In Chapter 9 the discussion of the interaction of fluid flows with solidification fronts focused on how individual cells or dendrites are affected by the motion of the melt. The discussion was confined to the onset, or near onset, of morphological instability and the influence of laminar flows because the systems had small scale and the rate of solidification could be readily controlled. There are many situations in industrial or natural situations in which the systems have large scale and the freezing rates are externally provided.

When the freezing rate is not carefully controlled near M = Mc, the typical morphology present is dendritic (or eutectic) and strongly nonlinear in the parameter space V – C∞ of Figure 3.6. The region within which there are both dendrites and interstitial liquid is called a mushy zone. Such zones should not be described pointwise in the same sense that one would not want to describe flow pointwise in a porous rock. Instead, the zone is treated as a porous region that is reactive in the sense that the matrix melts and the liquid freezes and whose properties are described in terms of quantities averaged over many dendrite spacings. There still is a purely liquid region and a purely solid region, but now they are separated by an intermediate layer, the mushy zone.

When the length scale of the system is large and the fluid is subjected to gravity, the fluid in the fully liquid system will undergo buoyancy-driven convection. The large scale may imply that the Rayleigh number is large enough that the convection is unsteady, laminar, or turbulent.