform isotropic porous media

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a change 1n source strength over an entire domain, implying an infinite
speed of signal propagation (Sundaresan, et al., 1980).
B.l Ihg Breakthrough Problem
A common experimental method for studying longitudinal dispersion
is to displace a resident solution from a porous column by continually
injecting a solution of different solute concentration at the inlet of
the column (Rose and Passioura, 1971). The well-known breakthrough
curve results when the change in concentration with time is measured at
a particular longitudinal position along the column. Theoretical
solutions to this problem have employed equation (B.1) along with
appropriate initial and boundary conditions. While the initial
condition poses no difficulty, a significant body of literature is
devoted to the interpretation of the boundary conditions (Pearson,
1959; Werner and Wilhelm, 1956; Gershon and Nir, 1969; Choi and
Perlmutter, 1976; Kreft and Zuber, 1978). The three physical domains
to be investigated here are an infinite medium (- 00 < x < + 00), a semi-
infinite medium (0 < x < + 00), and a finite medium (0 < x < L). The
boundary conditions for the infinite medium are
Lim c(x,t) = Co t > 0
x -+-00
Lim c(x, t) = c
r
x-+ oo
t > 0
(B.2)