Nonlinear Physical Chemistry Unit
Service de Chimie Physique et Biologie
Théorique
When a fluid displaces a more viscous one, the interface between the two fluids does not remain flat and perpendicular to the flow axis. Instead, since, for a given pressure gradient, the less viscous fluid moves faster than the more viscous one, it deforms the interface into fingers growing in time (see Figure). Such a fingering instability occurs typically when less viscous water displaces more viscous oil in underground reservoirs leading to viscous fingering which produces flow nonuniformity and reduces oil recovery. Fingering poses also problems in contaminant transport in aquifers, in packed bed reactors, and is particularly detrimental to chromatographic separation techniques. Indeed, since samples injected in chromatographic columns or pollution zones have generally a viscosity different from that of the carrier fluid, fingering occurs at the front or tail of the sample zone when the sample viscosity is, respectively smaller or larger than that of the invading fluid. In any case, this instability leads to distortion and broadening of the samples. The resulting deterioration of the separation can be serious, especially for highly concentrated samples in preparative or size-exclusion chromatography and for highly viscous aquifer contaminants. In this context, it is our goal to investigate both experimentally and theoretically the influence of viscous fingering on the spreading of viscous samples.
Viscous fingering of a finite sample of glycerol (yellow) displaced from left to right in a Hele-Shaw cell by less viscous water colored in blue. The frontal interface is stable while the rear interface where water displaces less viscous glycerol features a viscous fingering instability.
Numerical simulation of the viscous fingering of the rear front of a finite viscous sample displaced from left to right by a less viscous miscible fluid. The dynamics is shown in a frame moving with the injection speed.
References:
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M. Mishra, M. Martin and A. De Wit, Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio, Phys. Rev. E. 78, 066306 (2008).
M. Mishra, M. Martin and A. De Wit, Miscible viscous fingering with linear adsorption on the porous matrix, Phys. Fluids. 19, 073101 (2007).
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G. Rousseaux, A. De Wit and M. Martin, Viscous fingering in packed chromatographic columns: linear stability analysis, J. Chromatography A. 1149, 254-273 (2007).
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A. De Wit, Y. Bertho and M. Martin, Viscous fingering of miscible slices, Phys. Fluids. 17, 054114 (2005).
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A. De Wit and G.M. Homsy, Nonlinear interactions of chemical reactions and viscous fingering in porous media, Phys. Fluids, 11, 949-951 (1999).
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A. De Wit and G.M. Homsy, Viscous fingering in reaction-diffusion systems, J. Chem. Phys., 110, 8663-8675 (1999).
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A. De Wit and G.M. Homsy, Viscous Fingering in Periodically Heterogeneous Porous Media. Part I: Formulation and Linear Instability, J. Chem. Phys. 107, 9609-9618 (1997).
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A. De Wit and G.M. Homsy, Viscous Fingering in Periodically Heterogeneous Porous Media. Part II: Numerical Simulations, J. Chem. Phys. 107, 9619-9628 (1997).