Influence of the disorder on solute dispersion in a flow channel

¹ Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, 1063 Buenos Aires, Argentina
² Laboratoire Fluides, Automatique et Systèmes Thermiques, UMR No. 7608, CNRS, Universités Paris 6 et 11, Bâtiment 502, Campus Paris Sud, 91405 Orsay Cedex, France

Corresponding author: hulin@fast.u-psud.fr

Received: 9 May 2007
Accepted: 12 June 2007
Published online: 12 July 2007

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 Péclet 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 Péclet 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.