Hydrodynamic interaction and complex viscosity of multi-bead rods
Bibliographic record
Abstract
One good way to explain the elasticity of a polymeric liquid is to just consider the orientation distribution of the macromolecules. When exploring how macromolecular architecture affects the elasticity of a polymeric liquid, we find the general rigid bead–rod theory to be both versatile and accurate. This theory sculpts macromolecules using beads and rods. Whereas beads represent points of Stokes flow resistances, the rods represent rigid separations. In this way, how the shape of the macromolecule affects its rheological behavior in suspension is determined. Until recently, general rigid bead–rod theory has neglected interferences of the Stokes flow velocity profiles between nearby beads. We call these hydrodynamic interactions, and we here employ our new method for exploring how these interactions affect the complex viscosity of suspensions of multi-bead rods. These multi-bead rods are also called shish-kebabs. We use the center-to-center distance between adjacent beads as the characteristic length. We proceed analytically, beginning with a geometric expression for the shish-kebab bead positions. Our analytical solution for the complex viscosity presents as one for N=3,5,6,7,8,…, one for N=4, and another for the rigid dumbbell, N=2. We find that for shish-kebabs, hydrodynamic interactions (i) increase zero-shear viscosity, (ii) increase zero-shear first normal stress coefficient, (iii) decrease the real part of the dimensionless complex viscosity, and (iv) increase minus the dimensionless imaginary part. We find that the combination of (iii) and (iv) explains crossovers of the parts of the complex viscosity. We further find that for a monodisperse polystyrene solution, the general rigid bead–rod theory with hydrodynamic interaction, for both parts of the complex viscosity, provides stunning improvement over without.
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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".