Abstracts - KTH Mechanics

vii
Fluid mechanics of phase change
Gustav Amberg a
One crucial step in almost all materials processes is solidification in one form or
other. The conditions under which the melt resolidifies will be crucial for the final
microstructure of the material. The size and morphology of the individual grains
that make up a polycrystalline material, the homogeneity of a monocrystal, the
actual phase that is formed, as well as its local composition, is determined by the
interplay between local heat and mass transfer and the thermodynamics of the
phase change. Even though the microstructure of the material may change
considerably during subsequent cooling and following process steps, the
foundation has been laid at the point of solidification. Since local heat and mass
transfer governs the phase change, it is obvious that any convection in the melt will
be paramount in determining the structure of the material, thus making this an area
of important applications that should interest fluid dynamicists. Aside from the
technological processes referred to above, there are also numerous phenomena in
nature where the interplay of convection and phase change is crucial, from the
formation of ice on sea and lakes, to solidification of magma into rock.
In this lecture I will outline some basic solidification phenomena, following a
path of increasing geometrical complexity, and discuss different effects of
convection and fluid flow as I go along. In the simplest situation, a solid growing
very slowly may form a planar interface, but as the driving force for phase change
increases, this becomes unstable to shape perturbations, which may develop into
highly complex patterns. One common morphology is a dendritic crystal, which
grows in a tree-like shape. Eventually a complex solid-liquid two-phase system is
formed. In all of these processes the presence of convection and melt motion will
have a crucial effect on the structures that are formed. As an example, in forced
convection past a growing array of dendrites, the dendritic forest will tend to tilt
upstream into the wind. Around a single, large, slowly growing crystal, natural
convection may be important, causing an enhanced growth downwards, in the
direction of gravity. Many relevant materials processes involve free liquid melt
surfaces, and in such cases additional important driving forces for fluid motion are
capillarity and wetting, and surface tension gradients due to temperature or
concentration gradients.
In discussing these problems I will also have to briefly introduce the phase field
method, a diffuse interface method where model equations for phase change are
derived using the principles of phenomenological non-equilibrium
thermodynamics.
a KTH Mechanics, SE-100 44 Stockholm, Sweden.