Thermodynamic description of metastable fcc/liquid phase equilibria and solidification kinetics in Al-Cu alloys

The thermodynamic description of the fcc phase in the Al-Cu system has been revised, allowing for the prediction of metastable fcc/liquid phase equilibria to undercoolings of Δ T = 421 K below the eutectic temperature. Hypoeutectic Al-Cu alloys that are prone to pronounced microsegregation were solidified containerlessly in electromagnetic levitation. Solidus and liquidus concentrations were experimentally determined from highly undercooled samples employing energy-dispersive X-ray analysis. Solid concentrations at a rapidly propagating solid/liquid interface were additionally calculated using a sharp interface model that considers all undercoolings and is based on solvability theory. Modelling results (front velocity versus undercooling) were also corroborated by in situ observation with a high-speed camera. A newly established thermodynamic description of the fcc phase in Al-Cu is compatible with existing CALPHAD-type databases. Inconsistencies of previous descriptions such as a miscibility gap between Al-fcc and Cu-fcc on the Al-rich side, an unrealistic curvature of the solidus line in the same composition range or an azeotropic point near the melting point of Cu, are amended in the new description. The procedure to establish the description of phase equilibria at high undercoolings can be transferred to other alloy systems and is of a general nature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

A review on the theory of stable dendritic growth

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented. The sharp interface model and stability criteria for various crystallization conditions and crystalline symmetries met in actual practice are formulated and discussed. The review is also focused on the determination of the main process parameters—the tip velocity and diameter of dendritic crystals as functions of the melt undercooling, which define the structural states and transitions in materials science (e.g. monocrystalline-polycrystalline structures). Selection criteria of stable dendritic growth mode for conductive and convective heat and mass fluxes at the crystal surface are stitched together into a single criterion valid for an arbitrary undercooling. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Sharp interface limit of a multi-phase transitions model under nonisothermal conditions

A vectorial Modica–Mortola functional is considered and the convergence to a sharp interface model is studied. The novelty of the paper is that the wells of the potential are not constant, but depend on the spatial position in the domain $$\Omega $$ Ω . The mass constrained minimization problem and the case of Dirichlet boundary conditions are also treated. The proofs rely on the precise understanding of minimizing geodesics for the degenerate metric induced by the potential.

Parameter Estimation of a Decision-Support Seawater Intrusion Model Using Multiple Well and Geophysical Data

<p>In coastal areas, seawater intrusion is a main driver of groundwater salinization and numerical models are widely used to support sustainable groundwater management. Sharp interface models, in which mixing between freshwater and seawater is not explicitly simulated, have fast run times which enable the implementation of parameter estimation and uncertainty analysis. These are essential steps for decision-support modeling, however their implementation in sharp interface models has remained limited. Few guidelines exist regarding which observations to use, and what processing and weighting strategies to employ. We developed a data assimilation framework for a regional, sharp interface model designed for management purposes. We built a sharp interface model for an island aquifer using the SWI2 package for MODFLOW. We then extracted freshwater head observations from shallow wells, pumping wells and deep open wells, and observations of the seawater-freshwater interface from deep open wells, time-domain electromagnetic (TDEM) and electrical resistivity tomography (ERT) surveys. After quantification of measurement uncertainties, parameter estimation was conducted with PEST and a data worth analysis was carried out using a linear approach. Model residuals provided insight on the potential of different observation groups to constrain parameter estimation. The data worth analysis provided insight on these groups’ importance in reducing the uncertainty of model forecasts. Overall a satisfying fit was obtained between simulated and observed data, but observations from deep open wells were biased. While observations from deep open wells and geophysical surveys had a low signal-to-noise ratio, parameter estimation effectively reduced predictive uncertainty. Interface observations, especially from geophysical surveys, were essential to reduce the uncertainty of model forecasts. The use of different types of observations is discussed and recommendations are provided for future data collection strategies in coastal aquifers. This framework was developed in the Magdalen Islands (Quebec, Canada) and could be carried out more systematically for sharp interface seawater intrusion modeling.</p>

A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.