Gas-melt Interface Research Articles

Generation of CO2-rich melts during basalt magma ascent and degassing

To test mechanisms of basaltic magma degassing, continuous decompressions of volatile-bearing (2.7–3.8 wt% H2O, 600–1,300 ppm CO2) Stromboli melts were performed from 250–200 to 50–25 MPa at 1,180–1,140 °C. Ascent rates were varied from 0.25 to ~1.5 m/s. Glasses after decompression show a wide range of textures, from totally bubble-free to bubble-rich, the latter with bubble number densities from 104 to 106 cm−3, similar to Stromboli pumices. Vesicularities range from 0 to ~20 vol%. Final melt H2O concentrations are homogeneous and always close to solubilities. In contrast, the rate of vesiculation controls the final melt CO2 concentration. High vesicularity charges have glass CO2 concentrations that follow theoretical equilibrium degassing paths, whereas glasses from low vesicularity charges show marked deviations from equilibrium, with CO2 concentrations up to one order of magnitude higher than solubilities. FTIR profiles and maps reveal glass CO2 concentration gradients near the gas–melt interface. Our results stress the importance of bubble nucleation and growth, and of volatile diffusivities, for basaltic melt degassing. Two characteristic distances, the gas interface distance (distance either between bubbles or to gas–melt interfaces) and the volatile diffusion distance, control the degassing process. Melts containing numerous and large bubbles have gas interface distances shorter than volatile diffusion distances, and degassing proceeds by equilibrium partitioning of CO2 and H2O between melt and gas bubbles. For melts where either bubble nucleation is inhibited or bubble growth is limited, gas interface distances are longer than volatile diffusion distances. Degassing proceeds by diffusive volatile transfer at the gas–melt interface and is kinetically limited by the diffusivities of volatiles in the melt. Our experiments show that CO2-oversaturated melts can be generated as a result of magma decompression. They provide a new explanation for the occurrence of CO2-rich natural basaltic glasses and open new perspectives for understanding explosive basaltic volcanism.

Numerical simulation of gas-assisted injection molding using CLSVOF method

It is a typical gas–liquid two phase flow phenomenon that gas penetrates the polymer melt in gas-assisted injection molding (GAIM) process. Numerical simulation is now playing an important role in GAIM, in which the accurate simulation of moving interface is of great importance. The level set (LS) method is a popular interface tracking method, but it does not ensure naturally mass-conservation. In order to improve the mass-conservation of LS method, a coupled level-set and volume-of-fluid (CLSVOF) method with mass-correction is presented for the numerical simulations of interfacial flows in GAIM. The performance of this CLSVOF method is demonstrated by two numerical tests including the three-dimensional deformation field test and the dam break problems. Finally the CLSVOF method is employed to simulate the 3D moving interfaces in GAIM, including gas–melt interface and the melt-front interface. The influences of melt temperature and gas delay time are also analyzed detailedly. As a case study, the processes that gas penetrates the polymer melt in complex cavities are also simulated using this method, and the simulation results are in agreement with those obtained by other researchers.

High speed imaging of the flow during close-coupled gas atomisation: Effect of melt delivery nozzle geometry

We describe the application of a high-speed still imaging technique to the study of close-coupled gas atomisation. A pulsed Nd:YAG laser is used to obtain pairs of still images with an effective 6 ns exposure time, from which velocity maps of the flow of the atomised fluid can be reconstructed. We demonstrate directly that the melt spray cone consists of a jet precessing around the surface of a cone. Further, we demonstrate that the width of this jet is directly related to the geometry of the melt nozzle. By applying Particle Image Velocimetry techniques we are also able to map the flow field in both the primary and secondary atomisation zones, demonstrating an asymmetric recirculation eddy exists at the circumferential edge of the gas–melt interface in the primary atomisation zone.

Modelling and simulation of moving interfaces in gas-assisted injection moulding process

The mathematical models of gas–liquid two-phase flow are introduced, in which the multi-mode eXtended Pom–Pom (XPP) model is selected to predict the viscoelastic behavior of polymer melt. The gas-penetration process is simulated using Level Set/SIMPLEC methods, which can capture the moving interfaces at different time, including the gas–melt interface and the melt front. The physical features such as velocity, temperature and elasticity are described at different time. The influences of gas delay time and injection pressure on gas-penetration time and penetration length are analyzed. The numerical results show that the Level Set/SIMPLEC methods can precisely trace the two moving interfaces in gas-penetration process, the fractional coverage increases at very low Deborah numbers, while at higher Deborah numbers the fractional coverage decreases, and the penetration length is affected significantly by gas delay time and injection pressure.

