Modeling the intrinsic viscosity of polydisperse disks
Bibliographic record
Abstract
In this work, we model the rheology of dilute colloidal oblate spheroids in their high aspect ratio limit of circular disks. Theoretical models for the intrinsic viscosity, [η], of disks in shear flow are reviewed: The shear-independent, monodisperse Kuhn-Kuhn model, its polydisperse form by van der Kooij, and the shear-dependent models of Stewart and Sorenson, Leal and Hinch, and Brenner. Based on these previous works, three analytical models are introduced to describe the shear response over the entire range of practically accessible rotational Peclet numbers (Pe) and aspect ratios. Using the fact that [η] is linearly additive for sufficiently dilute systems we derive a general expression for polydisperse disks as a function of the two independent variables of particle diameter D and thickness t, that is, assuming D and t to be uncorrelated independent variables. We then argue for continuum modeling being preferable to discrete for using rheological measurements to estimate particle size distribution parameters. Computational results are shown for the continuum model in shear flow and generalized to uniaxial and planar extension, as well as to different particle distributions such as lognormal, normal, and bimodal. Finally, a modified form of [η], which we describe as innate viscosity (η), is suggested as an alternative method of modeling rheology of dilute dispersions.
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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 | 0.001 |
| 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".