The rules for constructing the analytical approximation are formulated for the law of the accumul... more The rules for constructing the analytical approximation are formulated for the law of the accumulation of the condensing substance by droplets that have emerged at centers of different natures. The accuracy of the suggested approximation is tested for the limiting cases of homogeneous nucleation and nucleation at centers of the same type. A general algorithm is constructed for describing the nucleation stage at centers of different natures after instantaneous creation of vapor supersaturation. Numerical calculations are conducted for the numbers of droplets formed at positively and negatively charged univalent ions in water vapors.
The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The reli... more The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The relief of the free energy with surface excesses was analyzed, the valleys and ridges were described, their mutual interaction was studied. The new possibility to change the valley of nucleation is shown. The possibility to have one common valley instead of several neighbor ones which leads to the radical change in the height of the effective activation barrier and to the new value for the nucleation rate.
A system of a metastable phase with several sorts of the heterogeneous centers is considered. An ... more A system of a metastable phase with several sorts of the heterogeneous centers is considered. An analytical theory for the process of decay in such a system has been constructed. The free energy of formation of the critical embryo is assumed to be known in the macroscopic approach as well as the energy of solvatation. The process is split into some periods and the analytical description of every period is given. The most difficult to describe is the period of the essential formation of the embryos of a new phase. At first some asymptotes are investigated and then a general solution is suggested. Several approximate transformations are accomplished with the corresponding numerical estimates and some analytical justifications. 1 The case of condensation of the supersaturated vapor into the state of liquid droplets seems to be the simples one among the first order phase transitions. Traditionally this case is treated as a model to introduce some new theoretical constructions in the des...
Kinetics of the first order phase transition is investigated. In some rather wide spread situatio... more Kinetics of the first order phase transition is investigated. In some rather wide spread situations the property of avalanche growth of the objects of a new phase doesn't take place. This radically complicates the theoretical description of the nucleation kinetics and this case was completely investigated here. The power-like dependencies with decreasing absolute value of derivative on time were chosen as the model laws of embryos growth. All main characteristics of the nucleation period including the spectrum of sizes of the new phase objects were obtained. An analytical approximate description of nucleation in different external conditions was fulfilled. The errors of such description are found and proved to be small.
The situation of the metastable phase decay on the several types of heterogeneous centers is cons... more The situation of the metastable phase decay on the several types of heterogeneous centers is considered. This publication directly continues " [email protected] get 0001104 ", " [email protected] get 0001108" and " [email protected] get 0001112 " . In this section the approximation od the essential asymptotes is formulated. This approximation is more simple than the floating monodisperse approximation and the special monodisperse approximation. The evident advantage of this approximation is the absence of the exponential nonlinearity.
A new simple method for the first order phase transition kinetics is suggested. The metastable ph... more A new simple method for the first order phase transition kinetics is suggested. The metastable phase consumption can be imagined in frames of the modisperse approximation for the distribution of the droplets sizes. In all situations of the metastable phase decay this approximation leads to negligible errors in the total number of droplets appeared in the system. An evident advantage of the presented method is the possibility to investigate the situation of the metastable phase decay on several sorts of heterogeneous centers.
Theoretical description of the metastable phase decay kinetics in the presence of specific connec... more Theoretical description of the metastable phase decay kinetics in the presence of specific connections between the embryos of small sizes has been given. The theory of the decay kinetics in the presence of relaxation processes is constructed in analytical manner. Them-mers nucleation is investigated and the global kinetics of decay is also constructed in this case analytically.
A system of a metastable phase with a pseudo continuous set of the heterogeneous centers is consi... more A system of a metastable phase with a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of decay of the metastable phase in such a system is constructed. The free energy of formation of a critical embryo is assumed to be known in the macroscopic approach as well as the solvatation energy. The theory constructed below is based on the quasistationary approximation for the nucleation rate.
This part of the theory directly continues the derivation of the kinetic equation presented in th... more This part of the theory directly continues the derivation of the kinetic equation presented in the preprint 990958 of this archive. All definitions are the same and no special remarks are given.
