Long-wave linear stability theory for two-fluid channel flow including compressibility effects
Bibliographic record
Abstract
We present the linear stability of the laminar flow of an immiscible system of a compressible gas and incompressible liquid separated by an interface with large surface tension in a thin inclined channel. The flow is driven by an applied pressure drop and gravity. Following the air–water case, which is found in a variety of engineering systems, the ratio of the characteristic values of the gas and liquid densities and viscosities are assumed to be disparate. Under the lubrication approximation, and assuming ideal gas behaviour and isothermal conditions, this approach leads to a coupled non-linear system of partial differential equations describing the evolution of the interface between the gas and the liquid and the streamwise density distribution of the gas. This system also includes the effects of viscosity stratification, inertia, shear and capillarity. A linear stability analysis that allows for physically relevant non-zero pressure-drop base state is then performed. In contrast to the zero-pressure drop case which is amenable to the classical normal-mode approach, this configuration requires numerically solving a boundary-value problem for the gas density and interfacial deviations from the base state in the streamwise coordinate. We find that the effect of the gas compressibility on the interfacial stability in the limit of vanishingly small wavenumber is destabilizing, even for Stokes flow in the liquid. However, for finite wavenumber disturbances, compressibility may have stabilizing effects. In this regime, sufficient shear is required to destabilize the flow.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".