Instability of the self-similar front of a phase transition

The stability of self-similar diffusional processes with respect to small disturbances of plane, cylindrical, and spherical phase interfaces is investigated.Notation 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 - parameter of growth rate - coefficient of surface tension - parameter introduced in (8) or (21) - , dimensionless disturbance of surface of the front and its amplitude - , , , dimensionless coordinates - , angular coordinates - H dimensionless wave number - wavelength of disturbance - concentration in solid - dimensionless time - (), amplitudes of disturbances of concentration - dimensionless concentration - dimensionless growth increment of disturbancesIndices 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 variablesTranslated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 818–827, May, 1981.