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We analyse how solute rejects, concentrates and stabilises at the solidification front for your material system, producing concentration profiles, enrichment data and publication-ready figures within 3-5 business days.
To start, send us the domain the order is for and your brief describing the material system.
We simulate solute rejection, concentration build-up and impurity enrichment as your material solidifies directionally, whether that is a metal alloy, a ceramic suspension or an aqueous solution.
Using k0 = 0.14, C0 = 4.5 wt% and D = 3×10⁻⁹ m²/s, three growth rates were scanned:
| Growth rate | k_eff | Enrichment ratio |
|---|---|---|
| 1 μm/s | 0.144 | 7.42× |
| 10 μm/s | 0.185 | 7.89× |
| 100 μm/s | 0.82 | 1.88× |
The 7-8× enrichment seen at low speed lines up with published aluminium-copper segregation figures, which sit in the 6-10× range. At higher speed, solute trapping pulls the enrichment ratio back down.
Turnaround runs 3-5 business days and you receive the Python scripts, the figures in PNG and PDF, and a brief interpretation report.
The Burton-Prim-Slichter effective partition coefficient captures the balance between interface kinetics (k0) and mass transport, expressed through v·delta/D. This mirrors a survival-factor framework we have published, where the ratio of a coherence timescale to a perturbation timescale determines whether solute is rejected or absorbed into the growing solid.
ORCID 0009-0008-4540-1381; the underlying framework is published under Zenodo DOI 10.5281/zenodo.22771462.
This is an academic-style analysis and is not a legally valid engineering assessment for production use; treat results as research reference material.
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.
The Basic package is delivered in 3 business days, Standard in 5 business days and Advanced in 7 business days. If you need it sooner, add the rush delivery extra at checkout for an additional 30 USD, which cuts the turnaround by 2 days.
Please tell us the material system, for example an aluminium-copper alloy, sodium chloride in water, or seawater. We also need the equilibrium partition coefficient k0, or the composition so we can estimate it, plus the liquid diffusion coefficient D, or we can apply a typical value.
Optional extras include the boundary layer thickness delta, which defaults to 100 μm for metals and 500 μm for aqueous solutions, and your preferred growth rate range, which defaults to 1-100 μm/s.
That is fine. We can estimate k0 and D from published literature for most common alloy and aqueous systems, so just give us the composition, such as aluminium with 4.5 wt% copper, and we will handle the rest. Uncommon systems may need 1-2 extra days for research, at no additional cost for standard estimates.
As this is bespoke computational work, refunds are not offered once the simulation is under way. We do confirm your parameters beforehand, send a preview figure ahead of final delivery, and include one free revision if the output does not match your brief. If the preview does not satisfy you, we can cancel and refund 50 per cent.
Yes. Figures are publication-quality PNG and PDF files at a minimum of 1500x1000 pixels, suitable for journal manuscripts, theses or conference presentations. The Advanced package also adds a draft results paragraph for your manuscript, a methodology appendix and a literature comparison. We do not write full papers, but we supply the modelling, figures and interpretation you need for one.
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