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This service models how solutes redistribute as your material solidifies directionally, covering rejection, concentration build-up and impurity enrichment across your chosen material system.
Depending on the package chosen, deliverables can include a solute concentration profile built from the Scheil equation and the BPS effective partition coefficient, an enrichment ratio plotted against solidification rate, an effective partition coefficient analysis showing the solute trapping effect, and a boundary layer concentration profile. Work is presented as up to 4 publication-quality figures in PNG and PDF format, together with an interpretation report.
For an Al-Cu system with k0 = 0.14, C0 = 4.5 wt% and D = 3e-9 m²/s, a scan across growth rates gives the following:
| Growth rate | k_eff | Enrichment ratio |
|---|---|---|
| 1 um/s | 0.144 | 7.42x |
| 10 um/s | 0.185 | 7.89x |
| 100 um/s | 0.820 | 1.88x |
At the lower speeds, enrichment of around 7 to 8 times sits within the range reported for Al-Cu segregation in the literature (6-10x). At the higher rate, solute trapping reduces enrichment sharply.
Useful for alloy solidification work (Al-Cu, Al-Si, nickel-based superalloys, high-entropy alloys), freeze casting and ice templating studies, progressive freeze concentration in food and pharmaceutical contexts, semiconductor crystal growth such as silicon and GaAs, salt and mineral purification, metal additive manufacturing melt pools, and any system where solute rejection matters.
The analysis applies the Burton-Prim-Slichter effective partition coefficient, which balances interface kinetics (k0) against mass transport governed by velocity, boundary layer thickness and diffusivity.
ORCID 0009-0008-4540-1381; related preprint available via Zenodo DOI 10.5281/zenodo.22771462.
Turnaround runs from 3 to 7 business days depending on package. Please provide the domain this order is for and your brief.
This is academic analysis for research reference and does not serve as a legally valid engineering assessment for production processes.
Your order opens its own thread here the moment it is paid, and everything about that order - questions, changes and the final report - happens in it.
Basic orders are delivered in 3 business days, Standard in 5 business days, and Advanced in 7 business days. An express add-on is available at checkout for $20, which trims two days off the standard turnaround.
Please tell us your material system, such as an Al-Cu alloy, a NaCl-water mixture or sea water, and what you want to learn, for example how enrichment changes across growth rates. If you can supply k0, D, boundary layer thickness delta and a growth rate range that helps, but we can estimate these from published sources for common systems, defaulting to 1-100 μm/s for metals.
That is fine. For most common alloys and aqueous solutions we can pull k0 and D from published literature once you give us the composition, for example Al with 4.5 wt% Cu. Less common systems may need a day or two extra for research, at no additional cost for standard estimates.
As this is custom computational work, we cannot offer refunds once a simulation is underway. Before starting, we confirm your parameters with you and send a preview figure ahead of final delivery. Should that preview not line up with what you asked for, we include a revision at no extra cost, and if you remain unsatisfied at that stage we can cancel the order with half the fee returned.
Yes, figures are supplied at publication quality, in PNG and PDF at 1500x1000 or above, suitable for journal manuscripts, theses or conference material. The Advanced package additionally adds an interface stability analysis using the Mullins-Sekerka criterion, a comparison against published literature data, and an extended interpretation report. We handle the modelling, figures and interpretation, not manuscript writing itself.
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