A Mean Phi Model for Pressure Filtration of Fine and Colloidal Suspensions
Bibliographic record
Abstract
A working model for engineering analysis of pressure filtration is presented. Based on the filtration characteristics of fine and colloidal suspensions, the process was divided into two stages. A time-invariant spatially uniform volume fraction of solids approximation is invoked in the growing filter cake stage (stage 1). A time-dependent spatially uniform volume fraction of solids assumption is made in the cake consolidation stage (stage 2). The two models, named collectively as Mean Phi (M-P) model, have a common physical basis, seamless continuity between the stages and internal consistency. The M-P model has only three parameters: terminal or equilibrium volume fraction of solids in the filter cake that is related to its compressive yield stress, critical volume fraction of solids, which joins stage 1 and stage 2, and a permeability factor, which is common to stages 1 and 2. The model is validated with a large number of colloidal suspensions filtered under highly diverse physical-chemical process conditions. A Pareto profile is identified that relates the timescale of filtration and the extent of dewatering achieved, the two most important performance indices of the process. On présente un modèle d'analyse de procédé pour la filtration sous pression. Le procédé a été divisé en deux étapes d'après les caractéristiques de filtration des suspensions colloïdales et des fines. Une fraction volumique de solides spatialement uniforme et ne variant pas dans le temps de l'approximation des solides est utilisée pour l'étape de croissance du gâteau de filtration (étape 1). L'hypothèse d'une fraction volumique de solides spatialement uniforme et dépendante du temps est utilisée pour l'étape de consolidation du gâteau (étape 2). Les deux modèles, qu'on appelle collectivement modèle M-P (Mean Phi), ont une base physique commune, à savoir une continuité sans interruption entre les étapes et une cohérence interne. Le modèle M-P n'a que trois paramètres : la fraction volumique terminale ou d'équilibre des solides dans le gâteau de filtration qui est reliée à la contrainte seuil de compression, la fraction volumique critique des solides, qui joint les étapes 1 et 2, ainsi qu'un facteur de perméabilité, qui est commun aux étapes 1 et 2. Le modèle est validé à l'aide d'un grand nombre de suspensions colloïdales filtrées dans des conditions de procédé physicochimique extrêmement diverses. On a déterminé un profil Pareto qui relie l'échelle de temps de la filtration et le degré de déshydratation obtenus, qui sont les deux plus importants indices du procédé.
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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".