Sekerka instability, Mullins

Its characteristic wavelength is subject to the transport of latent heat from the growing interface. This is known as Mullins-Sekerka instability (11), The interface of a growing dendritic crystal provides an open system to support die dissipative structure with its characteristic wavelength(s), and the molecules or ions incorporated into the growing crystal are regarded to be self-assembled into the specific coordinate of dendritic crystal by die assistance of the dissipative structure. 

In most penetration scans performed in surfactant dissolution experiments the phases are homogeneous and the interface between them is sharp. However, in some cases the interface becomes unstable and dramatic instobilities can be observed. There are many examples of instabilities that are well understood that maybe rationalized in terms of kinetic maps or dissolution paths, or dynamic instabilities involving fluid flow (e.g. Marangoni effects) or other Laplacian growth instabilities , such as Mullins-Sekerka instabilities (3J). However, myelins (Figure 1) are an example of an instability that remains poorly understood. 

Returning to the diffusion control of morphology, Goldenfeld reviewed the subject with respect to spherulite structure [95]. His contention that the diffusion length 5 = DIG describes large-scale variations in the shape of the spherulite envelope has been confirmed by experiments on random copolymers with many non-crystallizable sequences [96]. More importantly, he identified the lamellar width W with the Mullins-Sekerka instability size Ad 5. When crystals... 

Similarly, we can pick another example in crystal growth in melt. In this case, the growth occurs at the interface between the melt and a substrate that is kept at a constant temperature that is lower than the critical temperature for crystallization. The morphology characteristic of the instability is formed by the coupling of the heat flux and the surface-form fluctuation. This problem was first theoretically analyzed by Mullins and Sekerka.57-62... 

The problem of morphological instability was solved theoretically by Mullins and Sekerka [20], who proposed a linear theory demonstrating that the morphology of a spherical crystal growing in supercooled melt is destabilized due to thermal diffusion the theory dealt quantitatively with and gave linear analysis of the interface instability in one-directional solidification. 

Mullins and Sekerka (88, 89) analyzed the stability of a planar solidification interface to small disturbances by a rigorous solution of the equations for species and heat transport in melt and crystal and the constraint of equilibrium thermodynamics at the interface. For two-dimensional solidification samples in a constant-temperature gradient, the results predict the onset of a sinusoidal interfacial instability with a wavelength (X) corresponding to the disturbance that is just marginally stable as either G is decreased... 

The classical linear stability theory for a planar interface was formulated in 1964 by Mullins and Sekerka. The theory predicts, under what growth conditions a binary alloy solidifying unidirectionally at constant velocity may become morphologically unstable. Its basic result is a dispersion relation for those perturbation wave lengths that are able to grow, rendering a planar interface unstable. Two approximations of the theory are of practical relevance for the present work. In the thermal steady state, which is approached at large ratios of thermal to solutal diffusivity, and for concentrations close to the onset of instability the characteristic equation of the problem... 

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