Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Manufacturing of uniformly-sized silicon particles for solar cell from molten metal jet by electromagnetic pinch force

Spherical silicon solar cells are expected to serve as a technology to reduce silicon usage of photovoltaic (PV) power systems[1, 2, 3]. In order to establish the spherical silicon solar cell, a manufacturing method of uniformly sized silicon particles of 1mm in diameter is required. However, it is difficult to mass-produce the mono-sized silicon particles at low cost by existent processes now. We proposed a new method to generate liquid metal droplets uniformly by applying electromagnetic pinch force to a liquid metal jet[4]. The electromagnetic force was intermittently applied to the liquid metal jet issued from a nozzle in order to fluctuate the surface of the jet. As the fluctuation grew, the liquid jet was broken up into small droplets according to a frequency of the intermittent electromagnetic force. Firstly, a preliminary experiment was carried out. A single pulse current was applied instantaneously to a single turn coil around a molten gallium jet. It was confirmed that the jet could be split up by pinch force generated by the current. And then, electromagnetic pinch force was applied intermittently to the jet. It was found that the jet was broken up into mono-sized droplets in the case of a force frequency was equal to a critical frequency[5], which corresponds to a natural disturbance wave length of the jet. Numerical simulations of the droplet generation from the liquid jet were then carried out, which consisted of an electromagnetic analysis and a fluid flow calculation with a free surface of the jet. The simulation results were compared with the experiments and the agreement between the two was quite good.

Magnetic modelling and magneto-hydro-dynamic simulations of an aluminium production electrolytic cell

A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto-hydro-dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

Magneto-hydro-dynamic analysis of an electrolysis cell for aluminum production

An electrolytic cell for Aluminum production contains molten metal subject to high currents and magnetic flux density. The interaction between these two fields creates electromagnetic forces within the liquid metal and can generate oscillations of the fluid similar to the waves at the free surface of oceans and rivers. The study of this phenomenon requires the simulation of the current density field, of the magnetic flux density field and the solution of the equations of motion of the liquid mass. An attempt to analyze the dynamical behavior of this problem is made by coupling different codes, based on different numerical techniques, in a single tool. The simulations are presented and discussed.

Three-phase computations of the continuous casting process

In this paper, the continuous casting process for steel slab production is modelled using a mult-physics approach. For this purpose, a Finite Volume (FV) numerical model was constructed in 3D, with the following characteristics: Time dependent, turbulent fluid flow and heat transfer in the molten steel and flux regions, solidification of the skin layer, under prescribed heat loss boundary conditions, particle tracking simulation of argon bubbles injected with the metal into the mould, full coupling between bubbles and liquid through buoyancy and interfacial forces using a novel gas accumulation technique, and a full transient simulation of flux-metal interface behaviour under the influence of gravity and fluid inertial forces and bubble plume buoyancy. The unstructure mesh FV code PHYSICA developed at Greenwich was used for carry out the simulations with physical process data and properties supplied by IRSID SA.

Obtaining data to validate a model of an induction skull melting furnace

A casting route is often the most cost-effective means of producing engineering components. However, certain materials, particularly those based on Ti, TiAl and Zr alloy systems, are very reactive in the molten condition and must be melted in special furnaces. Induction Skull Melting (ISM) is the most widely-used process for melting these alloys prior to casting components such as turbine blades, engine valves, turbocharger rotors and medical prostheses. A major research project is underway with the specific target of developing robust techniques for casting TiAl components. The aims include increasing the superheat in the molten metal to allow thin section components to be cast, improving the quality of the cast components and increasing the energy efficiency of the process. As part of this, the University of Greenwich (UK) is developing a computer model of the ISM process in close collaboration with the University of Birmingham (UK) where extensive melting trials are being undertaken. This paper describes the experimental measurements to obtain data to feed into and to validate the model. These include measurements of the true RMS current applied to the induction coil, the heat transfer from the molten metal to the crucible cooling water, and the shape of the column of semi-levitated molten metal. Data are presented for Al, Ni and TiAl.

Modelling the performance of lead-Free solder interconnects for copper bumped flip-chip devices

Traditionally, before flip chips can be assembled the dies have to be attached with solder bumps. This process involves the deposition of metal layers on the Al pads on the dies and this is called the under bump metallurgy (UBM). In an alternative process, however, Copper (Cu) columns can be used to replace solder bumps and the UBM process may be omitted altogether. After the bumping process, the bumped dies can be assembled on to the printed circuit board (PCB) by using either solder or conductive adhesives. In this work, the reliability issues of flip chips with Cu column bumped dies have been studied. The flip chip lifetime associated with the solder fatigue failure has been modeled for a range of geometric parameters. The relative importance of these parameters is given and solder volume has been identified as the most important design parameter for long-term reliability. Another important problem that has been studied in this work is the dissolution of protection metals on the pad and Cu column in the reflow process. For small solder joints the amount of Cu which dissolves into the molten solder after the protection layers have worn out may significantly affect solder joint properties.

