Assigning macromolecular meaning to nonlinear continuum rheology
Bibliographic record
Abstract
The Oldroyd 8-constant continuum framework has yielded elegant analytical solutions for many polymer processing flows. However, continuum frameworks are silent on macromolecular structure. We can assign macromolecular meaning to the continuum constants by bridging continuum frameworks to the macromolecular theory of polymeric liquid dynamics. When the Oldroyd 8-constant framework has been bridged to rigid dumbbell theory (two-step), no higher order rheology was predicted (ν1=ν2=0). By higher order, we mean the nonlinear rheology. This troubled Bird (1972), motivating his modified Oldroyd 8-constant continuum framework, which does predict higher order rheology, to which meaning in rigid dumbbell theory is assigned. By two-step, we mean we get the three Jeffreys model constants from the macromolecular expression for the complex viscosity, and then solve five equations simultaneously for the five remaining constants. In this paper, in three steps, we bridge the Bird 8-constant framework to the more versatile rotarance theory (general rigid bead-rod theory). By three-step, we mean we get the three Jeffreys model constants from the macromolecular expression for the complex viscosity, and then solve three equations simultaneously for the next three, and finally solving two equation simultaneously for the remaining two higher order constants. By versatile, we mean accommodating any axisymmetric macromolecular structure (including the rigid dumbbell). We find the constants in the Bird 8-constant framework to be explicit functions of just one dimensionless macromolecular attribute: the ratio of the moment of inertia about the molecular axis, to the moment about either transverse axis. We thus assign macromolecular meaning to the higher order rheology. In passing, we also discover a new bridge to the Oldroyd 8-constant framework (three-step), which also assigns macromolecular meaning to the higher order rheology.
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 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".