Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow
Bibliographic record
Abstract
We report two-dimensional simulations of drop dynamics on a substrate subject to a wetting gradient and an external pressure gradient along the substrate. A phase-field formulation is used to represent the drop interface, and the moving contact line is modelled by Cahn–Hilliard diffusion. The Navier–Stokes–Cahn–Hilliard equations are solved by finite elements on an adaptively refined unstructured grid. For a single drop and a pair of drops, we consider three scenarios of drop motion driven by the wetting gradient only, by the external flow only, and by a combination of the two. Both the capillary force and the hydrodynamic drag depend strongly on the shape of the drop. Since the drop adapts its shape to the local wetting angles and to the external flow on a finite time scale, hysteresis is a prominent feature of the drop dynamics under opposing forces. For each wetting gradient, there is a narrow range of the magnitude of the external flow within which a single drop can achieve a stationary state. The equilibrium drop shape and position depend on its initial shape and the history of forcing. For a pair of drops, the wetting gradient or external flow alone tends to produce catch-up and coalescence. The flow-driven coalescence arises from a viscous shielding effect that relies on the asymmetric shape of the trailing drop once it is deformed by flow. This mechanism operates at zero Reynolds number, but is much enhanced by inertia. With the two forces opposing each other, the external flow favours separation while the wetting gradient favours coalescence. The outcome depends on their competition.
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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 | 0.001 |
| 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".