This chapter unashamedly takes as its theme the idea that `the'
problem in alloy solidification is the formation of freckles in, for
example, lead-tin alloys. The sequence of the chapter is then much as
for chapter 14; the phase diagram for a
eutectic forming binary alloy is described, and an averaged model is
given, which treats the solid phase of a dendritically crystallising
solid as a reactive porous medium, the pore fluid being able to melt
back the solid, or crystallise on it.
The near eutectic limit is introduced, which allows the convective
problem to be reduced to one very similar to that for a non-reactive
porous medium. Linear stability is described, and an attempt at a
boundary layer theory is given, whose status is unclear; Grae Worster
published a different asymptotic theory in 1991, and more recently has
re-examined the issue (see Schulze and Worster, J. Fluid
Mech. 356, 199-220 (1998), and
also Ann. Rev Fluid Mech. 29, 91-122 (1997)).