Hydrodynamic Models for Rheologically Complex Fluids in Co- and Countercurrent Gas−Liquid Packed-Bed Bioreactors
Bibliographic record
Abstract
Processes implying the flow of rheologically complex fluids simultaneously with a gas phase through packed beds are multitudinous in biochemical processing. Paradoxically, conceptual models relating the packed-bed bioreactor hydrodynamics to the rheological characteristics of the non-Newtonian fluids in play are virtually nonexistent in this particular area. An attempt has, therefore, been made with this contribution to fill in this gap by providing a series of hydrodynamic models for the prediction of pressure drop and liquid holdup in cocurrent and countercurrent two-phase flow through packed beds in the so-called film-flow conditions, i.e., trickle-flow, preloading, and near-loading zones. The class of slit models has been generalized by extending the modeling to yield-stress inelastic non-Newtonian fluids such as Herschel−Bulkley and Bingham plastic fluids and, as particular cases, to the Ostwald−De Waele and Newtonian fluids. Model asymptotic formulations have also been derived for Herschel−Bulkley fluids flowing downward with stagnant gas (pure trickle flow) to yield their liquid holdup under gravity-driven flows, as well as in single-phase-flow conditions to yield the single-phase frictional pressure drops. The response of these models to changes in yield stress, consistency and power-law index, and gas density, for both cocurrent downflow and countercurrent flow, reveals that non-Newtonian fluids behave qualitatively as their Newtonian homologues in terms of fluid throughputs, apparent viscosity, and gas density.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".