Dielectric Force and Relative Motion between Two Spherical Particles in Electrophoresis
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Bibliographic record
Abstract
When two particles close to each other are in electrophoretic motion, each particle is under the influence of the nonuniform electric field generated by the other particle. Two particles may attract or repel each other due to the dielectric force, depending on their positions in the nonuniform electric field. In this work, the dielectric interaction and the subsequent relative motion of the two arbitrarily oriented spherical particles are analyzed. The dielectric force is obtained by integrating the Maxwell stress. The result is valid for arbitrary orientations of the particles under the thin electrical-double-layer assumption. The magnitude of the dielectric force is compared to the so-called inertia-induced force, which shows that the dielectric force is normally much greater than the inertia-induced force. The relative velocity of particles is determined by the force balance between the dielectric force and the Stokes drag. The regions of attraction and repulsion are defined. It is shown that a pair of particles eventually aligns parallel to the externally applied electric field, except in the case where the two particles are initially oriented perpendicular to the electric field. A closed-form analytical solution is obtained for the particle trajectory by using the approximate expression for the dielectric force valid for not-too-closely located particles.
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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