Hydrodynamic Cell Model: General Formulation and Comparative Analysis of Different Approaches
Bibliographic record
Abstract
Abstract This paper is concerned with the Cell Model method of addressing hydrodynamic flow through system of solid particles. The starting point of the analysis is the general problem formulation intended for describing a pressure driven flow through a diaphragm which can be considered as a set of representative cells having arbitrary shape and containing any number of particles. Using the general problem formulation, the hydrodynamic field inside an individual representative cell is interrelated with the applied pressure difference and the external flow velocity. To this end, four relationships containing integrals over the outer boundary of a representative cell are derived in the paper. Assuming that the representative cell is a sphere containing a single particle in the centre, the derived general relationships are transformed into outer cell boundary conditions employed in the literature by different authors. The general number of the obtained outer boundary conditions is more than the required number. Accordingly, by choosing different sets of the outer boundary conditions, different models are considered and compared with each other and with the results obtained by others for regular particle arrays. The common and different features of the hydrodynamic and electrodynamic versions of the Cell Model approaches are analyzed. Finally, it is discussed which version of the cell model gives the best approximation while describing pressure and electrically driven flows through a diaphragm and sedimentation of particles.
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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 | 0.000 |
| 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 | 0.000 |
| 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".