Instability of falling films of discontinuously shear-thickening fluid
Bibliographic record
Abstract
Aqueous suspensions of cornstarch abruptly increase their viscosity on raising either shear rate or stress, and display the formation of large-amplitude waves when flowing down inclined channels. The two features have been recently connected using constitutive models designed to describe discontinuous shear thickening. By including time-dependent relaxation and spatial diffusion of the frictional contact density responsible for shear thickening, an analysis of steady sheet flow and its linear stability is presented. The inclusion of such effects is motivated by the need to avoid an ill-posed mathematical problem in thin-film theory and the resulting failure to select any preferred wavelength for unstable linear waves. Relaxation, in particular, eliminates an ultraviolet catastrophe in the spectrum of unstable waves and furnishes a preferred wavelength at which growth is maximized. The nonlinear dynamics of the unstable waves is briefly explored. It is found that the linear instability saturates once disturbances reach finite amplitude, creating steadily propagating nonlinear waves. These waves take the form of a series of steep, shear-thickened steps that translate relatively slowly in comparison with the mean flow.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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".