Modelling of liquid film migration in Al-Cu alloys

Microstructural evolution in the presence of liquid film migration (LFM) is simulated for Al-Cu alloys using a cellular automaton (CA) model. Simulations are performed for the microstructural evolution and concentration distribution in an Al-4 wt.%Cu alloy with initially equiaxed grain structures holding in a temperature gradient. A slight deviation from local equilibrium, estimated from experimental data, is considered to be the driving force for LFM. The direction of LFM is triggered by concentration fluctuations setting a concentration gradient as a further driving force. The simulation successfully reproduces the experimentally observed microstructures generated by LFM accompanied by a particle free zone behind the liquid film. The solid concentration in the particle free zone is found to be the equilibrium solid concentration. The simulated concentration profile across the migrating liquid film agrees well with experimental measurements. The simulated grain structure becomes coarser and highly elongated after holding in the temperature gradient. The results reveal that the increase in transversal grain width is mainly controlled by LFM, while the grain elongation in longitudinal direction is attributed to both LFM and temperature gradient zone melting. The solid concentration decreases from the initial (supersaturated) composition to the local equilibrium solid concentration corresponding to the local temperature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Особенности применения теоремы вириала для магнитных систем с квазибессиловыми обмотками

The article shows that in a magnetic system with a thin-walled balanced winding close to a force-free one, a significant increase in the parameter θ=WM γ/M σМ , is possible, which, according to the virial theorem, characterizes the ratio of the energy of the magnetic system WM to the weight of equipment with a material density γ, where under the action of electromagnetic forces there appears a mechanical stress σМ. In a quasi-force-free magnetic system, the main part of the winding is in a state of local equilibrium, and only a relatively small part of the equipment is subject to stress. This part determines the weight of the entire system, and this weight can be minimized. The configurations of balanced thin-walled windings are developed, at the boundaries two boundary conditions are fulfilled simultaneously - the absence of the induction component normal to the boundary and the constancy of the product of induction and radius. The authors consider an example of a system consisting of a main part - a sequence of balanced "transverse" modules in the form of flat discs and end parts, consisting of a combination of "transverse" modules and "longitudinal" ones, having the form of rings elongated along the axis with balanced end parts. It is shown that in the system under consideration, the characteristic dimensionless parameter θ with an unlimited increase in the number of elements of the main part can reach a value of about 24, and when the number of these elements changes within 20 - 40, it changes from 6 to 9.

Nb/Sn Liquid-Solid Reactive Diffusion Couples and Their Application to Determination of Phase Equilibria and Interdiffusion Coefficients of Nb-Sn Binary System

Nb3Sn plays an irreplaceable role in superconducting parts due to its stable performance under high field conditions. Accurate phase equilibria and interdiffusion coefficients are of great significance for designing novel Nb3Sn superconductors. However, the related experimental information is still in a state of scarcity because of the difficulty in fabrication of Nb-Sn alloys caused by the large difference in melting points of Nb and Sn. In this paper, a simple but pragmatic approach was first proposed to prepare the Nb/Sn liquid-solid reactive diffusion couples (LSDCs) at 1100 °C and 1200 °C, of which the phase identification of the formed layer and the measurement of composition-distance profiles were conducted. The formed layer in Nb/Sn LSDCs was confirmed to be Nb3Sn compound. While the measured composition profiles were employed to determine the phase equilibria according to the local equilibrium hypothesis and the interdiffusion coefficients with an aid of the latest version of HitDIC software. The determined phase equilibria of Nb3Sn, (Nb) and liquid show good agreement with the assessed phase diagram. While the calculated interdiffusion coefficients and activation energy for diffusion in Nb3Sn are consistent with both experimental and theoretical data in the literature. Moreover, the growth of the formed Nb3Sn layer in Nb/Sn LSDCs was also found to be diffusion controlled. All the obtained phase equilibria and interdiffusion coefficients are of great value for further thermodynamic and kinetic modeling of the Nb-Sn system. Furthermore, it is anticipated that the presently proposed approach of fabricating liquid-solid reactive diffusion couple should serve as a general one for various alloy systems with large differences in melting points.

Ideal Spin Hydrodynamics from the Wigner Function Approach

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number Kn and the average spin polarization χs have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order Kn and χs .

Inferring temporal dynamics from cross-sectional data using Langevin dynamics

Cross-sectional studies are widely prevalent since they are more feasible to conduct compared with longitudinal studies. However, cross-sectional data lack the temporal information required to study the evolution of the underlying dynamics. This temporal information is essential to develop predictive computational models, which is the first step towards causal modelling. We propose a method for inferring computational models from cross-sectional data using Langevin dynamics. This method can be applied to any system where the data-points are influenced by equal forces and are in (local) equilibrium. The inferred model will be valid for the time span during which this set of forces remains unchanged. The result is a set of stochastic differential equations that capture the temporal dynamics, by assuming that groups of data-points are subject to the same free energy landscape and amount of noise. This is a ‘baseline’ method that initiates the development of computational models and can be iteratively enhanced through the inclusion of domain expert knowledge as demonstrated in our results. Our method shows significant predictive power when compared against two population-based longitudinal datasets. The proposed method can facilitate the use of cross-sectional datasets to obtain an initial estimate of the underlying dynamics of the respective systems.

