Freezing front

Fig. 3.4.11 Two-dimensional slice images ta- (e) freezing front and (f) freezing front. The ken from a three-dimensional Spiral-SPRITE measurement parameters were FOV 60x60 cyclical freezing and thawing experiment. x 60 mm, acquisition points 64 x 64 x 32,...

In all early works, it has been assumed that there exists two well-defined planner interfaces. However, in the actual experiments a partially solidified zone (P.S.Z.) or mushy region and a partially melted zone (P.M.Z.) always exist between the completely resolidified and fresh solids. The existence of a P.S.Z. (mushy region) behind the freezing front is especially important since it offers the greatest resistance to the forward solute transfer and can trap the solute flowing backward and can affect the nature and the extent of macrosegregation. ... 

Fig. 5.18. The regolith layer (0.5 km) molal concentrations as the freezing front moves through the Martian profile. Minerals that should theoretically precipitate within the profiles either from the initial evaporative concentration or later from freezing concentration are listed...

The process in which a particle dispersed in one phase is overtaken by an advancing interface and surrounded by a second phase. Example when a freezing front (the interface between a solid and its freezing liquid phase) overtakes a particle, the particle will either be pushed along by the front or else be engulfed by the front, depending on its interfacial tensions with the solid and with the liquid. See also Freezing Front Method. 

J. K. Spelt, M.A.Se. thesis, Surface Tension Measurements of Biological Cells Using the Freezing Front Technique," University of Toronto, 1980. 

Representative snapshots from brine rejection simulations are given on Figure 1. It can be clearly seen that both sodium and chloride are rejected by the freezing front into the remaining liquid solution (save a single chloride which got trapped in the ice lattice). At the end of the simulation, a thin layer of unfrozen concentrated brine solution with glassy character is formed. There is a slow tendency to incorporate more of the remaining water molecules into the ice lattice however this process exceeds the time scale of present simulations. 

A more detailed analysis revealed that the freezing proceeds by the following mechanism. First, there is a fluctuation (decrease) of salt density near the freezing front followed by the buildup of the new ice layer. 

The first crystallization nucleus forms in the subsurface approximately at 45 ns. The second subsurface nucleus occurs 110 ns after the beginning of the simulation. Freezing proceeds independently from both nuclei and the freezing fronts meet at 160 ns, forming a somewhat disordered contact zone. Cubic ice Ic forms predominantly in the simulations and many defects can be identified in the ice lattice. Freezing to cubic ice is consistent with the recent findings that small droplets and thin water films prefer this crystal modification over hexagonal ice Ih." ... 

Design (velocity of freezing front)(liquid boundary layer thickness that depends on mixing)/(dif-fusivity of solute impurity in the liquid) = 1. 

Liquid Marbles, Fig. 4 The sketch shows the cross section of the liquid marble with the proposed gap between the freezing front and the coating due to preferential nucleation. The arrow indicates the flow of water to the gap due to Marangoni effects (Reproduced with permission from Hashmi et al. [6])... 

The slight sideways expansion and the formation of a crater at the completion of the freezing process of a half-marble may probably be due to the same effect as previously described a gap between the water-particle interface and the freezing front receives water flow from Marangoni effects. 

Heat transfer coefficient Ksu) from the heat transfer medium in shelves to the freezing front (kJ/m h°C) 260 115... 

Overall, wettability measurement of small particles is a difficult problem that is further aggravated in the case of heterogeneous surfaces. Some of these problems can result from the presence of patches of different composition in the same particle. It is considered that if these patches are below a critical size of 0.1 mm, the surface is homogeneous regarding its wettability. Several indirect techniques have been developed to measure the surface tension, and thus the wettability of small particles. In these techniques, the surface tensions of the particles are derived from thermodynamic models and include the advancing solidification front or freezing front, sedimentation volume, and particle adhesion techniques [44, 45]. 

As a final example of regular perturbation in this chapter, consider the freezing of a saturated liquid in a semi-infinite region [13]. A saturated liquid is initially at its freezing temperature Tf. At some time, the face is maintained at a constant subfreezing temperature < Tf). As heat is removed from the liquid, it freezes. If the freezing front at any time t is at X and if it can be assumed that the uniform liquid remains at Tf throughout the process, what is the temperature profile T(x, t) in the solid phase ... 

In order to derive an expression for the progress of the freezing front with respect to time, recall that... 

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