A. Birovljev et al., SCALING STRUCTURE OF TRACER DISPERSION FRONTS IN POROUS-MEDIA, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(6), 1994, pp. 5431-5437
Experiments on the miscible displacement of a clear fluid by a dyed fl
uid of the same viscosity and density in a rectangular quasi-two-dimen
sional porous medium are presented. Equiconcentration dispersion front
s were identified using computer image processing. The fronts taken at
three different concentrations are fractal curves with approximately
the same box fractal dimension D congruent-to 1.45. In an alternative
analysis the fronts were reduced to single valued functions and the dy
namic scaling behavior investigated using a self-affine scaling formal
ism. The Hurst exponent H = 0.55 and the dynamic exponent beta = 0.5,
found by collapsing height difference correlation function data, are c
onsistent with the results obtained through other analysis methods. Th
e average concentration profile across the dispersion front was found
to follow the classical solution of the diffusion-convection equation.
The dependence of the width of the equiconcentration dispersion front
sigma on time yields dispersion coefficients D(sigma) over one order
of magnitude less than the longitudinal dispersion coefficient D(paral
lel-to).