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Linear Stability of Miscible Displacement Processes in Porous Media in the Absence of Dispersion
Author(s) -
Hickernell F. J.,
Yortsos Y. C.
Publication year - 1986
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198674293
Subject(s) - wavenumber , displacement (psychology) , porous medium , dispersion (optics) , diffusion , linear stability , stability (learning theory) , mechanics , compressibility , linear growth , growth rate , mathematical analysis , instability , physics , mathematics , thermodynamics , materials science , porosity , geometry , optics , psychology , machine learning , computer science , composite material , psychotherapist
The linear stability of miscible displacement processes in porous media is examined in the absence of diffusion and dispersion. Bounds for the rate of growth of the disturbance are derived. The asymptotic behavior of the rate of growth as a function of the wavenumber of the disturbance and the mobility profile characteristics is obtained for both small and large wavenumbers. A closed‐form solution is also presented for a particular mobility profile. It is shown that such displacement processes are linearly unstable in the case when the mobility profile contains any segments of decreasing mobility, and marginally stable in the opposite case. The effect of gravity on linear stability, in the case of compressible flows, is also briefly discussed.