Viscous fingering of miscible slices

Anne de Wit (1) , Yann Bertho (1, 2) , Michel Martin (3)

1 SCPBT - Service de Chimie-Physique et Biologie Théorique and Center for Nonlinear Phenomena and Complex Systems
2 MRC - Microgravity Research Center
3 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

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, the length of the slice, the Péclet number and the ratio between transverse and axial dispersion coefficients. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.

Mots clés: viscous fingering; instability; Saffman-Taylor

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]

Anne de Wit, Yann Bertho, Michel Martin. Viscous fingering of miscible slices. Physics of Fluids, 2005, 17, pp.054114. ⟨10.1063/1.1909188⟩. ⟨hal-00192143⟩