Fluid-sphere electrophoresis at low surface charge
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".