The effect of solute on ultrasonic grain refinement of magnesium alloys

An experimental study has been conducted to assess the structural refinement of magnesium and its alloys by ultrasonic irradiation during solidification. It is shown that (i) ultrasonic irradiation leads to significant refinement only in the presence of adequate solute, which is alloy dependent; (ii) the attendant grain density increases linearly with increase in solute content at a given irradiation level; (iii) increasing the solute content at a low irradiation level above the cavitation threshold is more effective than substantially increasing the irradiation intensity; and (iv) the difference in the grain size between two ultrasonicated magnesium alloys is mainly determined by the solute content rather than the irradiation intensity. In view of these, the effect of ultrasonic irradiation on solute redistribution in a solidifying magnesium alloy seems rather limited even at a substantial intensity level such as 1700 W cm⁻². The implications of these findings are discussed and a mechanism is proposed to account for the experimental observations.     

Molecular dynamics simulations of the crystal–melt interface mobility in HCP Mg and BCC Fe

The temperature profile around the moving solid–liquid interface during non-equilibrium molecular dynamics (MD) simulations of crystallization and melting is examined for HCP Mg and BCC Fe. An evident spike (valley) is found around the solid–liquid interface during solidification (melting). Considering the effect of a non-uniform temperature distribution, it is found that, if the actual interface temperature is adopted to compute the interface mobility, rather than the thermostat temperature (or the mean temperature of the whole system), the kinetic coefficient is approximately a factor of two larger than previous estimates. Although the magnitude of the kinetic coefficient is larger than the previous estimates, the crystalline anisotropies derived in the current work are consistent with earlier calculations.     

Three-dimensional global analysis of thermal stress and dislocations in a silicon ingot during a unidirectional solidification process with a square crucible

A three-dimensional global model was used to obtain the solution of a thermal field within the entire furnace during a unidirectional solidification process of multicrystalline silicon with a square crucible. Then the thermal stress distribution in the silicon ingot was solved. Based on the solution of thermal stress, relaxation of stress and multiplication of dislocations were performed by using the Haasen–Alexander–Sumino model (HAS model). The influence of crucible constraint on stress levels and dislocations was investigated. It was found that the crucible constraint had significant influence on the thermal stresses and dislocations in the ingot. The results indicated that it is important to reduce the crucible constraint in order to relax thermal stresses and reduce dislocations in a silicon ingot during the solidification process.     

Analysis of Natural Convection During Solidification of a Pure Metal

A numerical study of solidification of gallium in a closed cavity is presented and the influence of natural convection on phase change is investigated.

The mathematical formulation is based on the enthalpy-porosity method, while the equations are discretized on a fixed grid by means of a finite volume technique. Advancing in time is obtained using the SIMPLE algorithm, while the solution of the elliptic equation for pressure correction is obtained by means of a preconditioned BI-CGStab method.

As a test case a square cavity with Ra ranging from 4.68 × 10³ to 9.36 × 10⁵ is adopted. Results will be presented in terms of streamlines, isotherms, solid-liquid interface position and Nu and compared, when possible with available data.     

Determination of four acidic nonsteroidal anti‐inflammatory drugs in wastewater samples by dispersive liquid–liquid microextraction based on solidification of floating organic droplet and high‐performance liquid chromatography

A simple, environmentally friendly, and sensitive dispersive liquid–liquid microextraction based on solidification of floating organic droplet for the extraction of four acidic nonsteroidal anti‐inflammatory drugs (ketoprofen, naproxen, ibuprofen, and diclofenac) from wastewater samples subsequent by high‐performance liquid chromatography analysis was developed. The influence of extraction parameters such as pH, the effect of solution ionic strength, type of extraction solvent, disperser solvent, and extraction solvent volume were studied. High enrichment factors (283–302) were obtained through the developed method. The method provides good linearity (r > 0.999) in a concentration range of 1–100 μg/L, good intra‐ and inter‐day precision (relative standard deviation < 7%) and low limits of quantification. The relative recoveries of the selected compounds were situated over 80% both in synthetic and real water samples. The developed method has been successfully applied for the analysis of the selected compounds in wastewater samples.     

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type is imposed on the fixed face x=0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q ₀ is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x=0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo viene imposta sulla faccia fissa x=0. Si analizzano differenti casi dipendenti da parametri fisici e la soluzione esplicita viene ottenuta se e solo se risulta verificata una diseguaglianzo per il coefficiente termico q ₀. Si ottiene altresi un miglioramento della condizione di esistenza di una soluzione di similarità per lo stesso problema al contorno libero con temperatura costante sulla faccia fissa x=0.     

Development of Dispersive Liquid‐Liquid Microextraction Based on Solidification of Floating Organic Drop for the Determination of Trace Cobalt in Water Samples

A liquid‐phase microextraction technique was developed using dispersive liquid‐liquid microextraction based on solidification of floating organic drop combined with flame atomic absorption spectrometry, for the extraction and determination of trace amounts of cobalt in water samples. Microextraction efficiency factors, such as the type and volume of extraction and dispersive solvents, pH, extraction time, the chelating agent amount, and ionic strength were investigated and optimized. Under optimum conditions, an enrichment factor of 160 was obtained from 10.0 mL of water sample. The calibration graph was linearin the range of 1.15‐110 μg L^?1 with a detection limit of 0.35 μg L^?1. The relative standard deviation for ten replicate measurements of 10 and 100 μg L^?1 of cobalt were 3.26% and 2.57%, respectively. The proposed method was assessed through the analysis of certified reference water or recovery experiments.     

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids: Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.     

Temperature profiles in a controlled-stress parallel plate rheometer

Actual melt temperatures are rarely measured directly when conducting rheological characterisations of materials in non-ambient conditions despite the potentially large influence temperature may have on the rheological data. For rheometers that use only a temperature-regulated lower plate, it is likely that the set point and true melt temperatures differ, an effect that becomes significant when characterising melts or suspensions close to phase-change events like crystallisation. This work investigates the magnitude of these effects for a controlled-stress rheometer featuring a temperature-controlled lower plate. The lower plate was fitted with a serrated cover disc that was found to exacerbate temperature deviations from the desired set point. Steady-state radial and vertical temperature profiles within the sample were measured and compared with the predictions of a finite element analysis model. The deviations between set point and measured temperatures were successfully predicted by the simulation for two typical gap heights for a thermoplastic, ceramic paste. The non-ideal heat transfer characteristics were also investigated numerically for a representative polymer system that demonstrated the increased deviations from ideal values for lower thermal conductivity materials.

Fractional Steps Scheme to Approximate the Phase-Field Transition System with Non-Homogeneous Cauchy–Neumann Boundary Conditions

The paper presents a proof of the convergence for an iterative scheme of fractional steps type associated to the phase-field transition system (a nonlinear parabolic system) with non-homogeneous Cauchy–Neumann boundary conditions. The advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of a nonlinear parabolic system. On the basis of this approach, a numerical algorithm in the two dimensional case is introduced and an industrial implementation is made.