Mathematical Model for Mixing Reactants in a Capillary Microreactor by Transverse Diffusion of Laminar Flow Profiles
Bibliographic record
Abstract
Transverse diffusion of laminar flow profiles (TDLFP) was recently suggested as a generic approach for mixing reactants inside a capillary microreactor. Conceptually, solutions of reactants are injected inside the capillary by high pressure as a series of consecutive plugs. Because of the laminar nature of the flow inside the capillary, the nondiffused plugs have parabolic profiles with predominantly longitudinal interfaces between the plugs. After the injection, the reactants are mixed by transverse diffusion across the longitudinal interfaces. TDLFP-based mixing is still in its infancy as only the principle was proved. Here, we develop the theory of TDLFP and introduce a dimensionless parameter, York number, which can be used in predicting the quality of TDLFP-based mixing. The theory uses a single simplifying assumption that the longitudinal diffusion is negligible; this assumption is readily satisfied. We then develop a numerical model of TDLFP and use it to simulate the concentration profiles of three reactants mixed by TDLFP in the capillary. The correlation between the York number and quality of mixing is analyzed. Two ways of improving the quality of TDLFP-based mixing are suggested and studied: (i) increasing the longitudinal interface between the plugs by a long last plug of a solvent and (ii) "shaking" the injected reactants by a series of alternating negative and positive pressure pulses. The developed theory and computational simulation of TDLFP will stimulate the practical use of capillary microreactors.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".