On a modified Becker–Döring model for two-phase materials (original) (raw)
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Aiche Journal, 2009
The Rachford-Rice expressions [Rachford HH, Rice JD, Petroleum Trans AIME 1952;195:327-328] have been modified to include interfacial contributions in the calculation of the equilibrium coexistence between two macroscopic phases. It is shown that two-phase equilibrium states for first-order phase transitions from nucleation to the presence of evolved macroscopic phases can be characterized by using these generalized expressions. Thus, this new treatment allows the determination of the critical inclusion of nucleation of the so-called dispersed phase in a way similar to the determination of incipient new-phase formation points of a saturated phase on the binodal curve. © 2009 American Institute of Chemical Engineers AIChE J, 2010
Phase-field approach to heterogeneous nucleation
Physical Review B, 2003
We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe homogeneous as well as heterogeneous nucleation starting from several general hypotheses. Thus we can investigate the influence of grain boundaries, localized impurities, or any general kind of imperfections in a systematic way. We also put forward the applicability of our model to study other physical situations such as island formation, amorphous crystallization, or recrystallization.
Theory for the nucleation of a crystalline droplet from the melt
Physical review. B, Condensed matter, 1985
An expression is derived for the nucleation rate of a crystalline solid from its melt. In particular, the dynamical prefactor for the nucleation rate is obtained, using Langer s field theory of nucleation. The analysis makes use of the formalism of Ramakrishnan and Yussouff, as extended to solid-melt interfaces by Oxtoby, Haymet, and Harrowell. The theoretical result can be tested experimentally.
EPJ Web of Conferences, 2013
In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories. 2 Nucleation Thermodynamic system consisting of the liquid and its vapor is in saturated state if it is in thermodynamic equilibrium stable to all fluctuations. In this state, temperature T ,
Solid phase properties and crystallization in simple model systems
The European Physical Journal Special Topics, 2014
We review theoretical and simulational approaches to the description of equilibrium bulk crystal and interface properties as well as to the nonequilibrium processes of homogeneous and heterogeneous crystal nucleation for the simple model systems of hard spheres and Lennard-Jones particles. For the equilibrium properties of bulk and interfaces, density functional theories employing fundamental measure functionals prove to be a precise and versatile tool, as exemplified with a closer analysis of the hard sphere crystal-liquid interface. A detailed understanding of the dynamic process of nucleation in these model systems nevertheless still relies on simulational approaches. We review bulk nucleation and nucleation at structured walls and examine in closer detail the influence of walls with variable strength on nucleation in the Lennard-Jones fluid. We find that a planar crystalline substrate induces the growth of a crystalline film for a large range of lattice spacings and interaction potentials. Only a strongly incommensurate substrate and a very weakly attractive substrate potential lead to crystal growth with a non-zero contact angle.
Kinetic theory of nonisothermal binary nucleation: the stage following thermal relaxation
Physica A: Statistical Mechanics and its Applications, 1999
A kinetic theory is constructed for a nonisothermal binary nucleation at the stage following the thermal relaxation of nuclei. The three-dimensional kinetic equation to be solved reaches beyond the framework of the Fokker-Planck approximation even if one of two components has a large value of condensation heat. It is shown that, by successively applying the method of Enskog-Chapman and the method of complete separation of variables to that kinetic equation, one can reduce the problem of constructing the three-dimensional kinetic theory to the well-investigated problem of solving an one-dimensional kinetic equation of ÿrst-order phase transition, in the nonstationary case as well as in the stationary one. For the steady state, the main characteristics of nucleation, including the nucleation rate, are found. Theoretical results are numerically evaluated for the nucleation in ethanol-hexanol system and compared with predictions of classical (isothermal) theory and experimental data.
Asymptotic and numerical studies of the Becker-Doering model for transient homogeneous nucleation
2006
Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-D\"oring kinetic equations with the Turnbull-Fisher discrete diffusivity. After an initial stage in which the number of monomers decreases, many clusters of small size are produced and a continuous size distribution is created. During the second era, nucleii are increasing steadily in size in such a way that their distribution appears as a wave front advancing towards the critical size for steady nucleation. The nucleation rate at critical size is negligible during this era. After the wave front reaches critical size, it ignites the creation of supercritical clusters at a rate that increases monotonically until its steady value is reached. Analytical formulas for the transient nucleation rate and the time lag are obtained that improve classical ones and compare very well with direct numerical so...
Function space theory of dynamic nucleation during solidification at high cooling rates
Bulletin of Materials Science, 1997
An analytical theory is proposed to study the dynamic nucleation of crystals from melt at very high cooling rates (10-6 to 10-12 °K/see). The mathematical framework is found to be isomorphic with the function space theory, wave and matrix mechanics, which enables application of various approximate methods of the latter disciplines. In principle, the mathematical apparatus and concepts of function space and wave mechanics can be utilized to study the time varying nucleation process. The Arrhenius law has been used to extrapolate the self-diffusion coefficient as a function of temperature above the melting point than those below. Since, applicability of Arrhenius equation at very high degrees of supercooling is not known and has to be substituted with appropriate constitutive relationship based on free volume theory of transport, the conclusion derived from the present analysis will not be unique with respect to the certainty of crystallization during the solidification process.