Rapid eutectic growth: from rod growth to diffusionless solidification

Numerous experimental data on the rapid solidification of eutectic systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by the suppression of eutectic decomposition due to diffusionless (chemically partitionless) solidification beginning at a high but finite growth velocity of crystals. In the present work, a model is suggested for the diffusionless growth to analyse the atomic diffusion in the rod eutectic couples growing into supercooled liquid. A simplified calculating method for the equation related to the Bessel function in the solution of the growth of rod eutectics is obtained. This method can also be used in the calculation of other rod eutectic growth models. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Comparison of selected mathematical functions for the analysis of growth behavior of items and physical interpretation of AvramiWeibull function

Empirical data of sigmoidal-shaped y(t) growth behavior of different types of items, such as papers and citations earned by individual and all successively published papers of selected top-cited authors, germination of tomato seeds and three different bacteria, are analyzed and compared by Avrami-Weibull, Verhulst (logistic) and Gompertz functions. It was found that: (1) Avrami-Weibull function describes different types of the data better than Gompertz and Verhulst funtions, and (2), in comparison with Verhulst and Gompertz functions, Avrami-Weibull function, expressed in the form: y(t)/ymax = 1-exp[(t/Q)q] (where ymax is the maximum value of y(t) when t ® ¥, and Q and q are constants), is equally very versatile in explaining the generation rate dy(t)/dt of items in terms of its parameters Q and q. Using the basic concepts involved in the derivation of Avrami-Weibull function for overall crystallization from melt and supersaturated solution, the growth behavior of cumulative number y(t) of items produced at time t by individual (simple) sources and collectives or groups of simple sources (i.e. complex or composite sources) is presented. Comparison of the process of receiving of citations by papers with the processes of occurrence of chemical reactions and crystallization of solid phases from melts and supersaturated solutions shows that this process is similar to that of overall crystallization of solid phases from melts and solutions. Analysis of growth of citations using Avrami-Weibull function to individual papers published by different authors shows that 1 < q < 4 for most cases. This suggests that the process of citations to individual articles is mainly determined by progressive nucleation mode involving both diffusion and integration of published knowledge.

A Comparative Evaluation of Thermodynamic Models for Prediction of Wax Deposition

Wax deposition on inner surfaces of pipelines is a costly problem for the petroleum industry. This flow assurance problem is of particular interest during the production and transportation of waxy oils in cold environments. An understanding of known mechanisms and available thermodynamic models will be useful for the management and planning of mitigation strategies for wax deposition. This paper presents a critical review of wax prediction models used for estimation of wax deposition based on chemical hydrocarbon compositions and thermobaric condition. The comparative analysis is applied to highlight the effective mechanisms guiding the wax deposition, and how this knowledge can be used to model and provide solutions to reducing wax deposition issues. One group of thermodynamic models assume that the precipitated wax is a solid solution. These models are divided into two categories: ideal (Erickson and Pedersen models) and non-ideal solutions (Won and Coutinho models). In the other group of models, the wax phase consists of many solid phases (Lira-Galeana model). The authors summarized the limitations of the models, evaluated, and identified ways to represent the overview of existing thermodynamical models for predicting wax precipitation. Within the strong demand from industry, the results of this manuscript can aid to aspire engineers and researcher.

The Effect of Reaction Conditions and Presence of Magnesium on the Crystallization of Nickel Sulfate

Recycling of valuable metals such as nickel is instrumental to meet the need from the dramatic increase in electric vehicle battery production and to improve its sustainability. Nickel required in the battery manufacture can be recovered from the hydrometallurgical industrial process streams by crystallization of nickel sulfate. Here, crystallization of nickel sulfate is studied from an industrial point of view, investigating the effects of temperature, seeding and presence of magnesium on the formation of various solid phases for the evaluation of their potential influence on the process design. Results showed that the precipitating phase was dictated both by seed amount and reaction temperature. Transformation of metastable phases both in suspension and in a dry state was observed over time. Presence of magnesium was shown to promote formation of NiSO4·7H2O in solution and increased its stability in a dry form. In their dry state, nickel sulfate that was formed in the absence of magnesium transformed towards α-NiSO4·6H2O, whereas those precipitated in the presence of high magnesium concentrations transformed towards β-NiSO4·6H2O, indicating that magnesium inhibited the phase transformation towards α-NiSO4·6H2O. Knowledge about various solid phases of varying crystal morphology and stability can be used as input to decisions for the best suited solid product type and how this relates to the initial conditions of the sidestreams.

The influence of conformational defects on the development of structural phase transition in tetracosane C24H50

The kinetics of the first-order solid-state structural transition in monodisperse n-alkanes samples of even tetracosane C24H50 was studied by FTIR spectroscopy. The existence of many irregular conformers in solid phases of tetracosane, the concentration of which reaches a maximum when approaching the melting temperature, has been demonstrated. The existence of these defective molecules promotes transitions between different rotator phases in the solid state.

The first-order phase transition of melting for molecular crystals by Frost–Kalkwarf vapor- and sublimation-pressure equations

Thermodynamic quantities in the coexistence of the liquid and the solid phases for Frost–Kalkwarf vapor- and sublimation-pressure equations are investigated at an isobaric process. Gibbs free energy changes in the gaseous and the liquid phases, ΔG GL, has been derived from the Frost–Kalkwarf vapor-pressure equation. Similarly, Gibbs free energy changes in the gaseous and the solid phases, ΔG GS, may be estimated by the Frost–Kalkwarf sublimation-pressure equations which are determined by data of sublimation pressures and temperatures for 24 substances. In coexistence between the liquid and the solid phases, Gibbs free energy changes in the liquid and the solid phases, ΔG LS, may be expressed as the difference of ΔG GL and ΔG GS. The melting temperatures and enthalpy changes of melting are evaluated by numerical calculations for 24 substances. The behaviors of H2O for the neighborhood at the melting and the boiling points are investigated. The Gibbs free energy indicates two polygonal lines. Entropy, volume and enthalpy jump from the solid to the liquid phase at the melting point and from the liquid to the gaseous phase at the boiling point. The heat capacity does not diverge to infinity but shows a finite discrepancy at the melting and the boiling points. This suggests that first-order phase transitions at the melting and the boiling points may occur.

Improved Efficient Projection Density Function Based on Topology Optimization

Topology optimization is a powerful tool having capability of generating new solution to engineering design problems, while these designs enhance manufacturability and reduce manufacturing costs in a computational setting. Mesh-independent convergence and other techniques have been widely used as topology optimization technique, but they produce gray transition regions which is not a favorable condition for any material. In this article, a modified topology optimization formulation using a new function has been proposed. The suggested scheme makes use of the Heaviside Projection Method (HPM) to continuum topology optimization. Such technique is helpful to obtain the minimum length scale influence on void and solid phases. Application of this proposed approach is implemented to obtain the minimum compliance for macrostructures. Numerical remarkable examples illustrate the noteworthy value of the proposed approach.