Thermodynamically consistent phase-field modelling of activated solute transport in binary solvent fluids
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Bibliographic record
Abstract
Active diffusion of substances in binary immiscible and incompressible fluids with different densities occurs universally in nature and industry, but relevant mathematical models and numerical simulation have been studied scarcely so far. In this paper, a thermodynamically consistent phase-field model is established to describe the activated solute transport in binary fluids with different densities. A mixed free-energy function for multiple solutes is proposed, which leads to different solute chemical potentials in binary solvent fluids, thus it has the ability to characterize the solubility difference of the solutes in two solvents. The two-phase flow is governed by a general hydrodynamic phase-field model that can account for general average velocity and different densities. The proposed model is derived rigorously using the second law of thermodynamics. Moreover, a general multi-component solute diffusion model is established using the Maxwell–Stefan approach, which involves the crossing influences between different solutes. To solve the model effectively, an efficient, linearized and decoupled numerical method is proposed for the model as well. The proposed numerical method can preserve the thermodynamical consistency, i.e. obeying an energy dissipation law at the discrete level, as well as guarantee the mass conservation law for the solutes and solvent fluids. Numerical experiments are carried out to show that the proposed model and numerical method can simulate various processes of the solute active diffusion in two-phase solvent fluids.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it