Open Boundaries, Anomalous Diffusion and the Darcy-Bénard Instability

The classical problem of the Darcy-Bénard instability in a horizontal porous layer saturated by a binary fluid mixture and subject to a non-uniform solutal concentration field is revisited. In particular, a generalised anomalous diffusion model departing from the classical Fickian diffusion and acco...

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Published inTransport in porous media Vol. 152; no. 4; p. 27
Main Authors Barletta, A., Rees, D. A. S., Celli, M., Brandão, P. V.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.04.2025
Subjects
Binary fluids
Concentration gradient
Density stratification
Equilibrium
Partial differential equations
Phenomenology
Random variables
Solvents
Stability
Stability analysis
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Summary:The classical problem of the Darcy-Bénard instability in a horizontal porous layer saturated by a binary fluid mixture and subject to a non-uniform solutal concentration field is revisited. In particular, a generalised anomalous diffusion model departing from the classical Fickian diffusion and accounting for subdiffusion or superdiffusion phenomena is employed. At the porous layer boundaries, a uniform vertical concentration gradient is imposed, so that an unstable density stratification arises. The boundaries are modelled as open, meaning that uniform pressure conditions are prescribed. A linear stability analysis of the basic rest state is carried out, showing how the departure from the classical Fickian diffusion affects dramatically the conditions for the onset of the instability.
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ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-025-02160-w