Time-dependent changes of the electrical conductivity of basaltic melts with redox state

The electrical conductivity of basaltic melts has been measured in real-time after fO 2 step-changes in order to investigate redox kinetics. Experimental investigations were performed at 1 atm in a vertical furnace between 1200 and 1400 °C using air, pure CO 2 or CO/CO 2 gas mixtures to buffer oxygen fugacity in the range 10 −8 to 0.2 bars. Ferric/ferrous ratios were determined by wet chemical titrations. A small but detectable effect of fO 2 on the electrical conductivity is observed. The more reduced the melt, the higher the conductivity. A modified Arrhenian equation accounts for both T and fO 2 effects on the electrical conductivity. We show that time-dependent changes in electrical conductivity following fO 2 step-changes monitor the rate of Fe 2+/Fe 3+ changes. The conductivity change with time corresponds to a diffusion-limited process in the case of reduction in CO–CO 2 gas mixtures and oxidation in air. However, a reaction at the gas–melt interface probably rate limits oxidation of the melt under pure CO 2. Reduction and oxidation rates are similar and both increase with temperature. Those rates range from 10 −9 to 10 −8 m 2/s for the temperature interval 1200–1400 °C and show activation energy of about 200 kJ/mol. The redox mechanism that best explains our results involves a cooperative motion of cations and oxygen, allowing such fast oxidation–reduction rates.

Analysis of diffusion mechanism between gas and melt in gas-assisted injection molding

Abstract In the process of gas-assisted injection molding (GAIM), the high-pressure gas such as N 2 comes to a supercritical state. The supercritical N 2 diffuses into the polymer melt. After unloading the pressure, the N 2 in the polymer melt achieves a super-saturation state. The super-saturated N 2 close to the gas–melt interface diffuses through it, and the N 2 close to the internal wall delays to diffuse and remains in the polymer melt to form the small bubble, the inner pressure of small bubbles is bigger than outside pressure, so the small bubble has grown up gradually. Finally the cellular gas bubble blemish was formed. To decrease the gas bubble blemish, the gas holding pressure should be reduced in the precondition of the product quality is reached. And to eliminate the gas bubble blemish, the gas holding time should be increased as long as possible, and gas pressure should vent until molding part temperature comes down below its glassily temperature.

Droplet spreading, imbibition and solidification on porous media

The spreading, imbibition and solidification of a hot two-dimensional droplet on a cooler porous substrate is studied. Lubrication theory and asymptotic reduction are used to derive a coupled system of evolution equations for the droplet thickness and vertical extents of the solid/melt boundary and the saturation front within the porous medium. This medium is assumed to be a membrane composed of an array of pores having fixed width. A precursor layer model and a disjoining pressure are used to relieve the singularity at the contact line. When the solidification and imbibition time scales are similar to those associated with spreading, the dynamics follow two stages: spreading and imbibition accompanied by solidification within the pores leading to their blockage, followed by contact line arrest and basal solidification of the droplet; the possibility of crust formation at the gas–melt interface is excluded from the present study. The dependence of the dynamics on the relevant system parameters is elucidated. Furthermore, our modelling predictions compare favourably with experimental data also obtained as part of the present work.

The contribution of surface tension driven flows in flux line erosion

An interesting manifestation of surface tension driven flows is the phenomenon of “flux line erosion.’’ It consists of the scouring or erosion of the refractory crucible by a melt in the vicinity of a gas-melt interface. A mathematical model has been developed on the assumption that the wall erosion profile can be explained by the disruption of the dissolution concentration gradients by buoyancy and surface tension driven convective flows. The problem is formulated by considering the Navier–Stokes equations coupled with the energy and diffusion equations. The velocity field is determined by the equations of motion and energy, whereas the concentration distribution is determined by the convective diffusion equation. All these equations are mutually dependent since the surface tension is a concentration function. The concentration distribution depends on the velocity distribution, and the driving forces of the flow are the buoyancy and surface tension forces. The relative contributions of these forces in determining the shape and rate of the erosion profile have been studied. It was found that surface tension flows play a significant role in determining the erosion patterns of the refractory walls.

A Mathematical Model for the Reduction Kinetics of Iron Oxide in Electric Furnace Slags by Graphite Injection.

A three-phase, solid-gas-liquid, reactive jet is mathematically modeled in time domain for the injecting operation of graphite particles in complex electric furnace steelmaking slags to reduce the iron oxide contents. The model takes into account the jet penetration in the liquid, the physical changes that the slag suffers due to chemical composition variations, the surface active effects of silica in molten slags and the coupling-uncoupling flow characteristics between the carrier gas and the solid particles in the molten phase. The mathematical simulations indicate that at small particle sizes (100-150 μm) the reaction kinetics is controlled by the gas-melt interface, under this regime acid slags show higher reduction rates than basic ones. At larger sizes this reaction is controlled by the mass transfer of iron oxide from the bulk phase to the gas-melt interface and basic slags show higher reduction rates than acid ones. To obtain a given reduction rate of iron oxide there is an optimum particle size at which the consumption rate of the reducing agent is minimum. Below this size the particle is consumed by the reaction without reaching high efficiencies. Above this minimum the particle size is so large that it exits the molten bath only partially reached decreasing also the efficiency of the reaction. Just at this minimum the particle is totally consumed by the reaction with a minimum consumption rate of the reducing agent.

