Electrostatic Double Layer Force between a Sphere and a Planar Substrate in the Presence of Previously Deposited Spherical Particles
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Bibliographic record
Abstract
A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.
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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 | 0.000 |
| 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 it