Velocity gradient statistics in turbulent shear flow: an extension of Kolmogorov's local equilibrium theory

This paper presents an extension of Kolmogorov's local similarity hypotheses of turbulence to include the influence of mean shear on the statistics of the fluctuating velocity in the dissipation range of turbulent shear flow. According to the extension, the moments of the fluctuating velocity gradients are determined by the local mean rate of the turbulent energy dissipation $\left \langle \epsilon \right \rangle$ per unit mass, kinematic viscosity $\nu$ and parameter $\gamma \equiv S (\nu /\left \langle \epsilon \right \rangle )^{1/2}$ , provided that $\gamma$ is small in an appropriate sense, where $S$ is an appropriate norm of the local gradients of the mean flow. The statistics of the moments are nearly isotropic for sufficiently small $\gamma$ , and the anisotropy of moments decreases approximately in proportion to $\gamma$ . This paper also presents a report on the second-order moments of the fluctuating velocity gradients in direct numerical simulations (DNSs) of turbulent channel flow (TCF) with the friction Reynolds number $Re_\tau$ up to $\approx 8000$ . In the TCF, there is a range $y$ where $\gamma$ scales approximately $\propto y^ {-1/2}$ , and the anisotropy of the moments of the gradients decreases with $y$ nearly in proportion to $y^ {-1/2}$ , where $y$ is the distance from the wall. The theoretical conjectures proposed in the first part are in good agreement with the DNS results.

Local Equilibrium Mechanistic Simulation of CO2-Foam Flooding

Mechanistic modeling of the non-Newtonian CO2-foam flow in porous media is a challenging task that is computationally expensive due to abrupt gas mobility changes. The objective of this paper is to present a local equilibrium (LE) CO2-foam mechanistic model, which could alleviate some of the computational cost, and its implementation in the Matlab Reservoir Simulation Tool (MRST). Interweaving the LE-foam model into MRST enables users quick prototyping and testing of new ideas and/or mechanistic expressions. We use MRST, the open source tool available from SINTEF, to implement our LE-foam model. The model utilizes MRST automatic differentiation capability to compute the fluxes as well as the saturations of the aqueous and the gaseous phases at each Newton iteration. These computed variables and fluxes are then fed into the LE-foam model that estimates the bubble density (number of bubbles per unit volume of gas) in each grid block. Finally, the estimated bubble density at each grid block is used to readjust the gaseous phase mobility until convergence is achieved. Unlike the full-physics model, the LE-foam model does not add a population balance equation for the flowing bubbles. The developed LE-foam model, therefore, does not add much computational cost to solving a black oil system of equations as it uses the information from each Newton iteration to adjust the gas mobility. Our model is able to match experimental transient foam flooding results from the literature. The chosen flowing foam fraction (Xf) formula dictates to a large extent the behavior of the solution. An appropriate formula for Xf needs to be chosen such that our simulations are more predictive. The work described in this paper could help in prototyping various ideas about generation and coalescence of bubbles as well as any other correlations used in any population balance model. The chosen model can then be used to predict foam flow and estimate economic value of any foam pilot project.

The Distribution Behavior of Elements during the Top-Blowing Smelting Process of Electronic Waste

In this work, the local equilibrium modeling method of a non-equilibrium multi-phase reaction system in the top-blowing melting process of electronic waste was studied. The automatic judgment mechanism of phase transformation and the improvement of the trace component solving algorithm were explored to build the mathematical model of the element migration and transformation. Secondly, to determine the distribution mechanism of various elements in top-blowing smelting of electronic waste, the thermodynamic digital simulation system was developed according to the software platform of metallurgical process calculation. On this basis, combined with the industrial production practice, the coupling simulation experiment was carried out to investigate the influence of oxygen:feed ratio, oxygen concentration, amount of additive iron powder and CaO:SiO2 ratio of the slag on the smelting process. In addition, the direct yields of metals in the slag were Cu 90.69 wt%, Au 98.57 wt%, Ag 94.84 wt%, and Pd 97.87 wt% under the optimum conditions. Finally, the simulated values were consistent with industrial data, which can provide theoretical guidance for the industrial production practice of the top-blowing smelting of electronic waste.

Research on the Mathematical Model of Local Equilibrium in the Top-Blown Smelting Process of Electronic Waste

In the present study, the local equilibrium modeling and division method of the multiphase non-equilibrium for the top-blowing smelting process of electronic waste was investigated based on the local equilibrium hypothesis. And the mathematical description of the multi-phase equilibrium of each local area and the correlation method between the local areas were studied by analysis of relationships among the valence state, phase, composition, and Gibbs free energy of each element. Afterward, the reaction characteristic data such as melting material, product phase, composition, temperature, atmosphere, etc. were obtained via industrial measurement experiments. Based on these, a mathematical model of local equilibrium for the top-blowing smelting process of electronic waste was established. Finally, the thermodynamic digital simulation system was developed via the calculation of metallurgical process and online control platform MetCal Desk (v7.00, MetCal, Ganzhou, China), which can investigate the element distribution behavior during the smelting process and provide theoretical guidance for the industrial production practice.