Modelling the metal arc weldpool

Traditionally, before flip chips can be assembled the dies have to be attached with solder bumps. This process involves the deposition of metal layers on the Al pads on the dies and this is called the under bump metallurgy (UBM). In an alternative process, however, Copper (Cu) columns can be used to replace solder bumps and the UBM process may be omitted altogether. After the bumping process, the bumped dies can be assembled on to the printed circuit board (PCB) by using either solder or conductive adhesives. In this work, the reliability issues of flip chips with Cu column bumped dies have been studied. The flip chip lifetime associated with the solder fatigue failure has been modeled for a range of geometric parameters. The relative importance of these parameters is given and solder volume has been identified as the most important design parameter for long-term reliability. Another important problem that has been studied in this work is the dissolution of protection metals on the pad and Cu column in the reflow process. For small solder joints the amount of Cu which dissolves into the molten solder after the protection layers have worn out may significantly affect solder joint properties.

Cold crucible melting of reactive metals using combined DC and AC magnetic fields

Cold crucible furnace is widely used for melting reactive metals for high quality castings. Although the water cooled copper crucible avoids contamination, it produces a low superheat of the melt. Experimental and theoretical investigations of the process showed that the increase of the supplied power to the furnace leads to a saturation in the temperature rise of the melt, and no significant increase of the melt superheat can be obtained. The computer model of theprocess has been developed to simulate the time dependent turbulent flow, heat transfer with phase change, and AC and DC magnetohydrodynamics in a time varying liquid metal envelope. The model predicts that the supermimposition of a strong DC field on top of the normal AC field reduces the level of turbulience and stirring in the liquid metal, thereby reducing the heat loss through the base of the crucible and increasing the superheat. The direct measurements of the temperature in the commercial size cold crucbile has confirmed the computer redictions and showed that the addition of a DC field increased the superheat in molten TiAl from ~45C (AC field only) to ~81C (DC+AC fields). The present paper reports further predictions of the effect of a dDC field on top of the AC field and compares these with experimental data.

High electric current density-induced interfacial reactions in micro ball grid array (μBGA) solder joints

The effect of a high electric current density on the interfacial reactions of micro ball grid array solder joints was studied at room temperature and at 150 °C. Four types of phenomena were reported. Along with electromigration-induced interfacial intermetallic compound (IMC) formation, dissolution at the Cu under bump metallization (UBM)/bond pad was also noticed. With a detailed investigation, it was found that the narrow and thin metallization at the component side produced “Joule heating” due to its higher resistance, which in turn was responsible for the rapid dissolution of the Cu UBM/bond pad near to the Cu trace. During an “electromigration test” of a solder joint, the heat generation due to Joule heating and the heat dissipation from the package should be considered carefully. When the heat dissipation fails to compete with the Joule heating, the solder joint melts and molten solder accelerates the interfacial reactions in the solder joint. The presence of a liquid phase was demonstrated from microstructural evidence of solder joints after different current stressing (ranging from 0.3 to 2 A) as well as an in situ observation. Electromigration-induced liquid state diffusion of Cu was found to be responsible for the higher growth rate of the IMC on the anode side.

Effect of 0.5 wt % Cu addition in Sn–3.5% Ag solder on the dissolution rate of Cu metallization

The dissolution of thin film under-bump-metallization (UBM) by molten solder has been one of the most serious processing problems in electronic packaging technology. Due to a higher melting temperature and a greater Sn content, a molten lead-free solder such as eutectic SnAg has a faster dissolution rate of thin film UBM than the eutectic SnPb. The work presented in this paper focuses on the role of 0.5 wt % Cu in the base Sn–3.5%Ag solder to reduce the dissolution of the Cu bond pad in ball grid array applications. We found that after 0.5 wt % Cu addition, the rate of dissolution of Cu in the molten Sn–3.5%Ag solder slows down dramatically. Systematic experimental work was carried out to understand the dissolution behavior of Cu by the molten Sn–3.5%Ag and Sn–3.5%Ag–0.5%Cu solders at 230–250 °C, for different time periods ranging from 1 to 10 min. From the curves of consumed Cu thickness, it was concluded that 0.5 wt % Cu addition actually reduces the concentration gradient at the Cu metallization/molten solder interface which reduces the driving force of dissolution. During the dissolution, excess Cu was found to precipitate out due to heterogeneous nucleation and growth of Cu6Sn5 at the solder melt/oxide interface. In turn, more Cu can be dissolved again. This process continues with time and leads to more dissolution of Cu from the bond pad than the amount expected from the solubility limit, but it occurs at a slower rate for the molten Sn–3.5%Ag–0.5%Cu solder. © 2003 American Institute of Physics.