Experimental observation of interface shapes in the float zone of lithium niobate during a CO 2 laser melting

The radiosity from a rod of lithium niobate that was heated uniformly by a CO 2 laser with an axisymmetric ring-shaped beam was measured by a two-dimensional infrared imaging radiometer with bandpass filters chosen to be 3–5, 8–12, and 10.6 μm. The radiative characteristics of the volumetric emission and the significant difference of the emitted thermal radiation between the solid or melt and background for wavelengths of 3–5 μm was used to determine the interface shapes of the float zone during the CO 2 laser melting process. The trend of the power distribution impinging on the rod surface may be deduced from the reflection of the CO 2 laser. The gas bubbles existing in the melt may also be monitored. The surface temperature was determined from the distribution of the radiosity for wavelengths of 8–12 μm. The surface temperature distribution is modified significantly be thermocapillary convection. With an increase of the input power, the gas-melt interface changes from concave towards the melt to convex at the upper zone and concave at the lower zone due to the effect of gravity.

Oxygen transport mechanism in Si melt during single crystal growth in the Czochralski system

Silicon single crystals were grown in crucibles with and without a carbon sheet at the bottom to investigate how oxygen dissociates from the crucible and transfers to the crystals. Oxygen concentration in the crystals grown in the sheet-attached crucible was lower than that of crystals grown in the sheetless crucible when crucible rotation rate was high. A three-dimensional numerical simulation clarified that with a high crucible rotation rate, about 20% of the oxygen in the grown crystals was transferred by convection in the melt from the bottom of the crucible. For a low crucible rotation rate, a melt with a small oxygen concentration was directly transferred from the gas-melt interface to the crystal-melt interface; therefore, oxygen concentration in crystals grown at a low crucible rotation rate was lower than that for crystals grown at a high rotation rate.

Measurement of the surface temperature distribution in the float zone of LiNbO 3

The thermal radiation emitted from a LiNbO 3 rod in a CO 2 laser-heated float-zone system has been measured by a two-dimensional thermal imaging radiometer with the spectral bandpass selected to be 3–5, 10.6 and 8–12 μm. When the float zone is formed, the interference of the monochromatic CO 2 laser with the thermal emission at the wavelengths of 10.6 and 8–12 μm can be minimized because the deformable gas-melt interface is optically smooth. The present results show that the emission of thermal radiation at the wavelengths of 10.6 and 8–12 μm is a surface phenomena, while that of 3–5 μm is a volumetric phenomena. The emission of thermal radiation in the 3–5 μm spectrum is used to determine the shape of the float-zone interface by using the method developed by Chen and Hu [J. Crystal Growth 149 (1995) 87]. Because the temperature at the gas-melt-solid interface is the melting point of the material, the emissivities for the wavelengths of 10.6 and 8–12 μm for the melting temperature can be obtained from the Planck radiation law, and they are around 0.92 and 0.98, respectively. Since the emissivity at these wavelengths is insensitive to the variation of the temperature, the surface temperature can be obtained from the thermal radiation distribution.

Linear stability analysis of thermocapillary convection in the floating zone

The stability of thermocapillary convection in the floating zone for molybdenum (Mo) and lithium niobate (LiNbO 3) has been studied using a linear theory. The input power induced by the heat source is assumed to be a Gaussian distribution. The steady, axisymmetric basic state is solved numerically using a finite difference method, employing the boundary-fitted curvilinear coordinate system. The linear disturbance equations for axisymmetric disturbances, which are partial differential equations, are treated by a mixed finite difference spectral method. The critical zone lengths and the critical input powers of Mo for axisymmetric disturbances are predicted. The thermocapillary instability of the LiNbO 3 melt may not appear before the capillary instability (originating from the gas-melt interface) sets in.

Measurement of the float-zone interface shape for lithium niobate

A new technique has been developed to locate the interface shape in the floating zone of lithium niobate materials. The floating zone is formed and uniformly heated by a CO 2 laser with an axisymmetric ring-shaped beam generated by an axicon optical system. The emitted thermal radiation from the hot object has been measured by an imaging radiometer. The interference of the CO 2 laser with the measurement of the radiometer is avoided by setting the spectral bandpass of radiation to 3–5 μm. The location of the gas-solid or gas-melt interface is determined through the significant difference of the emitted radiation between the solid or melt and the background. Since the lithium niobate is viewed as a semitransparent material and the emittances of the solid and melt are significantly different, the locations of the melt-solid and gas-melt-solid interfaces are determined according to the change of the emitted radiation intensity. The floating zone is resolidified, and the interior of the resultant solid is observed by SEM (scanning electron microscopy) to identify the location and shape of the melt-solid interface. The results predicted by the variation of radiation intensity are consistent with those observed from the SEM.

