Supercooling pattern formation

While eonstitutional supercooling explains why one bump grows, it does not account for a line of bumps with wavenumber q. The outstanding question of pattern formation is still Where does q come from Nevertheless, at the... 

Shimada, W. and Furukawa, Y. (1997) Pattern formation of ice crystals during free growth in supercooled water. J. Phys. Chem. B, 101 (32), 6171-6173. 

The phase-field simulations reproduce a wide range of microstructural phenomena such as dendrite formation in supercooled fixed-stoichiometry systems [10], dendrite formation and segregation patterns in constitutionally supercooled alloy systems [11], elastic interactions between precipitates [12], and polycrystalline solidification, impingement, and grain growth [6]. 

Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

Are any of these structures typical of those that would be observed in a pure amphiphile The role played by the probe, which is essential to the fluorescence method, is not completely clear. It has been argued that the formation of dendritic structures in phospholipids is the result of constitutional supercooling, a mechanism that depends on the differential solubility of an impurity between two phases. This may not be the case similar patterns have been observed in LB films by surface-plasmon microscopy, for which no probe is added. The foam structures at the LE-G transition have also been attributed by some to the presence of the probe, but foams have also been observed in monolayers composed solely of a labeled amphiphile. 

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