Petr Kubíček

Diffusion in melt with nonstationary interphase boundary

This work deals with the diffusion in a melt which is in contact with a solid. Due to the dissolution and diffusion of the solid in the melt the interphase boundary moves. The mathematical description leads to the solution of the diffusion equation, the constant Dirichlet boundary condition of which is defined on the non-stationary interphase boundary of the diffusion field. The problem is solved by means of the thermal potential of a double layer. The values of diffusion coefficients obtained from experimental data according to this theory are smaller than in the case where the movement of the interphase boundary is not taken into account.

Diffusion in solid phase with nonstationary interphase boundary

This paper deals with the diffusion in a solid phase which is in contact with a melt. Due to dissolution and diffusion of the solid in the melt the interphase boundary moves. The mathematical description leads to the solution of the diffusion equation, the constant Dirichlet boundary condition of which is defined on the nonstationary boundary of the diffusion field. The problem is solved by means of the thermal potential of a double layer. The values of diffusion coefficients obtained from experimental data according to this theory are higher than in the case where the movement of the interphase boundary is not taken into account.

Thermodiffusion and vaporization of metal from levitated droplet I. Calculation of temperature field

In the present paper the initial partial differential equations resulting from the thermodynamics of irreversible processes and Onsager theory are presented and transformed in a way describing convective thermodiffusion in the proximity of a levitated droplet in forced laminar flow. To solve the temperature field the procedure used by Levich for describing diffusion to the falling particle was applied. This procedure was generalized for the temperature dependence of the temperature conductivity coefficient. The results of this solution were compared with the case when the mean constant value of this coefficient is used and an acceptable agreement of the results was stated. The derived theory will be used as the basis for calculation of the vaporization rate of metal from the levitated droplet taking into account metal vapour condensation in the temperature and diffusion boundary layer.

Evaluation of experimental data of diffusion in semiinfinite two-phase systems with nonstationary interphase boundary by means of thermal potentials I. Theory

The present work proceeds from the diffusion equation solution for the nonstationary interphase boundary by means of the thermal potentials. The relations for the amount of material determination in the sample after diffusion and the Matano plane position are derived as well as the original balance equations of the first type from these relations. Furthermore, the balance equations of the second type characterizing the relations between the immediate diffusion flows densities on the interphase boundary are presented. It was possible to make the analytical expression of the concentration gradients on the interphase boundary movement velocity calculation from the experimentally determined concentration profiles. These methods proceed from the knowledge of the areas below these curves, from the concentration gradients on the interphase boundary, from the product of both the quantities and from the knowledge of the area, gradient and interphase movement distance.Twelve equations including the balance equations are derived for three diffusion characteristics calculation. Three equations in which the experimentally determined quantities are burdened by the least experimental error are used for the diffusion characteristics calculation and the remaining ones are used for checking.

Evaluation of experimental data of diffusion in semiinfinite two-phase systems with nonstationary interphase boundary by means of thermal potentials II. Application of the theory to the diffusion characteristics determination

In this work, the survey of twelve final relations for the diffusion characteristics calculation from the experimental data under the assumption of the interphase boundary movement in time according to the parabolic law is presented. The diffusivities determination can be performed by means of four methods which utilize the knowledge of the area below the concentration curves and the knowledge of the concentration gradients on the interphase boundary. The presented relations were applied to the diffusion evaluation of Al in the Ni3Al-Ni system atT=1100°C from the published data by two author teams. The calculated diffusivity values had mostly a smaller dispersion that the values obtained by means of the Matano-Boltzmann method. The new procedures of the diffusivity evaluation can be utilized with advantage in the cases when the diffusivity concentration dependence is little significant.

Thermodiffusion and Vaporization of Metal from Levitated Droplet V. Determination of Condensation Rate and Thermodiffusion Parameters of Mn, Fe, and Ni Vapours

In the present paper the experimental data of vaporization from levitated droplet for Mn, Co, Ni in the flow of argon obtained from the bibliography were evaluated by means of the new method published in the previous work [Czech. J. Phys. 50 (2000) 737]. The rate constants of condensation, thermodiffusion ratios, thermodiffusion coefficients and the corresponding temperature dependencies were determined together with other physical quantities for Mn vapour at the temperature 2000 K and for Fe, Ni at 2200 K. The rate constant of condensation and the thermodiffusion ratio are higher for Ni than for Fe. The value of thermodiffusion coefficient determined for Mn is rather high and the rate constant of condensation is higher than for Ni. The increase of vaporization resulting from condensation and thermodiffusion for Mn was only 2.7-times and for Fe and Ni (5.5-5.65)-times. The process of vaporization from a levitated droplet includes molecular diffusion and convective diffusion, molecular thermodiffusion with vapour condensation and condensation without thermodiffusion. The proportions of these processes were for Mn in the range (37-29) condensation dominated and its share was over 70 accurate experimental data and this is the reason why the evaluation of the Co vaporization was unsuccessful. The work also presents some proposals of experimental procedures leading to the data accuracy improvement.

Diffusion in multiphase systems with nonstationary boundaries III. Solution of diffusion in the region with boundaries moving in opposite directions

In this work the problem of diffusion in a multiphase system whose both boundaries move in one direction according to the parabolic law with different velocities is analysed. The mathematical problem is solved exactly by means of thermal potentials of a double layer. The solution of the diffusion equation in the proximity to the boundary was derived and the concentration gradients on these boundaries were calculated. The numerical procedure of determining the diffusion characteristics from experimental concentration gradients on the phase boundaries was presented. As the zero approximation the result of calculations according to Vasileff and Smoluchowski, that can lead to considerable differences in the determined diffusion coefficients, was used.

Comparison of wagner’s relations for diffusivity determination in binary systems with moving joint boundary with the results of generalized theory

Approximate Wagner’s relations for the diffusion description in semiinfinite systems with nonstationary interphase boundary are compared with the results of the exact solution of the problem. The cases of diffusion from phaseα into phaseβ and from phaseα into phaseα +β were taken into consideration. In dependence on the interphase boundary concentrations and direction of the boundary displacement, the results obtained from Wagner’s relations can differ only slightly from the results of the generalized theory. However, we can also encounter the cases when the differences are some hundreds of per cent. It is impossible to state a priori when Wagner’s solution is sufficiently exact and when the exact solution must be used for calculations.

Thermodiffusion and vaporization of metal from levitated droplet IV. relations for experimental data analysis and their application for evaporation of iron

In the present paper the mathematical relations for analysing experimental results obtained at levitated droplet vaporization were derived. The calculations resulted in a system of nonlinear equations where the unknown quantities characterize condensation rate, thermodiffusion and their temperature dependences. The numerical solution was performed for vaporization of iron in the flow of argon. The thermodiffusion and vapour condensation increase the vaporization rate 5.4-times at 2200 K. The thermodiffusion ratio is negative in order 10−3 and its temperature dependence is important. The temperature dependence of vapour condensation was determined with the accuracy of 2%, the rate constant of condensation was determined approximately as a consequence of experimental data inaccuracy.

Thermodiffusion and vaporization of metal from levitated droplet III. Vaporization rate at molecular diffusion and total vaporization rate

In the present paper the problem of the molecular diffusion in the proximity of the levitated droplet surface respecting the metal vapour condensation influence and temperature dependences of basic physical quantities was solved. The molecular diffusion flow density was derived and the final relation for the mean total thermodiffusion flow density from the droplet surface, i.e. the vaporization rate, was presented. The results are completed by some numerical values and the accuracy of some calculations performed in the linear approximations was analyzed.