Temperature Coefficient Of Surface Tension Research Articles

Dynamic surface tension measurements on a molten metal-oxygen system: The behaviour of the temperature coefficient of the surface tension of molten tin

In order to point out the interactions of oxygen with a liquid metal and to study the influence of the actual operating conditions, dynamic surface tension measurements of a liquid test metal (tin), were performed under vacuum conditions by using the large drop method. This classical method has been improved by applying a new experimental procedure which allowed to obtain reliable surface tension measurements at high temperature as a function of time and varying the oxygen content. Further, complementary information on molten metal-oxygen interactions can be obtained. In particular, in this work, the trend of the surface tension temperature coefficient has been analysed as a function of different operative parameters, highlighting some crucial points such as the dependence of the temperature coefficient on the accuracy of the surface tension experimental data and the influence of the dissolved oxygen. It was demonstrated that the surface tension and its temperature coefficient do not depend on the quantity of dissolved oxygen when this is inside a certain range of values.

Sensitivity analyses of the thermophysical properties of silicon melt and crystal

A set of global numerical simulations based on a simple, laminar, axisymmetric and pseudo steady model of a small silicon CZ furnace was conducted to reveal the influences of the thermophysical properties of the melt and crystal on the non-dimensional crystal pulling rate, i.e., the Peclet number Pe, and the deflection of the melt/crystal interface Δz, for the sensitivity analyses of the properties. The properties investigated here are the temperature coefficient of surface tension, viscosity, thermal conductivity, the thermal expansion coefficient and emissivity of the melt, and the thermal conductivity and emissivity of the crystal. The results demonstrated that, concerning the thermophysical properties of the melt, emissivity is relatively sensitive to Pe and Δz. Concerning the crystal properties, thermal conductivity is more sensitive to Pe, while emissivity is more sensitive to Δz.

Application of a Front Tracking Method in Gas Metal Arc Welding (GMAW) Simulation

A numerical model is developed to simulate the short-circuiting metal transfer process during gas metal arc welding (GMAW). The energy equation and the Marangoni convection are considered for the first time in analyzing the short-circuiting time. A front-tracking free surface method explicity tracks the profile of the liquid bridge. The electromagnetic field, distribution of velocity, pressure, and temperature are calculated using the developed model. Effects of welding current, surface tension temperature coefficient, and initial drop volume on short-circuiting duration time are examined. The results show that both the electromagnetic force and Marangoni shear stress play significant roles in short-circuiting transfer welding.

Effects of temperature coefficient of surface tension on oxygen transport in a small silicon Cz furnace

In order to understand the effects of temperature coefficient of surface tension ( γ T) on oxygen transport as well as on the heater power and the melt/crystal interface shape in a small silicon Czochralski furnace, a set of global numerical simulations is conducted using the finite-element method for a wide range of γ T between 0 and 0.35×10 −3 N/m K. The results for cases without rotations of crystal and crucible indicate that the larger Marangoni effect enhances a toroidal roll cell in the crucible and reduces the heater power and oxygen concentration in the crystal but makes the melt/crystal interface more convex toward melt. When the crystal and the crucible are rotating in counter directions, an upwelling flow near the axis from the bottom of the crucible takes important role in determining the radial distributions of oxygen concentration. γ T gives significant effects on the flow pattern, oxygen concentration, heater power and interface shape.

Motion of droplets induced by the Marangoni force on a wall with a temperature gradient

AbstractMotion of silicone oil and water droplets induced by the Marangoni force was numerically simulated by using two‐ and three‐dimensional second‐order finite difference methods with the CIP and the level set methods. The surface tension was introduced by the continuum surface force (CSF) method. The results clearly showed the flow induced by the Marangoni force and the dependence of droplet velocity on droplet size, contact angle, temperature gradient, and fluid properties. The Marangoni force balanced with the viscous force in the small contact angle case; on the other hand, in the large contact angle case, it balanced with the normal component of surface tension. As for the effect of fluid properties on droplet motion, the temperature coefficient of surface tension had a much larger effect than did viscosity, thermal diffusivity, or surface tension. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(2): 81–93, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20004

Effect of oxygen partial pressure on silicon single crystal growth by floating zone technique: surface oxidation and Marangoni flow

AbstractSilicon single crystals were grown by the floating‐zone method using an infrared image furnace in the wide range of oxygen partial pressure defined at the inlet of the furnace from 1×10−2Pa to 8.2×102Pa (Po2surface = 5.3 × 10−24Pa to 3.6 × 10−14Pa), so that the Marangoni number was changed from 2070 to 616. Degree of surface oxidation of the grown crystal was dependent on oxygen partial pressure of an ambient atmosphere. Striation pattern in almost all crystal shows a single frequency. At Po2inlet = 4.9 × 102Pa (Po2surface = 1.3 × 10−14Pa: imaginary Marangoni number of 700) precipitation of SiO2 was observed at the melt surface. At Po2inlet = 8.2 × 102Pa (Po2surface = 3.6 × 10−14Pa: imaginary Marangoni number of 616), which is over the equilibrium oxygen partial pressure for a SiO2 phase, the silicon specimen was polycrystallized and showed no growth striation. Temperature coefficient of surface tension |‐∂σ/∂T| less than 0.25 × 10−3 N/m‐K is not realistic, although many small values have been reported.

