Relating multicomponent mutual diffusion and intradiffusion for associating solutes. Application to coupled diffusion in water-in-oil microemulsions
Bibliographic record
Abstract
The binary mutual diffusion coefficient (D) for a dilute solution of a self-associating solute and the solute intradiffusion coefficient (D*) are related by D = D* + (dD*/dC), where C is the total solute concentration. This relation is extended to multicomponent systems. For solutions of two associating solutes, the ternary mutual diffusion coefficients D11, D12, D21, D22 and the solute intradiffusion coefficients D*1, D*2 are found to be related by D11 = D1* + C1∂D*1/∂C1, D12 = C1∂D*1/∂C2, D21 = C2∂D*2/∂C1, and D22 = D2* + C2∂D*2/∂C2. These results are used to interpret coupled diffusion in water + AOT (sodium bis(2-ethylhexyl)sulfosuccinate) + n-heptane (water-in-oil) microemulsions. Although the water(1) and AOT(2) components associate and intradiffuse together through the heptane–continuous solvent as AOT-coated water droplets, and hence D*1 ≈ D*2, the mutual diffusion of AOT is more rapid than that of water (D22 > D11), and there are counter-current coupled flows of AOT (D21 < 0) and large co-current coupled flows of water (D12 > 0). This behavior can be understood by noting that added water reduces the Brownian motion of the droplets by swelling the water cores (∂D*i/∂C1 < 0), whereas added AOT reduces the droplet size (∂D*i/∂C2 > 0) by providing more surfactant to coat the water. The predicted water and AOT intradiffusion coefficients are the eigenvalues of the mutual diffusion coefficient matrix.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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 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".