Hydrodynamic interaction for rigid dumbbell suspensions in steady shear flow
Bibliographic record
Abstract
From kinetic molecular theory, we can attribute the rheological behaviors of polymeric liquids to macromolecular orientation. The simplest model to capture the orientation of macromolecules is the rigid dumbbell. For a suspension of rigid dumbbells, subject to any shear flow, for instance, we must first solve the diffusion equation for the orientation distribution function. From this distribution, we then calculate the first and second normal stress differences. To get reasonable results for the normal stress differences in steady shear flow, one must account for hydrodynamic interaction between the dumbbell beads. However, for the power series expansions for these normal stress differences, three series arise. The coefficients for two of these series, (ck, dk), are not known, not even approximately, beyond the second power of the shear rate. Analytical work on many viscoelastic material functions in shear flow must be checked for consistency, in their steady shear flow limits, against these normal stress difference power series expansions. For instance, for large-amplitude oscillatory shear flow, we must recover the power series expansions in the limits of low frequency. In this work, for (ck, dk), we arrive at the exact expressions for the first 18 of these coefficients.
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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".