Corrections to a mean number of droplets appeared in the process of nucleation have been analyzed... more Corrections to a mean number of droplets appeared in the process of nucleation have been analyzed. The two stage model with a fixed boundary can not lead to a write result. The multi stage generalization of this model also can not give essential changes to the two stage model. The role of several first droplets have been investigated and it is shown that an account of only first droplet with further appearance in frame of the theory based on the averaged characteristics can lead to a suitable results. Both decay of metastable phase and smooth variations of external conditions have been investigated.
The periods after the end of the "primary" nucleation are considered. The approximate analytical ... more The periods after the end of the "primary" nucleation are considered. The approximate analytical description is given. The process is split into several periods which form the loop of evolution.
A new simple method for the first order phase transition kinetics is suggested. The metastable ph... more A new simple method for the first order phase transition kinetics is suggested. The metastable phase consumption can be imagined in frames of the modisperse approximation for the distribution of the droplets sizes. In all situations of the metastable phase decay this approximation leads to negligible errors in the total number of droplets appeared in the system. An evident advantage of the presented method is the possibility to investigate the situation of the metastable phase decay on several sorts of heterogeneous centers.
A new model to calculate the rate of nucleation is formulated. This model is based on the classic... more A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. As the result the free energy has to be recalculated which brings a new expression for the nucleation rate.
The properties of the evolution equation have been analyzed. The uniqueness and the existence of ... more The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated equation have been established. On the base of these facts taking into account some properties of behavior of solution the uniqueness of the equation appeared in the theory of homogeneous nucleation has been established. The equivalence of auxiliary problem and the real problem is shown.
A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is cons... more A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of the process of condensation in such a system is constructed. The free energy of formation of the critical embryo is assumed to be known in the capillary (macroscopic) approach as well as the solvatation energy of the embryo. The theory is based on the quasistationary approximation for the nucleation rate which has been justified analytically. An effective iteration procedure is presented. The iterationa are calculated analytically. The approximate universal form of the spectrum is established.
The rules for constructing the analytical approximation are formulated for the law of the accumul... more The rules for constructing the analytical approximation are formulated for the law of the accumulation of the condensing substance by droplets that have emerged at centers of different natures. The accuracy of the suggested approximation is tested for the limiting cases of homogeneous nucleation and nucleation at centers of the same type. A general algorithm is constructed for describing the nucleation stage at centers of different natures after instantaneous creation of vapor supersaturation. Numerical calculations are conducted for the numbers of droplets formed at positively and negatively charged univalent ions in water vapors.
The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The reli... more The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The relief of the free energy with surface excesses was analyzed, the valleys and ridges were described, their mutual interaction was studied. The new possibility to change the valley of nucleation is shown. The possibility to have one common valley instead of several neighbor ones which leads to the radical change in the height of the effective activation barrier and to the new value for the nucleation rate.
A system of a metastable phase with several sorts of the heterogeneous centers is considered. An ... more A system of a metastable phase with several sorts of the heterogeneous centers is considered. An analytical theory for the process of decay in such a system has been constructed. The free energy of formation of the critical embryo is assumed to be known in the macroscopic approach as well as the energy of solvatation. The process is split into some periods and the analytical description of every period is given. The most difficult to describe is the period of the essential formation of the embryos of a new phase. At first some asymptotes are investigated and then a general solution is suggested. Several approximate transformations are accomplished with the corresponding numerical estimates and some analytical justifications. 1 The case of condensation of the supersaturated vapor into the state of liquid droplets seems to be the simples one among the first order phase transitions. Traditionally this case is treated as a model to introduce some new theoretical constructions in the des...
Kinetics of the first order phase transition is investigated. In some rather wide spread situatio... more Kinetics of the first order phase transition is investigated. In some rather wide spread situations the property of avalanche growth of the objects of a new phase doesn't take place. This radically complicates the theoretical description of the nucleation kinetics and this case was completely investigated here. The power-like dependencies with decreasing absolute value of derivative on time were chosen as the model laws of embryos growth. All main characteristics of the nucleation period including the spectrum of sizes of the new phase objects were obtained. An analytical approximate description of nucleation in different external conditions was fulfilled. The errors of such description are found and proved to be small.
