Work

Open Boundaries, Anomalous Diffusion and the Darcy-Bénard Instability

Year: 2025

Type: article

Abstract: 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.

Source: Transport in Porous Media

DOI: 10.1007/s11242-025-02160-w

Authors: A. Barletta, D. A. S. Rees, M. Celli, P. V. Brandão

Institutions: University of Bologna, University of Bath

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funder: Università di Bologna