  Viscous fingering of a miscible high viscosity slice of fluid displaced by a
lower viscosity fluid is studied in porous media by direct numerical
simulations of Darcy's law coupled to the evolution equation for the
concentration of a solute controlling the viscosity of miscible solutions. In
contrast with fingering between two semi-infinite regions, fingering of finite
slices is a transient phenomenon due to the decrease in time of the viscosity
ratio across the interface induced by fingering and dispersion processes. We
show that fingering contributes transiently to the broadening of the peak in
time by increasing its variance. A quantitative analysis of the asymptotic
contribution of fingering to this variance is conducted as a function of the
four relevant parameters of the problem i.e. the log-mobility ratio R, the
length of the slice l, the Peclet number Pe and the ratio between transverse
and axial dispersion coefficients $\epsilon$. Relevance of the results is
discussed in relation with transport of viscous samples in chromatographic
columns and propagation of contaminants in porous media.
