Unidirectional freezing of binary aqueous solutions: an analysis of transient diffusion of heat and mass

The Front-Tracking ALE Method: Application to a Model of the Freezing of Cell Suspensions

“…The front velocities predicted by our model for B = 0.05, 0.1, and 0.2 K/s, as well as the solute concentration profiles ahead of the front, agreed well with the results obtained in [42].…”

Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions

“…The results shown in Figs. 6(a) and (b) are in excellent agreement with those in [58,59]. It is to be noted that the present sharp interface method captures the solute buildup on the liquid side of the interface as a discontinuity and also treats the diffusivity jump between the solid and liquid as a jump discontinuity.…”

“…In this section we compute the solidification in the stable and unstable modes for pure as well as impure materials and compare the results of our computations with exact solutions [56], the solvability theory results quoted in [15,28,48,57] and other numerical results [58,59]. The growth and material parameters are varied and the dendritic tip details such as radius, velocity and selection parameter are each compared with theoretical and computational results presented in the above papers.…”

“…Such a system occurs commonly in the cryopreservation of biological materials (cells and tissue). This one-dimensional case was solved using a moving coordinate system fixed at the advancing front by [58]. Numerical (finite-difference) solutions were obtained for the temperature and solute fields ahead of the front.…”

Solidification using smoothed particle hydrodynamics

“…In this case, when an element of the liquid solution reaches the liquidus temperature T L , further loss of heat results in some ice being formed and the concentration of salt in the solution increases. This problem was considered by Wollhö ver et al [27] assuming the interface between ice and solution was sharp. However, the conditions they assumed rapidly produce an unstable interface which then produces a mush comprising a mixture of dendritic ice crystals and solution (see for example [15]).…”