Nonlinear spin-up flow in magnetic colloidal suspensions under high-frequency rotating magnetic fields
Bibliographic record
Abstract
We investigate the spin-up flow dynamics of dilute ferrofluids under a rotating magnetic field with a focus on high frequencies. Three models are compared: the first- and second-order approximations of the orientational probability density function and the full Smoluchowski equation. The first-order approximation, while computationally simple, has not been tested for its validity in high-frequency regimes, nor has it been compared with experimental data in such regimes. A parametric study explores the effects of magnetic field intensity, nanoparticle concentration, and particle diameter in the clusterless regime. Two types of ferrofluids—water-based and oil-based—are considered, each with different behaviors at high frequencies. The results show a transition in spin-up behavior from increasing torque and velocity with frequency to a regime where torque flattening causes flow attenuation. While the full Smoluchowski model captures additional nonlinear effects, the second-order approximation offers a computationally efficient and accurate alternative. It provides a good balance between accuracy and efficiency, especially when additional phenomena, such as the Kelvin body force, come into play.
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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 | 0.001 |
| 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".