Finite element simulation of combined buoyancy and thermocapillary driven convection in open cavities

AbstractThermocapillary‐induced and buoyancy‐driven convective flows that commonly occur in crystal growth are numerically simulated using Galerkin finite element method. The physical domain comprises of a open cavity with aspect ratio one and differentially heated vertical walls. The top gas–melt interface is free to deform subject to 90° contact angle boundary conditions at the two vertical walls. The unsteady two‐dimensional Navier–Stokes equations are discretized in time using Chorin‐type splitting scheme and pressure is determined from the Poisson's equation. The free surface is taken to be resting on vertical spines and its evolution in time is determined from the kinematic free surface equation. The governing equations for heat and momentum are solved in the Arbitrary Lagrangian Eulerian frame of reference to handle the moving boundary. The influence of Grashof number, Marangoni number, Bond number, Ohnesorge number and Prandtl number on the flow field and heat transfer is investigated.

Thermocapillary convection and melt-solid interface in the floating zone

A series of numerical computations is used to study both the amount of power required to form a molten zone and the fluid flow inside the melt. The Navier-Stokes equations and energy equation are solved by a finite difference method, employing a boundary-fitted curvilinear coordinate system. The influences considered include: the magnitude of the input power, the width of the heated region, the fluid properties in the melt, and the heat-transfer condition of the ambient on the solid-melt interface. The present results show that the height of the molten zone increases significantly as the strength of the thermocapillary convection increases. For small Prandtl number fluids, when the input power increases, thermocapillary-flow instability in the melt may appear before the capillary instability (originating from the gas-melt interface) sets in. For higher Prandtl number fluids, the appearance of the capillary instability is more likely than thermocapillary-flow instability. The appearance of thermocapillary-flow instability may be also influenced by the ratio of the surface tension to the viscous force in the melt, the width of the heated region, and the heat loss to the ambient.

REACTION ENHANCED VAPORIZATION OF MOLTEN SALT

Vaporization of molten salts results in serious problems in the operation of many combustion systems. Salt vaporization of special importance in the burning of kraft black liquor, where combustion occurs in a molten Na2S/Na2CO3 environment. In this paper, it is shown that the vaporization of alkali carbonate during air oxidation of Na2S/Na2CO3 results from Na oxidation in the gas phase. Oxidation of Na in the gas phase significantly lowers the partial pressure of Na. Since the driving force for vaporization is the difference between the equilibrium vapor pressure of Na at the gas-melt interface and the partial pressure of Na in the gas phase, this reduction in partial pressure of Na significantly increases Na vaporization rates and allows fuming to proceed with only mild reducing conditions in the melt.

Hydrolysis of fused calcium chloride at high temperature

The hydrolysis of fused calcium chloride occurs at the initial step in the nickel segregation. This reaction was studied at 1113, 1173 and 1223 K under the experimental condition that equilibrium was attained at the gas-melt interface and the overall rate of the reaction was controlled by the gas diffusion to and from the gas-melt interface by using a slender platinum container. The weight loss of the sample and the amount of the evolved HC1 gas were continuously measured. The overall rate of the reaction was raised at higher temperature and higher moisture content in the mixed feed gas of N2 and H2O. It was found that CaO was formed above 1170 K. It was also formed at 1113 K when the moisture content of the feed gas was 19 pct or less. When the moisture content is higher than 24 pct at 1113 K, however, the reaction becomes more complicated; Ca(OH)2 is formed in addition to CaO both of which are dissolved in the melt. A theoretical calculation was made regarding the hydrolysis in which only CaO is formed in order to verify that the overall rate is controlled by the gas diffusion; it was assumed that the equilibrium is attained at the gas-melt interface and the theoretical weight loss was calculated from the rate of counter-diffusion of H2O and HC1 in the stagnant N2 gas. The theoretical value was in excellent agreement with the measurement.

Oxidation kinetics of antimony in lead-antimony melts

The kinetics of the selective oxidation of Sb in molten Pb-Sb, Pb-Sb-Ag and Pb-Sb-Bi alloys have been examined with the aim of improving methods of treatment of anode slimes from the electrolytic refining of lead. The rate of oxidation was determined by a thermobalance; the results indicate that the rate of oxidation is controlled at the gas-melt interface with an activation energy of 25 ± 2 kcal/mole. A mechanism for the oxidation reaction, involving the intermediate gaseous compound SbO, is proposed and a rate expression has been derived therefrom; rates calculated from this expression are fully in accord with those determined experimentally.