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The solution of this mathematical model for solute transport considered that the contribution of convection and dispersion terms was deduced using the single-step, trace-back method and routine finite element method (FEM).
The authors discuss several solution approaches of historical interest, and provide a complete transport model for solute A based on the laws of conservation of mass and momentum, from which the local Sherwood number, Sh, can be obtained as a function of the dimensionless axial distance into the mass transfer zone and the Damköhler number, Da.
The trend was simulated using a simple mass transfer model for solute uptake at the calcite surface.
The SFV calculated from the KGT model was then input into the continuous growth model for solute trapping developed by Aziz to predict the deviation from equilibrium partitioning during solidification for all pulse energy levels employed.
The liquid drop surface is assumed to be a spherical cap, while the isothermal model for solute transport with simplified hydrodynamics computes the evolution of the solid liquid interface.
This SFV corroborated the chemical mapping data, and therefore supported the solute trapping hypothesis, as the continuous growth model for solute trapping as developed by Aziz and Kaplan (Acta Metallurgica 1988; 36 2335) predicts significant trapping of lithium at a SFV of 1 m s−1.
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Although modified LB models have been developed to simulate fluid flow in such media, models for solute transport are relatively limited.
The model predictions for solute partitioning, diffusion and convection were validated via in situ X-ray radiographic measurements in Ga 25 wt.% In alloy, showing good agreement.
In addition to self-consistent determination of the cap shape at which balance of pressures and physico-chemical equilibrium are satisfied, this model accounts for solute transport across the cap in three different cases.
The model accounts for solute advection and diffusion and geochemical reactions such as aqueous complexation, acid base, cation exchange, protonation/deprotonation by surface complexation and dissolution/precipitation of calcite, chalcedony and gypsum.
The former was consistent with the Labusch model for local solute obstacles, and the latter was related to the athermal plateau stress due to the long range solute effect.
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CEO of Professional Science Editing for Scientists @ prosciediting.com