The situation of the metastable phase decay on the several types of heterogeneous centers is cons... more The situation of the metastable phase decay on the several types of heterogeneous centers is considered. This publication directly continues " [email protected] get 0001104 ", " [email protected] get 0001108" and " [email protected] get 0001112 " . In this section the approximation od the essential asymptotes is formulated. This approximation is more simple than the floating monodisperse approximation and the special monodisperse approximation. The evident advantage of this approximation is the absence of the exponential nonlinearity.
A new simple method for the first order phase transition kinetics is suggested. The metastable ph... more A new simple method for the first order phase transition kinetics is suggested. The metastable phase consumption can be imagined in frames of the modisperse approximation for the distribution of the droplets sizes. In all situations of the metastable phase decay this approximation leads to negligible errors in the total number of droplets appeared in the system. An evident advantage of the presented method is the possibility to investigate the situation of the metastable phase decay on several sorts of heterogeneous centers.
Theoretical description of the metastable phase decay kinetics in the presence of specific connec... more Theoretical description of the metastable phase decay kinetics in the presence of specific connections between the embryos of small sizes has been given. The theory of the decay kinetics in the presence of relaxation processes is constructed in analytical manner. Them-mers nucleation is investigated and the global kinetics of decay is also constructed in this case analytically.
A system of a metastable phase with a pseudo continuous set of the heterogeneous centers is consi... more A system of a metastable phase with a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of decay of the metastable phase in such a system is constructed. The free energy of formation of a critical embryo is assumed to be known in the macroscopic approach as well as the solvatation energy. The theory constructed below is based on the quasistationary approximation for the nucleation rate.
This part of the theory directly continues the derivation of the kinetic equation presented in th... more This part of the theory directly continues the derivation of the kinetic equation presented in the preprint 990958 of this archive. All definitions are the same and no special remarks are given.
Corrections to a mean number of droplets appeared in the process of nucleation have been analyzed... more Corrections to a mean number of droplets appeared in the process of nucleation have been analyzed. The two stage model with a fixed boundary can not lead to a write result. The multi stage generalization of this model also can not give essential changes to the two stage model. The role of several first droplets have been investigated and it is shown that an account of only first droplet with further appearance in frame of the theory based on the averaged characteristics can lead to a suitable results. Both decay of metastable phase and smooth variations of external conditions have been investigated.
The periods after the end of the "primary" nucleation are considered. The approximate analytical ... more The periods after the end of the "primary" nucleation are considered. The approximate analytical description is given. The process is split into several periods which form the loop of evolution.
A new simple method for the first order phase transition kinetics is suggested. The metastable ph... more A new simple method for the first order phase transition kinetics is suggested. The metastable phase consumption can be imagined in frames of the modisperse approximation for the distribution of the droplets sizes. In all situations of the metastable phase decay this approximation leads to negligible errors in the total number of droplets appeared in the system. An evident advantage of the presented method is the possibility to investigate the situation of the metastable phase decay on several sorts of heterogeneous centers.
A new model to calculate the rate of nucleation is formulated. This model is based on the classic... more A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. As the result the free energy has to be recalculated which brings a new expression for the nucleation rate.
The properties of the evolution equation have been analyzed. The uniqueness and the existence of ... more The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated equation have been established. On the base of these facts taking into account some properties of behavior of solution the uniqueness of the equation appeared in the theory of homogeneous nucleation has been established. The equivalence of auxiliary problem and the real problem is shown.
A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is cons... more A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of the process of condensation in such a system is constructed. The free energy of formation of the critical embryo is assumed to be known in the capillary (macroscopic) approach as well as the solvatation energy of the embryo. The theory is based on the quasistationary approximation for the nucleation rate which has been justified analytically. An effective iteration procedure is presented. The iterationa are calculated analytically. The approximate universal form of the spectrum is established.
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