Near-wall estimates of the concentration and orientation distribution of a semi-dilute rigid fibre suspension in Poiseuille flow
Bibliographic record
Abstract
A model is presented to predict the orientation and concentration state of a semi-dilute, rigid fibre suspension in a plane channel flow. A probability distribution function is used to describe the local orientation and concentration states of the suspension and evolves according to a Fokker–Planck equation. The fibres are free to interact with each other hydrodynamically and are modelled using the approach outlined by Folgar & Tucker ( J. Reinf. Plast. Comp. vol. 3, 1984, p. 98). Near the channel walls, the no-flux boundary conditions as proposed by Schiek & Shaqfeh ( J. Fluid Mech. vol. 296, 1995, p. 271) are applied on the orientation distribution function. With this approach, geometric constraints are used to couple the fibres' rotary motion with their translational motion. This eliminates physically unrealistic orientation states in the near-wall region. The concentration distribution is modelled in a similar manner to that proposed by Ma & Graham ( Phys. Fluids vol. 17, 2005, art. 083103). A two-way coupling between the fibre orientation state and the momentum equations of the suspending fluid is considered. Experiments are performed to validate the numerical model by visualizing the motion of tracer fibres in an index-of-refraction matched suspension. The orientation distribution function is determined experimentally based on these observations of fibre motion and a comparison is made with the model predictions. Good agreement is shown particularly near the channel walls. The results indicate that at distances less than one-half of a fibre length from the channel walls, the model accurately predicts the available fibre orientation states and the distribution of fibres amongst these states. The model further predicts a large concentration gradient in this region that is also observed experimentally. The magnitude of the concentration gradient in the near-wall region is shown to increase with increasing fibre concentration.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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 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".