Analytical solution to the equations of a two-phase layer with allowance for the convective heat and mass transfer in a binary liquid

The model equations describing directional crystallization of a binary system with a two-phase layer and taking into account the convective heat and mass transfer mechanism in the liquid phase are formulated. The system of formulated nonlinear heat and mass transfer equations is solved analytically in the case of steady-state crystallization scenario. The temperature and concentration distributions, the solid phase fraction, the two-phase layer thickness and its boundaries, solid phase - mushy layer and mushy layer - liquid phase, are found. The steady-state crystallization velocity is determined as a function of fixed model parameters. The developed model and its analytical solutions describe the case of intensive motions of a binary liquid (the case of turbulent flows in the ocean, for example). © 2019 Author(s)

Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: at + eZ1(t), where Z1(t) = ßt7/2 and Z1(t) = ßt2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters a, ß and e are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.Российский Фонд Фундаментальных Исследований (РФФИ), RFBRData accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present research article. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by project no. 16-08-00932 from the Russian Foundation for Basic Research

Examination of evidence for collinear cluster tri-partition

In a series of the experiments at different time-of-flight spectrometers of heavy ions we have observed manifestations of a new at least ternary decay channel of low excited heavy nuclei. Due to specific features of the effect, it was called collinear cluster tri-partition (CCT). The experimental results obtained initiated a number of theoretical articles dedicated to different aspects of the CCT. We compare theoretical predictions with our experimental data, only partially published so far. The model of one of the most populated CCT modes that gives rise to the so called "Ni-bump" is discussed. Detection of the 68-72Ni fission fragments with a kinetic energy E<25 MeV at the mass-separator Lohengrin is proposed for an independent experimental verification of the CCT.Comment: 16 pages, 14 figure

Aromaticity in a Surface Deposited Cluster: Pd4_4 on TiO2_2 (110)

We report the presence of \sigma-aromaticity in a surface deposited cluster, Pd$_4$ on TiO$_2$ (110). In the gas phase, Pd$_4$ adopts a tetrahedral structure. However, surface binding promotes a flat, \sigma-aromatic cluster. This is the first time aromaticity is found in surface deposited clusters. Systems of this type emerge as a promising class of catalyst, and so realization of aromaticity in them may help to rationalize their reactivity and catalytic properties, as a function of cluster size and composition.Comment: 4 pages, 3 figure

Dissolution of polydisperse ensembles of crystals in channels with a forced flow

A non-stationary integro-differential model describing the dissolution of polydisperse ensembles of crystals in channels filled with flowing liquid is analysed. The particle-size distribution function, the particle flux through an arbitrary cross-section of the channel, the particle concentration profile, as well as the disappearance intensity of particles are found analytically. It is shown that a nonlinear behaviour of solutions is completely defined by the source term of particles introduced into the channel. In particular, the model approximately describes the processes of dissolution and transport of drug microcrystals to the target sites in a living organism, taking into account complex dissolution kinetics of drug particles. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 18-19-00008Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present research article. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (grant no. 18-19-00008)

Phase transformations in metastable liquids combined with polymerization

This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space-time regions by means of the Laplace transform. Two functional integrodifferential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddlepoint technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue 'Heterogeneous materials: Metastable and nonergodic internal structures'. ©2019 The Author(s)Published by the Royal Society

Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering–Volmer and Frenkel–Zeldovich–Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time. © 2021 John Wiley & Sons, Ltd.Russian Foundation for Basic Research, РФФИ: 20-08-00199; Ministry of Education and Science of the Russian Federation, Minobrnauka: FEUZ-2020-0057This study is divided into two parts, theoretical and numerical. The theoretical part is supported by the Russian Foundation for Basic Research (project no. 20-08-00199). The numerical part was made possible due to the support from the Ministry of Science and Higher Education of the Russian Federation (project no. FEUZ-2020-0057)