Parallel superposition of oscillatory shearing on steady shear flow: Normal stresses
Bibliographic record
Abstract
Of the many rheological material functions, the two most important are (i) steady shear flow and (ii) oscillatory shear flow. Another canonical rheological material function is constructed by superposing, in parallel, at small-amplitude, romanette (ii) upon (i). To this, complex fluids, including polymeric liquids, will respond with a complex viscosity that depends on both the steady shear rate of (i) and the angular frequency of (ii). Our recent work [Phys. Fluids 36(8), 083121 (2024)] uncovers the macromolecular origins of this complex viscosity dependence using rotarance theory. By rotarance, we mean at least involving the hydrodynamic resistances of the macromolecules to reorientation. However, to parallel superposition, complex fluids also respond with two normal stress differences. We devote this paper to uncovering the macromolecular origins of both of these normal stress differences, using rotarance theory. For both the first and second normal stress differences, we arrive at analytical expressions for the complex normal stress coefficients. We find that these increase with the lopsidedness of the macromolecular structure, be this lopsidedness prolate or oblate. We further find that, whereas the real and minus imaginary parts of the parts of the complex components of the primary normal stress difference are signed identically, the real and minus imaginary parts of the corresponding secondary are signed oppositely.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".