Pattern method for higher harmonics of first normal stress difference from molecular orientation in oscillatory shear flow
Bibliographic record
Abstract
This study examines the simplest relevant molecular model of a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow: rigid dumbbells suspended in a Newtonian solvent. For such suspensions, the viscoelastic response of the polymeric liquid depends exclusively on the dynamics of dumbbell orientation. Previously, the explicit analytical expressions of the zeroth, second, and fourth harmonics of the alternating first normal stress difference response in LAOS have been derived. In this paper, we correct and extend these expressions by seeking an understanding of the next higher harmonic. Specifically, this paper continues a series of studies that shed light on molecular theory as a useful approach in investigating the response of polymeric liquids to oscillatory shear. Following the general method of Bird and Armstrong [“Time-dependent flows of dilute solutions of rodlike macromolecules,” J. Chem. Phys. 56, 3680 (1972)], we derive the expression of the first normal stress coefficient up to and including the sixth harmonic. Our analysis relies on the extension of the orientation distribution function to the sixth power of the shear rate. Our expression is the only one to have been derived from a molecular theory for a sixth harmonic and thus provides the first glimpse of the molecular origins of a first normal stress difference higher than the fourth.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.010 | 0.004 |
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".