Thursday, 7 October 2004

Handout (246.7 kB)

Papers [1,2] have shown, that under phase transition a fluid - solid phase the interface under the some conditions becomes unstable. At a eutectic composition of a fluid mixture this instability leads to formation of periodic eutectic pattern. The dependence of period of the component distribution of the solid on a interface velocity coincides with experimental [3,4]. This instability leads also to forming cellular interface [5]. We guess that this instability arises under phase transition the gas – fluid. Let a binary gas mixture condenses in drops. The equilibrium between components is featured by the eutectic phase diagram. Let binary gas mixture condenses in drops. Let's assume that the condensation of a drop is stationary with constant interface velocity Vs. The interface velocity depends on the difference of temperature of phase transition and gas temperature on the interface. This difference is termed as a kinetic supercooling. The velocity is more at the greater value of the kinetic supercooling. We consider a stability of the interface of stationary regime of the mixture condensation to perturbations of concentration. It is known, that the size of a diffusion layer of the gas phase D is commensurable with a size of a hydrodynamic layer H. This is follows from that number of Peclet Pe = VL/D ~ 1. Here V is velocity of gas concerning the drop far from interface boundary, L is size of the drop, D is diffusion constant of gas mixture. Let's designate boundary between area of a unlimited solubility 0 < C < C1 and area C1 < C < Ceut of a restricted miscibility of components of the mixed fluid as C1. Let the component concentration in the gas is less than saturation concentration of the liquid 0 < C < C1. In this case, increase of the component concentration on interface leads to a diminution of phase transition temperature, and therefore to a diminution of the kinetic supercooling. The diminution of the kinetic supercooling leads to a diminution of the interface velocity. Former value of concentration on interface thus is restoring. The system is stable. The stability of the condensation regime is explained by dependence of temperature of phase transition on interface concentration of the gas phase. They are bound by lines of boil and condensation of the phase diagram. Let now the component concentration in the gas is more than concentration of saturation of the liquid phase on a small quantity C = C1 + С. We consider a variation of partial velocities of gas in the hydrodynamic layer to find component concentration on interface. According to the equilibrium phase diagram the concentration on the interface in this case is equal to eutectic. The solution of an one-dimensional boundary value problem of a diffusion on an infinite interval does not satisfy to a conservation law of a mass flow in this case. Therefore we consider a solution of the problem on a segment which length is equal H. The padding partial velocities of components arise in a hydrodynamic layer in order the conservation law of the mass flow was satisfied. Hence padding diffusion flows arise in the hydrodynamic layer. These diffusion flows lead to padding partial pressure between components of gas mixture. This pressure is balanced between components in the bulk of gas mixture. However on boundary with a fluid the padding pressure at C(0) = Ceut is not balanced, since the composition of a fluid does not vary at the variation of the gas concentration in this case. In order the disbalance of pressure was balanced on interface, the component concentration has to vary as C(0) = Ceut + C’. The value of concentration on interface now will be located in the area of the increasing curve of condensation of the phase diagram. Let's consider the stability of such stationary regime. Increase of the component concentration on interface leads to increase of temperature of phase transition, and therefore to increase of the kinetic supercooling. The increase of the kinetic supercooling leads to increase of the interface velocity. Hence concentration on interface will increase even more. The system is instable. Similarly we shall obtain instability at a diminution of component concentration on the interface. As is easy to see the size of the hydrodynamic layer decreases at increase of the gas velocity concerning the drop V. Therefore the instability arises at sufficiently great values of V. It is known that for example tornado is forming on boundary between warm and cold atmosphere fronts. This fact conforms to the reduced theory. Precomputations similar [1,2] have shown, that the growth increment (the calculations are made in an approximation of flat boundary) 106 ([1]). If to guess, that the growth velocity is restricted to the sound velocity, the range estimate of the drop sizes gives 1 mm. Let's remark, if not it is taken into account of atmosphere hydrodynamics, that theoretically velocity of movement of air is restricted to the sound velocity. We obtain process to similar vacuum explosion. In contrast to chemical explosions, in the inside area of drops shaping, in this case the pressure will be cushioned by a restricted size of drops and by emergent hydrodynamic flows between them. Agrees [6] the physical mechanism tornado completely yet is not ascertained. The basic hindrance to an explanation of the mechanism of tornado rise is the impossibility to explain an energy source necessary for existence tornado. This energy on existing estimates should have magnitude approximately 3.5 MW. Our preliminary calculations demonstrate that phenomenon of condensation has enough energy for tornado maintaining. References. 1. A.P.Guskov. Bulletin of the Russian Academy of Sciences “Physics”. Allerton Press, Inc. V. 63, N9, p. 1772-1782, 1999. 2. A.Gus’kov, Computational Materials Science 17, 555, (2000). 3. A.P.Gus’kov. Technical Physics, Vol. 48, No5, 2003,pp. 569-575. 4. A.Gus’kov, A.Orlov. Computational Materials Science 24, 93-98, (2002). 5. A.P.Gus'kov, Physics - Doklady, v.387, N2, 2002, pp.181-183. 6. Adrian E. Scheidegger. Physial aspects of natural catastrophes. Elsevier scientific publishing company, 1975.

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