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Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

Published online by Cambridge University Press:  15 April 2010

S. H. HEJAZI ,
P. M. J. TREVELYAN ,
J. AZAIEZ  and
A. DE WIT
S. H. HEJAZI
Affiliation:
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, CanadaT2N 1N4
P. M. J. TREVELYAN
Affiliation:
Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université Libre de Bruxelles (ULB), CP 231, 1050 Brussels, Belgium
J. AZAIEZ
Affiliation:
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, CanadaT2N 1N4
A. DE WIT*
Affiliation:
Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université Libre de Bruxelles (ULB), CP 231, 1050 Brussels, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

When one solution of reactant A is displacing another miscible solution of reactant B, a miscible product C can be generated in the contact zone if a simple A + B → C chemical reaction takes place. Depending on the relative effect of A, B and C on the viscosity, different viscous fingering (VF) instabilities can be observed. In this context, a linear stability analysis of this reaction–diffusion–convection problem under the quasi-steady-state approximation is performed to classify the various possible instability scenarios. To do so, we determine the criteria for an instability, obtain dispersion curves both at initial contact time using an analytical implicit solution and at later times via numerical stability analysis. Along with recovering known results for non-reactive systems where the displacement of a more viscous fluid by a less viscous one leads to a VF instability, it is found that in the presence of a chemical reaction, injecting a more viscous fluid into a less viscous fluid can also lead to instabilities. This occurs when the chemical reaction leads to the build up of non-monotonic viscosity profiles. Various instability scenarios are classified in a parameter plane spanned by Rb and Rc representing the log-mobility ratios of the viscosities of the B and C solution respectively with respect to that of the injected solution of A. A parametric study of the influence on stability of the Damköhler number and of the time elapsed after contact of the two reactive solutions is also conducted.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 501 - 528
Copyright
Copyright © Cambridge University Press 2010

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