ABSTRACT
In this chapter, qualitative examples involving the flow of liquids are discussed in order to provide a broader context for instabilities and pattern formation in condensed matter. Small amplitude shape fluctuations that develop at interfaces of condensed matter tend to increase the free energy of the system. Attempts by the system to stabilize these fluctuations occur through various mechanisms engendered by effects associated with the surface tension, viscosity, or gravity, for example, where appropriate. If the dynamics are driven by gradients of an external field (e.g., mechanical forces or forces associated with gradients in temperature, gravity, potential energy, etc.) then certain dynamical modes in these fluctuations can become amplified. In other words, the system becomes unstable and its structure may subsequently evolve spatially and temporally into a final state characterized by different organizational patterns. Nature selects a range of patterns depending on the parameters that characterize the instability. Examples of such phenomena were discussed in Chapters 9 and 11. In Chapter 9, spinodal patterns were formed when local compositional fluctuations in an otherwise homogeneous mixture became amplified when the mixture was placed in the unstable region of the phase diagram. In Chapter 11, the moving solid/ melt interface of a crystal growing in its supercooled (or in a supersaturated environment) melt may become unstable toward shape fluctuations, forcing the system to exhibit different morphological patterns (e.g., dendrites).
