Mushy region

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. ... 

The existence of a P.S.Z. (mushy region) and its importance in solute transfer during solidification of a binary mixture have been recognized by more recent workers (24 through 29). Simple models... 

This study has been conducted with the objectives 1) to analyze and determine the effect of the free convective mixing in the melted zone upon the over-all solute transfer process in zone refining under various conditions and 2) to take into account the solute transfer both in the melted zone and in the adjacent P.S.Z. (mushy region) in predicting the rate of over-all solute transfer. The temperature distribution, composition, zone travel speed, zone dimension and other important parameters are considered in this study. 

Since the results of zone refining depend on the interaction of momentum, heat and mass transfer in the system, all the basic factors affecting these three processes, both molecular and convective, have to be taken into consideration. These basic factors are concentration W, Density f, viscosity /i, heat capacity Cp, temperature den-sification coefficient, thermal conductivity k, molecular dif-fusivity D, zone diameter d, zone length L, zone travel speed u, temperature difference in zone A T and acceleration g. The concentration W may affect, JJi, Cp,, k, and D as well as the properties of the P.S.Z. (mushy region). Aside from the concentration W, all... 

The thickness of a partially solidified zone (mushy region) in zone refining under most experimental conditions has been determined. The transfer of solute within this zone is, no doubt, most important in determining the overall solute transfer. All the zone refining theories have failed to take this most important factor into account. 

Figure 7.11 Paths to a semisolid state taken by rheocasting (heating a specially formed billet until partial melting occurs) and thixocasting (stirring a melt to break up dendrites while cooling into the liquid + solid, or mushy, region).

It appears that problems which have been solved along these lines are manifold Melting and solidification of alloys in metal casting, the occurrence of "mushy regions in (binary) systems of compositions deviating from the eutectic composition etc. See e.g. the beautiful book by John Crank (5), where only occasionally an exception is made from the lines sketched so far in the introduction. 

Figure 10.3 shows the velocity field and the extent of the mushy region calculated in the second case at r = 10, 30,50, and 70 s, respectively. In this case, nucleation rate was taken as = 10 1 /m s. In this figure (Fig. 10.3a), solid contours concentrate at the lower parts of the cavity indicating that much of the solid particle moves... 

Felicelli et al. [54] used a fixed finite element algorithm to calculate macrosegregation and the formation of channels and freckles in Pb-Sn alloys. They assumed that the mushy zone is a porous medium with an isotropic permeability and considered superficial velocity components for the fluid velocities in the mushy region. The superflcial velocities are... 

There are generally two main approaches for handling the mushy region in multi-domain methods. The first approach considers the planar interface between the solid and liquid regions and solves only transport equations for the liquid and solid phases. The interface is tracked explicitly with appropriate boundary conditions [87,89-92],... 

A typical set of transport equations for the mushy region employed by ChiareU et al. [87] and partly developed by Hills et al. [94], Roberts and Loper [98], Fowler [95] and Worster [99] are ... 

From the solution of the above equations, Lu and Chen [108] showed that a liquid plume which carries a cooler and less concentrated fluid is released from the mushy region and penetrates into the fluid layer, forming plume convection. It was shown that two types of convection patterns form in the system. The first is a convection pattern circulating between the mushy layer and the fluid layer with a length scale of about the height of the mushy layer. This pattern is called the mushy layer mode (MLM). The second pattern forms above the melt/mush interface and is called BLM. 

Voller VR, Prakash C (1987) A fixed grid numerical modeling methodology for convection-diffusion mushy region phase-change problems. Int J Heat Mass Transf 308 1709-1719... 

Ilegbusi OJ, Mat MD (1997) A hybrid model of the mushy region in phase-change problems. J Mater Process Manuf Sd 6 1-15... 

Worster MG (1992) Instabilities of the liquid and mushy regions during solidification of alloys. J Fluid Mech 237 649-669... 

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