SUITABILITY OF CRANK'S SOLUTIONS TO FICK'S SECOND LAW FOR WATER DIFFUSIVITY CALCULATION AND MOISTURE LOSS PREDICTION IN OSMOTIC DEHYDRATION OF FRUITS
Bibliographic record
Abstract
ABSTRACT Various solutions (Crank's) of Fick's law of diffusion have been used to predict moisture loss ( ML ) in osmotic dehydration, by correlating experimental data. Selection of a particular solution should depend on the sample geometry and the fulfillment of a number of assumptions made to obtain that solution. Crank developed solutions for long‐time, short‐time, and a solution for diffusion into a sample from a well‐stirred tank for sheets, cylinders and spheres. This work was carried out to find the most suitable Crank's solution to predict ML for a wide range of published data. The long‐time solution and the solution for a well‐agitated tank, for plane sheets, satisfactorily predicted ML of semi‐infinite sheets and semi‐infinite cylinders. PRACTICAL APPLICATIONS Crank's solutions of Fick's law for various geometric shapes are used in practice to determine the diffusivity from experimental data for unit operations governed by mass transfer. Once the diffusivity is known, those solutions can be used to predict the kinetics of mass transfer. One of the specific cases where this information is useful is in determining the loss of water for the process of osmotic dehydration. Crank developed solutions for several sets of initial and boundary conditions and for various product geometries. This article evaluates the suitability of Crank's solutions for a wide range of experimental data and indicates the most appropriate solution form to be used for each geometric shape.
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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 | 0.004 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".