The impact of convection on morphological instability of a planar crystallization front

Wavy Ice Patterns as a Result of Morphological Instability of an Ice–Water Interface with Allowance for the Convective–Conductive Heat Transfer Mechanism

“…As is easily seen, the migration rate increases with increasing the wavenumber of perturbations. Physical parameters used in calculations are [28,35,43]:…”

“…Here, the water-ice interface perturbation is assumed to be small, i.e., |η(x, t)| ≪ s 0 (t). At the interfacial boundary, fluid currents result in a conductive-convective heat flux at the fluid side [25][26][27][28]. In addition, the temperature continuity condition is fulfilled at this boundary.…”

“…Thus, the heat and mass fluxes at this interface become of a mixed type (conductiveconvective), i.e., they have both conductive and convective contributions [25][26][27]. Taking this fact into account, a complete mathematical model of the directional crystallization process of a binary liquid has recently been formulated with allowance for the conductiveconvective heat and mass transfer mechanism [28]. In this paper, a linear analysis of the morphological instability of a flat crystallization front in the presence of convection was also carried out and a new criterion for constitutional supercooling origination was derived, which demonstrated the existence of four crystallization scenarios.…”

“…In this paper, a linear analysis of the morphological instability of a flat crystallization front in the presence of convection was also carried out and a new criterion for constitutional supercooling origination was derived, which demonstrated the existence of four crystallization scenarios. The theory developed in [28] also showed a significant influence of convection on the crystallization process as a whole and on the stability criterion, which was thoroughly studied by various scientific groups after the classical theory by Mullins and Sekerka [18] was published. Below, we investigate the influence of convective heat transfer on the morphological stability of the liquid-solid interface, which leads to the appearance of so-called wavy ice layers (Figure 1) [29][30][31][32][33][34].…”

Desupersaturation dynamics in solutions with applications to bovine and porcine insulin crystallization

“…Another important direction for the development of the present approach is to combine the theories of bulk and directional crystallization, where the entire volume of the solution/melt moves in a spatial direction under the influence of a temperature and/or concentration gradient. To solve such a complex problem with two moving boundaries 'solid phase-two-phase region' and 'two-phase region-liquid phase', the methods considered in this paper should be combined with the theory of directional crystallization [53][54][55][56][57][58].…”