Stability analysis of two-phase buoyancy-driven flow in the presence of a capillary transition zone
Bibliographic record
Abstract
Natural convection that results from the dissolution of a diffusive species into a fluid saturated porous layer in the presence of a capillary transition zone is an important phenomenon in geological flows. The prediction of the onset of convection has remained elusive under the theory of gravitationally unstable multiphase flow in porous media. The present study offers a paradigm for the stability of two-phase buoyancy-driven flow in the presence of the capillary transition zone in a saturated porous medium, which allows for a quantitative description of the onset of natural convection. The analysis, which is based on the quasi-steady-state approximation, stresses the critical role of the capillary transition zone and the upward crossflow between the diffusive boundary layer and the capillary transition zone in the stability of the system, as well as in the transient growth of perturbations. We show that the instability problem can be characterized by capillary-dominant and buoyancy-dominant regimes with a transition in between. In the capillary-dominant regime, capillarity has a strong role in destabilizing the diffusive boundary layer. While in the buoyancy-dominant regime, the capillary transition zone is small enough that it can be ignored and the buoyancy force is the sole cause of the instability. Furthermore, our analysis shows that the capillary transition zone can potentially accelerate the evolution of the natural convection over 6 times faster than the buoyancy-dominant regime. Finally, the nonlinear dynamics of the system is studied using direct numerical simulations. The nonlinear simulations confirm the predictions from the linear stability analysis.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".