https://doi.org/10.1140/epjs/s11734-023-00824-6
Regular Article
Morphological stability analysis of a planar crystallization front with convection
Laboratory of Multi-Scale Mathematical Modeling, Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
Received:
13
February
2023
Accepted:
21
March
2023
Published online:
13
April
2023
A linear theory of morphological stability of flat crystallization front is constructed with allowance for convective motions in liquid. The cases of slow and intense convection described by conductive and convective heat and mass transfer boundary conditions are considered. The dispersion relations defining the perturbation frequency as a function of wavenumber (wavelength) and other process parameters are derived. The neutral stability curve found in the case of slow convection substantially depends on extension rate at the phase interface. This curve divides the domains of morphological instability (MI) and morphological stability (MS). In both of these domains, the constitutional supercooling (CS) condition takes place. Therefore, we arrive at two various crystallization regimes (1) CS and MI, and (2) CS and MS. These cases respectively correspond to the mushy and slurry layers developing ahead of the crystallization front. In addition, when the fluid flows from the front, it is morphologically unstable for various perturbation wavelengths. When the fluid flows to the front, it is stable for large extension rates and unstable for smaller extension rates. The dispersion relation found in the case of intense convection shows that the perturbation frequency is always negative and small morphological perturbations decay with time. It means that the crystallization process with intense convection in liquid is absolutely stable.
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