Stability Analysis of a Multicomponent Vapor–Gas Bubble in Contact with a Liquid–Gas Solution
Bibliographic record
Abstract
Stability of vapor–gas bubbles, homogeneously nucleated within a liquid–gas solution, depends on the temperature and pressure of the liquid phase, along with the concentration of dissolved gaseous components. While extensive theoretical and experimental investigations have been conducted on bubble nucleation within single-component systems, research on multicomponent systems has mainly focused on binary liquid–gas solutions comprising a solvent and one dissolved gas. Moreover, existing studies on the stability of vapor–gas bubbles have predominantly examined the stability with respect to bubble size, leaving other critical factors relatively unexplored. Here, we present a methodology to determine potential equilibrium states for a single vapor–gas bubble homogeneously nucleated within a large multicomponent liquid–gas solution, encompassing a subcritical solvent and n – 1 gaseous components, with temperature and liquid phase pressure held constant. Additionally, we assess equilibrium state stability by analyzing the free energy change of the system with respect to both bubble size and the composition of the vapor–gas phase within the bubble, using rigorous phase equilibrium equations to account for nonideal behavior in both liquid–gas and vapor–gas phases. We then apply this to investigate the number and nature of equilibrium states in a ternary system of water–oxygen–nitrogen across various scenarios of oxygen and nitrogen saturation levels in the liquid phase, while also meticulously examining the effects of liquid phase temperature and pressure on the stability of the system. The proposed model can be used to optimize the design of micro–nano bubble technologies for diverse engineering applications, ranging from agriculture to water treatment and biomedicine.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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".