A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium †
Abstract
:1. Introduction
2. The Base State
3. Mathematical Model
4. Stability Analysis
5. Two-Dimensional Results
6. Three-Dimensional Results
7. Conclusions
Funding
Conflicts of Interest
References
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Time-Evolving Base State | Step-Function Base Profile |
---|---|
Onset as function of time | Onset as function of boundary layer thickness |
Lack of a precise definition of stability | Mathematically precise definition of stability |
Stability of a time-dependent state | Steady analysis via normal modes |
Requires refined numerical techniques | Paper-and-pencil analysis |
Numerical tracking of the interface fluxes | Closed-form expressions for the interface fluxes |
Numerical extension to nonlinear regime | Analytically tractable weakly nonlinear convection state |
Challenging extension to three-dimensional case | Analytically tractable pattern formation study |
Approximate instability threshold values | Conservative instability threshold values |
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Hadji, L. A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium. Fluids 2018, 3, 60. https://doi.org/10.3390/fluids3030060
Hadji L. A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium. Fluids. 2018; 3(3):60. https://doi.org/10.3390/fluids3030060
Chicago/Turabian StyleHadji, Layachi. 2018. "A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium" Fluids 3, no. 3: 60. https://doi.org/10.3390/fluids3030060