longitudinal dispersion in nonuniform isotropic porous media

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proper boundary condition arises since the inlet chamber is a distinct
physical system which should be considered for a complete solution.
Mass transport in the inlet chamber is not well understood, however,
such that a complete model is not possible. Appendix B discusses the
behavior of the solutions of equation (1.3) for miscible displacements
according to various boundary conditions. The important conclusion
from Appendix B is that all of the solutions using the various boundary
conditions are convergent to the same solution only a short distance
downstream (Vsx/DL > 24). Therefore, to analyze the experimental data
we will use the simpler solution for an infinite medium with the
initial condition
C(x,O) = Co x < °
C(x,O) = ° x > °
In nondimensional form, this solution is (see Appendix B)
where X = Vsx/DL' T = (V s )2t/DL and erfc is the complementary error
function. Equation (4.4) may be used more conveniently in the
following form
where d is the geometric mean grain size and
g
(4.4)
(4.5)