Electrostatic Double Layer Force between Two Spherical Particles in a Straight Cylindrical Capillary: Finite Element Analysis
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Bibliographic record
Abstract
A numerical solution of the nonlinear Poisson−Boltzmann equation based on finite element approximation is developed to assess the interaction force between two identical spherical particles located inside a straight cylindrical capillary. The interaction forces for constant potential and constant charge particle surfaces are calculated for different surface potentials on the cylinder wall, various particle sizes, and different cylinder radii. The interaction force between the spheres was affected significantly by the proximity of the charged cylinder wall, particularly for constant surface potential particles. The influence of the cylinder wall on the particle−particle interaction force was most pronounced when the particle radius was comparable to the cylinder radius. The results suggest that when the cylinder and the particle surfaces are like-charged (bearing the same sign of the charge or surface potential), the electrostatic repulsion between the two spherical colloids is considerably suppressed. Conversely, the interparticle repulsion is more pronounced when the cylinder wall is oppositely charged with respect to the particles. The possibility of inducing a force modulation between two charged particles by altering the surface potential of the confining cylindrical wall appears to be viable on the basis of these simulations.
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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 | 0.001 |
| 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) | 0.002 | 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