Measurement of Ternary Mutual Diffusion Coefficients from Ill-Conditioned Taylor Dispersion Profiles in Cases of Identical or Nearly Identical Eigenvalues of the Diffusion Coefficient Matrix
Bibliographic record
Abstract
Taylor dispersion has gained popularity for the measurement of mutual diffusion coefficients ( D ik ) for multicomponent solutions. In practice, however, the analysis of dispersion profiles, like the analysis of free-diffusion boundaries measured by optical interferometry, becomes ill-conditioned for solutes of similar diffusivities if the eigenvalues of the D ik matrix differ by less than about (5 to 10) %. These numerical difficulties, well-known in studies of multiexponential decays with nearly identical decay constants, can produce large errors in measured D ik coefficients and even rule out studies of important systems, including solutions of isomers, oligomers, polydisperse polymers, strongly associated solutes, and mixed electrolytes composed of ions of similar mobility. To investigate diffusion in these systems, equations are derived for the Taylor dispersion profiles produced by ternary mutual diffusion with equal eigenvalues. Using these equations, a simple least-squares procedure is developed to evaluate D ik coefficients from equal-eigenvalue profiles. D ik coefficients are reported from the analysis of severely ill-conditioned refractive-index profiles measured for aqueous solutions of 1-propanol + 2-propanol, 1-propanol + glycine, and mannitol + tetra(ethyleneglycol). In cases where the eigenvalues are not identical, but differ by several percent, the resulting errors in the D ik coefficients are estimated to be small and similar in magnitude to the accuracy of the Taylor measurements.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".