Modeling the diffusion of solid copper into liquid solder alloys

During the soldering process, the copper atoms diffuse into liquid solders. The diffusion process determines integrity and the reworking possibility of a solder joint. In order to capture the diffusion scenarios of solid copper into liquid Sn–Pb and Sn–Cu solders, a computer modeling has been performed for 10 s. An analytical model has also been proposed for calculating the diffusion coefficient of copper into liquid solders. It is found that the diffusion coefficient for Sn–Pb solder is 2.74 × 10− 10 m2/s and for Sn–Cu solder is 6.44 × 10−9 m2/s. The modeling results reveal that the diffusion coefficient is one of the major factors that govern the rate at which solid Cu dissolve in the molten solder. The predicted dissolved amounts of copper into solders have been validated with the help of scanning electron microscopic analysis.

The influence of alkali metal chlorides on the loss of water from glass-ionomer dental cements

The water loss behaviour of a clinical glass-ionomer dental cement has been studied with and without the addition of alkali metal chlorides. Dehydrating conditions were provided by placing specimens in a desiccator over concentrated sulphuric acid. Cements were prepared using either pure water or an aqueous solution of metal chloride (LiCl, NaCl, KCl) at 1.0 mol/dm(3). In addition, NaCl at 0.5 mol/dm(3) was also used to fabricate cements. Disc-shaped specimens of size 6 mm diameter x 2 mm thickness were made, six performulation, and cured at 37 degrees C for 1 hour They were then exposed to desiccating conditions, and the mass measured at regular intervals. All formulations were found to lose water in a diffusion process that equilibrated after approximately 3 weeks. Diffusion coefficients ranged from 2.27 (0.13) x 10(9) with no additive to 1.85 (0.07) x 10(9) m(2)/s with 1.0 mol/dm(3) KCl. For the salts, diffusion coefficients decreased in the order LiCl > NaCl > KCl. There was no statistically significant difference between the diffusion coefficients for 1.0 and 0.5 mol/dm(3) NaCl. For all salts at 1.0 mol/dm(3) and also additive-free cements, equilibrium losses were, with statistical limits, the same, ranging from 6.23 to 6.34%. On the other hand, 0.5 mol/dm(3) NaCl lost significantly more water 7.05%.

Characterisation of products of tricalcium silicate hydration in the presence of heavy metals

The hydration of tricalcium silicate (C(3)S) in the presence of heavy metal is very important to cement-based solidification/stabilisation (s/s) of waste. In this work, tricalcium silicate pastes and aqueous suspensions doped with nitrate salts of Zn(2+), Pb(2+), Cu(2+) and Cr(3+) were examined at different ages by X-ray powder diffraction (XRD), thermal analysis (DTA/TG) and (29)Si solid-state magic angle spinning/nuclear magnetic resonance (MAS/NMR). It was found that heavy metal doping accelerated C(3)S hydration, even though Zn(2+) doping exhibited a severe retardation effect at an early period of time of C(3)S hydration. Heavy metals retarded the precipitation of portlandite due to the reduction of pH resulted from the hydrolysis of heavy metal ions during C(3)S hydration. The contents of portlandite in the control, Cr(3+)-doped, Cu(2+)-doped, Pb(2+)-doped and Zn(2+)-doped C(3)S pastes aged 28 days were 16.7, 5.5, 5.5, 5.5, and <0.7%, respectively. Heavy metals co-precipitated with calcium as double hydroxides such as (Ca(2)Cr(OH)(7).3H(2)O, Ca(2)(OH)(4)4Cu(OH)(2).2H(2)O and CaZn(2)(OH)(6).2H(2)O). These compounds were identified as crystalline phases in heavy metal doping C(3)S suspensions and amorphous phases in heavy metal doping C(3)S pastes. (29)Si NMR data confirmed that heavy metals promoted the polymerisation of C-S-H gel in 1-year-old of C(3)S pastes. The average numbers of Si in C-S-H gel for the Zn(2+)-doped, Cu(2+)-doped, Cr(3+)-doped, control, and Pb(2+)-doped C(3)S pastes were 5.86, 5.11, 3.66, 3.62, and 3.52. And the corresponding Ca/Si ratios were 1.36, 1.41, 1.56, 1.57 and 1.56, respectively. This study also revealed that the presence of heavy metal facilitated the formation of calcium carbonate during C(3)S hydration process in the presence of carbon dioxide.

Fluoride-releasing composite resins

This paper reviews the literature on fluoride-releasing composite resins. These materials have been available for several years, with fluoride release being achieved by adding soluble or sparingly soluble fluoride salts to the formulation. However, this has been shown to lead to a gradual reduction in the mechanical properties. These materials are also unable to undergo "fluoride recharge". Experimental fluoride-releasing composites have been prepared which supply fluoride by alternative mechanisms that do have the potential for fluoride recharge but, so far, these materials have not been made available for use in patients. Fluoride-releasing composite resins have been shown to be effective in preventing secondary caries in vitro. They have also been shown to reduce the size and depth of carious lesions. However, information on their clinical effectiveness is limited and the paper concludes that there is an urgent need for research on this topic.