Extension of a viscous thread with temperature-dependent viscosity and surface tension
Bibliographic record
Abstract
We consider the evolution of a long and thin vertically aligned axisymmetric viscous thread that is composed of an incompressible fluid. The thread is attached to a solid wall at its upper end, experiences gravity and is pulled at its lower end by a fixed force. As the thread evolves, it experiences either heating or cooling by its environment. The heating affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We develop a framework that can deal with threads that have arbitrary initial shape, are non-uniformly preheated and experience spatially non-uniform heating or cooling from the environment during the pulling process. When inertia is completely neglected and the temperature of the environment is spatially uniform, we obtain analytic solutions for an arbitrary initial shape and temperature profile. In addition, we determine the criteria for whether the cross-section of a given fluid element will ever become zero and hence determine the minimum stretching force that is required for pinching. We further show that the dynamics can be quite subtle and leads to surprising behaviour, such as non-monotonic behaviour in time and space. We also consider the effects of non-zero Reynolds number. If the temperature of the environment is spatially uniform, we show that the dynamics is subtly influenced by inertia and that the location at which the thread will pinch is selected by a competition between three distinct mechanisms. In particular, for a thread with initially uniform radius and a spatially uniform environment but with a non-uniform initial temperature profile, pinching can occur either at the hottest point, at the points near large thermal gradients or at the pulled end, depending on the Reynolds number. Finally, we show that similar results can be obtained for a thread with initially uniform radius and uniform temperature profile but exposed to a spatially non-uniform environment.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".