Influence of the disorder on solute dispersion in a flow channel

Abstract

Solute dispersion is studied experimentally in periodic or disordered arrays of beads in a capillary tube. Dispersion is measured from light absorption variations near the outlet following a steplike injection of dye at the inlet. Visualizations using dye and pure glycerol are also performed in similar geometries. Taylor dispersion is dominant both in an empty tube and for a periodic array of beads: the dispersivity l d increases with the Peclet number Pe respectively as Pe and Pe 0.82 and is larger by a factor of 8 in the second case. In a disordered packing of smaller beads ( 1/3 of the tube diameter) geometrical dispersion associated to the disorder of the flow field is dominant with a constant value of l d reached at high Peclet numbers. The minimum dispersivity is slightly higher than in homogeneous nonconsolidated packings of small grains, likely due to wall effects. In a weakly disordered packing with the same beads as in the periodic configuration, l d is up to 20 times lower than in the latter and varies as Pe γ with γ = 0.5 or = 0.69 (depending on the fluid viscosity). A simple model accounting for this latter result is suggested.