Abstract
The stability of self-similar diffusional processes with respect to small disturbances of plane, cylindrical, and spherical phase interfaces is investigated.
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Abbreviations
- c:
-
weight concentration in solution
- D:
-
coefficient of diffusion
- K:
-
curvature
- n:
-
angular number
- R:
-
radius of cylinder or sphere
- r, r′:
-
radial coordinate and disturbance of the surface r=R
- t:
-
time
- u:
-
velocity of front
- x, y, z:
-
linear coordinates
- X:
-
coordinate of front
- x′:
-
disturbance of a plane front
- α:
-
parameter of growth rate
- Г:
-
coefficient of surface tension
- γ:
-
parameter introduced in (8) or (21)
- δ, Δ:
-
dimensionless disturbance of surface of the front and its amplitude
- ξ, η, ζ, μ:
-
dimensionless coordinates
- θ, ψ:
-
angular coordinates
- H :
-
dimensionless wave number
- λ :
-
wavelength of disturbance
- ρ:
-
concentration in solid
- τ:
-
dimensionless time
- φ(μ), φ:
-
amplitudes of disturbances of concentration
- δ:
-
dimensionless concentration
- ω:
-
dimensionless growth increment of disturbances
- 0 and ∞:
-
states at a plane front and in the solution far from the front
- anasterisk:
-
state at a curved front
- m:
-
fastest growing disturbances
- a:
-
degree sign pertains to self-similar variables
Literature cited
K. Jackson, “Fundamental aspects of crystal growth,” J. Phys. Chem. Solids, Suppl., No. 1, 17–24 (1967).
Yu. A. Samoilovich, The Formation of an Ingot [in Russian], Metallurgiya, Moscow (1977).
W. W. Mullins and R. F. Sekerka, “Stability of a plane phase interface during crystallization of a dilute binary melt,” in: Problems of Crystal Growth [Russian translation], Mir, Moscow (1968), pp. 106–126.
J. Cutler and W. A. Tiller, “Allowance for the kinetics of attachment of particles to a crystal in the analysis of a cylinder crystallizing from a binary melt,” in: Problems of Crystal Growth [Russian translation], Mir, Moscow (1968), pp. 178–196.
W. W. Mullins and R. F. Sekerka, “Morphological stability of a particle growing by diffusion or heat flow,” J. Appl. Phys.,34, 323–329 (1963).
Yu. A. Buevich, “On one class of solutions of the first Stefan boundary problem in an unbounded space in cases of plane, axial, and spherical symmetry,” Inzh.-Fiz. Zh.,8, 801–806 (1965).
L. I. Rubinshtein, The Stefan Problem [in Russian], Zvaigzne, Riga (1967).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 818–827, May, 1981.
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Buevich, Y.A. Instability of the self-similar front of a phase transition. Journal of Engineering Physics 40, 497–505 (1981). https://doi.org/10.1007/BF00822115
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DOI: https://doi.org/10.1007/BF00822115