A Thermodynamic Interpretation of the “Excluded-Volume Effect” in Coupled Diffusion
Bibliographic record
Abstract
Strongly coupled diffusion has been reported for fluxes of solutes that differ significantly in molecular size. According to the excluded-volume model, a solute increases the effective concentrations of other solutes by reducing the volume of solution they can occupy. The flux of solute 2 produced by the gradient ∇ c 1 in the concentration of solute 1 is interpreted as the ordinary diffusion of solute 2 down its effective concentration gradient. Cross-diffusion coefficient D 21 = D 22 c 2 V 1,eff /(1 − c 1 V 1,eff ) 2 is predicted, where V 1,eff is the effective molar volume of solute 1. This model does not account for countercurrent coupled diffusion ( D 21 < 0) and is found to be inconsistent with the Onsager reciprocal relation (ORR). A thermodynamic model of coupled transport is developed by approximating the flux of solute i as the product of its concentration, mobility, and chemical potential gradient driving force (−∇μ i ), which gives D 21 = D 22 c 2 ( V 1 − V 0 )/[1 − c 1 ( V 1 − V 0 )], where V i is the partial molar volume of component i and the solvent is component 0. For dilute solutions with V 1 ≫ V 0, the thermodynamic prediction D 21 ≈ c 2 V 1 D 22 and the excluded-volume prediction D 21 ≈ c 2 V 1,eff D 22 are qualitatively similar, but the thermodynamic model does not require the assumption of effective concentrations or effective volumes, provides a physical explanation for coupled diffusion, and is consistent with the ORR. Moreover, because ∂μ 2 /∂ c 1 is proportional to V 1 − V 0, the thermodynamic model suggests that a concentration gradient in solute 1 can drive co-current or counter-current flows of solute 2, depending on the relative volumes of solute 1 and solvent 0. These features are illustrated by comparing measured and predicted D ik coefficients for solutions of n -octane(1) + n -hexadecane(2) in n -dodecane(0) at nine different compositions at 25 °C.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".