Computer-aided Modeling of the Time Dependences of the Current during Anisotropic Growth of Product Nuclei

A fast computer model, intended for the calculation of the overall reaction rate (current) of anisotropic or nonhomotetic growth of a new-phase nuclei on the basis of the Voronoi diagram, is designed. The model is used for studying the kinetics of a heterogeneous reaction in the conditions where hemispherical nuclei of the new phase acquire a semiellipsoid shape in the course of an anisotropic growth. The calculation of current transients (potentiostatic i vs. t dependences) is substantially complicated in the initial stage of reaction, where the size of growing nuclei exceeds the critical value by less than an order of magnitude. If semiellipsoid nuclei overlap, the overall reaction rate is not determined by variations in the overall area of the reaction surface, as opposed to the growth of hemispherical nuclei. The kinetics of a nonhomotetic nuclei growth may be described by models designed for an isotropic growth of hemispherical nuclei.     

Convection in a horizontal fluid layer with specific-volume inversion

The effect of the position of the inversion point within the layer on the critical values of the Rayleigh number and the amplitudes of the rectangular-cell convective flows is numerically investigated. The monotonic instability of the mechanical equilibrium of the fluid with respect to small perturbations periodic along the layer is studied by the linearization method. The Lyapunov-Schmidt method is used to construct the secondary steady convective flows. The applicability of these methods in incompressible fluid stability problems was demonstrated in [8–10]. The calculations show that, starting from a certain value of the parameter , the branching is subcritical for any cell side ratio and a fixed wave vector modulus. For smaller values of the nature of the branching depends on the cell side ratio. This points to subcritical branching and hysteresis effects in those cases in which the periodicity of the perturbations is determined by external factors (corrugation of the boundary, spatially periodic temperature modulation, etc.). It is noted that the rectangular convection amplitude tends to zero when the cell side ratio tends to 3, the value at which hexagonal cellular convection is possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 43–49, January–February, 1989.The author wishes to thank V. I. Yudovich for his interest and useful advice and the participants in the Rostov State University Computational Mathematics Department's Scientific Seminar for discussing the results.     

Penetrative convection in the isothermally incompressible fluid approximation

The onset of penetrative convection in an infinite horizontal fluid layer bounded by isothermal rigid or free nondeformable surfaces is numerically examined. It is assumed that the specific volume of the fluid depends quadratically on temperature and reaches a minimum inside the layer. The isothermally incompressible fluid convection model in which, as distinct from the Oberbeck-Boussinesq approximation, the thermal expansion is not assumed to be small is considered. Both the neutral stability curves of the conductive regime and the amplitudes of two-dimensional periodic and three-dimensional doubly-periodic convective flow are calculated. The results are compared with those previously obtained for the equations of penetrative convection in the Boussinesq approximation.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 40–52, March–April, 1996.     

Boussinesq approximation in the Rayleigh-Benard problem

Instability of mechanical equilibrium and initiation of plane steady-state convective flows in an infinite horizontal fluid layer heated from below (Rayleigh-Benard problem) are investigated. The convection model for an isothermal incompressible fluid is not assumed to have small thermal expansion (contrary to the Oberbeck-Boussinesq approximation). The influence of a supplementary thermal expansion parameter on the convection process is numerically investigated. The results are compared with the known results for the Oberbeck-Boussinesq approximation. It is shown that subcritical instability is possible if the thermal expansion parameter increases. The linearization and Lyapunov-Schmidt methods are applied.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–10, September–October, 1995.