Energy balance in viscous liquid containing a bubble: Rise due to buoyancy
Bibliographic record
Abstract
The total energy balance of a system consisting of a bubble (radius 0.74 mm) freely rising in viscous liquid under the action of buoyancy was considered. Values of bubble acceleration, local and terminal velocities, and shape deformations calculated by numerically solving the Navier‐Stokes equation are compared with experimentally determined values. Additionally, the energies of the system associated with bubble motion (kinetic, potential, and rate of viscous energy dissipation), obtained from simulations, are given. On the basis of energy balances obtained for the system, two independent relations describing the motion of a bubble (Lagrange and Joseph equations) were used to show that, for steady‐state conditions, the constant (terminal) velocity of the bubble is a result of balance between buoyancy force and the drag originating from energy dissipation due to fluid viscosity. According to the calculations performed, the discrepancy between the expected and actual results of the Lagrange and Joseph equations for the system considered was ∼1 %. The estimated added mass coefficient was in close agreement with expected theoretical value for deformed spheres, and increased with decreasing tube radius.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".