Dynamics of fixed-volume pinned films – dealing with a non-self-adjoint thin-film problem
Bibliographic record
Abstract
The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these applications are characterized by a finite amount of liquid in an impermeable domain. The global mass conservation constraint, together with common boundary conditions (e.g. pinning), create quantitatively and qualitatively different dynamics than those of infinite films. Mathematically, this manifests itself as a non-self-adjoint problem. This work presents a combined theoretical and experimental study for this problem. We provide a time-dependent closed-form analytical solution for the linearized non-self-adjoint system that arises from these boundary conditions. We highlight that, in contrast to self-adjoint problems, here, special care should be given to deriving the adjoint problem to reconstruct the solution based on the eigenfunctions properly. We compare these solutions with those obtained for permeable and periodic boundary conditions, representing common models for self-adjoint thin-film problems. We show that, while the initial dynamics is nearly identical, the boundary conditions eventually affect the film deformation as well as its response time. To experimentally illustrate the dynamics and to validate the theoretical model, we fabricated an experimental set-up that subjects a thin liquid film to a prescribed normal force distribution through dielectrophoresis, and used high-frame-rate digital holography to measure the film deformation in real time. The experiments agree well with the model and confirm that confined films exhibit a different behaviour which could not be predicted by existing models.
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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 | 0.001 |
| 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".