Stability criteria and convective mass transfer from the falling spherical drops, part I: Bingham plastic fluids
Bibliographic record
Abstract
Abstract This work deals with the flow and mass transfer around a falling spherical drop in Bingham plastic fluids. Bubbles, drops, and particles are often dispersed in a suspending fluid of non‐Newtonian nature. For example, suspensions of particles in a polymer solution are used in hydraulic fracturing slurries and swarms of bubbles are used in airlift bioreactors containing various biomacromolecules, as well as in foam production, degassing, and de‐volatilization of polymer melts. Governing equations for momentum and mass transfer and the Bingham constitutive equation are solved over a wide range of dimensionless groups as Reynolds number, ; Schmidt number, ; Bingham number, ; and viscosity ratio (0.1 and 10). The local underline transport processes are expressed using streamlines, concentration contours, and sheared and un‐sheared regions, whereas the average transport quantities are reported in terms of drag coefficient, critical yield‐stress parameter, and Sherwood number. A co‐existence of sheared and un‐sheared regions occurs within the flow domain due to the fluid‐yield stress. The sheared regions progressively diminish with the increasing value of the Bingham number. On the other hand, inertial effects (increasing ) promotes the expansion of the sheared region in the flow domain. The new modified dimensionless groups are defined by re‐scaling the governing equations based on the effective viscosity of the fluid. Finally, the present numerical values of the drag and average Sherwood number are correlated using the new modified dimensionless numbers.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".