Fluid-sphere electrophoresis at low surface charge
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Bibliographic record
Abstract
We derive an analytical Debye–Hückel approximate solution of Hill’s fluid-sphere electrophoresis model, generalizing Booth’s theory with interfacial Damköhler ( Da ), Péclet ( Pe ) and Marangoni ( Ma ) numbers, among others. Booth’s theory holds generally for Da → ∞ , which corresponds to fast interfacial-exchange kinetics and/or vanishing interfacial-charge mobility—conditions that are difficult to realized in practice. For nano- and micro-scale air bubbles in water at pH = 7 , nano-bubbles with reduced radius κ a ≪ 1 are in a regime where the electrophoretic mobility is independent of Da . On the other hand, micro-bubbles with κ a ≫ 1 have a mobility that varies significantly with Da . Nano-bubbles have a higher interfacial potential than their micro-bubble counterparts. For spherical micro- and macro-air bubbles in water at pH = 7 , the surface potential varies with bubble size ( − ζ ≈ 7 –28 mV), notably smaller in magnitude than from Smoluchowski’s model (for rigid spheres) or Booth’s model (for fluid spheres). Our theory, which provides the first compelling interpretation of Alty’s (1924) air-bubble mobilities in water, suggests that a large body of ζ -potentials may need to be reevaluated in the context of finite interfacial charge mobility and exchange kinetics.
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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