A macrotransport equation for the particle distribution in the flow of a concentrated, non-colloidal suspension through a circular tube
Bibliographic record
Abstract
Abstract A two-time-scale perturbation expansion is used to derive a cross-section-averaged convection–dispersion equation for the particle distribution in the flow of a concentrated suspension of neutrally buoyant, non-colloidal particles through a straight, circular tube. Since the cross-streamline motion of particles is governed by shear-induced migration, the Taylor-dispersion coefficient ${\mathscr{D}}_{eff} $ scales as ${U}^{\prime } {R}^{3} / {a}^{2} $ , ${U}^{\prime } $ , $R$ and $a$ being the characteristic velocity scale, the tube radius and the particle radius, respectively. Here ${\mathscr{D}}_{eff} $ is found to decrease monotonically with an increase in the particle concentration. The linear dependence of ${\mathscr{D}}_{eff} $ on ${U}^{\prime } $ implies that changes in the cross-section averaged axial concentration profile are dependent only on the total axial strain experienced by the suspension. This stipulates that the spatial evolution of a fluctuation in the concentration of particles in the flowing suspension, or the width of the mixing zone between two regions of different concentrations in the tube will be independent of the suspension velocity in the tube. A second interesting feature in particulate dispersion is that the effective velocity of the particulate phase is concentration-dependent, which, by itself (i.e. without considering Taylor dispersion), can produce either sharpening or relaxation of concentration gradients. In particular, shocks with positive concentration gradients along the flow direction can asymptotically evolve into time-independent distributions in an appropriately chosen frame of reference, and concentration pulses relax asymmetrically. These trends are contrasted with those expected from the classical problem of Taylor dispersion of a passive tracer in the same geometry. The results in this paper are especially relevant for suspension flows through microfluidic geometries, where the induction lengths for shear-induced migration are short.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.003 | 0.001 |
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".