Density, viscosity and surface tension of 50RO–50P 2O 5 (R: Mg, Ca, Sr, Ba, and Zn) glass melts

The density, surface tension and viscosity of the 50RO–50P 2O 5 (R: Mg, Ca, Sr, Ba and Zn) glass melts have been measured over the range, 1073–1623 K. The effects of R cations on these properties have been investigated. The density of the melt was found to increase in the order, R: Mg < Ca < Zn < Sr < Ba, with increasing molar weight of cation. The surface tension in the temperature range of 1373–1473 K increased approximately with cation in the order, R: Zn < Ba < Mg < Ca < Sr. The viscosity and the negative, temperature coefficient of surface tension increased in the order, R: Ba < Sr < Ca < Zn < Mg. All melts exhibited negative temperature coefficients of surface tension. The effect of Mg and Zn cations on the properties were different to that for Ba, Sr, and Ca cations and this is discussed using bulk glass data published in a previous report. The features of Mg and Zn metaphosphate glass melts, that is high values of viscosity, and temperature coefficient of surface tension, are related to the small Oxygen Coordination Number of the cations (=4) when compared with those of Ca, Sr, Ba metaphosphate glass melts.

The Surface Tension of Melts of Aluminum–Indium Binary System

The temperature and concentration dependences of the surface tension (ST) of alloys of the Al–In system are investigated by the sessile drop method. It is shown that small (up to 0.6 at. %) additions of indium significantly lower the ST of aluminum, and the temperature coefficients of ST of the investigated alloys have positive values in this range of compositions. The obtained data are used to calculate the adsorption of indium (according to Guggenheim–Adam, N option) and the number of its monolayers (according to Rusanov) in the surface layer of Al–In solutions. It follows from these data that the adsorption of indium on the melt surface reaches the maximal value with a bulk content of indium of about 0.1 at. %, and the excess of indium in the surface layer corresponds to three monolayers of indium.

A unified numerical modeling of stationary tungsten-inert-gas welding process

In order to clarify the formative mechanism of weld penetration in an arc welding process, the development of a numerical model of the process is quite useful for understanding quantitative values of the balances of mass, energy, and force in the welding phenomena because there is still lack of experimentally understanding of the quantitative values of them because of the existence of complicated interactive phenomena between the arc plasma and the weld pool. The present article is focused on a stationary tungsten-inert-gas (TIG) welding process for simplification, but the whole region of TIG arc welding, namely, tungsten cathode, arc plasma, workpiece, and weld pool is treated in a unified numerical model, taking into account the close interaction between the arc plasma and the weld pool. Calculations in a steady state are made for stationary TIG welding in an argon atmosphere at a current of 150 A. The anode is assumed to be a stainless steel, SUS304, with its negative temperature coefficient of surface tension. The two-dimensional distributions of temperature and velocity in the whole region of TIG welding process are predicted. The weld-penetration geometry is also predicted. Furthermore, quantitative values of the energy balance for the various plasma and electrode regions are given. The predicted temperatures of the arc plasma and the tungsten-cathode surface are in good agreement with the experiments. There is also approximate agreement of the weld shape with experiment, although there is a difference between the calculated and experimental volumes of the weld. The calculated convective flow in the weld pool is mainly dominated by the drag force of the cathode jet and the Marangoni force as compared with the other two driving forces, namely, the buoyancy force and the electromagnetic force.

Effects of Antimony on the Surface Tension of Molten Silicon

The effect of antimony concentration (CSb/mass%) on the surface tension of molten silicon has been determined with the sessile drop method in the temperature range from 1693 to 1773 K and in the range of the oxygen partial pressure, Po2, in an Ar atmosphere from 10−23 to 10−21 MPa. The results show that the surface tension of molten silicon decreases with increasing Sb concentration in the range of CSb<0.9 mass%, which indicates positive adsorption of Sb in molten silicon and can be fairly described with the Szyszkowski's equation. The maximum decrease rate of surface tension is about 65 mN m−1 (mass% CSb)−1, and the temperature coefficient of surface tension, (∂σ/∂T)CSb, increases with increasing CSb. The evaporation of the systems was only observed between the melting points of antimony (904 K) and silicon (1683 K), and the surface tension presents no dependence on measuring time above the melting point of silicon.

Surface Tension and Its Temperature Coefficient of Molten Silicon at Different Oxygen Potentials

Previous investigations on the effects of temperature and impurities on the surface tension of molten silicon, and relevant measurement methods have been reviewed, and the influence of oxygen partial pressure (PO2) in the atmosphere has been analyzed emphatically, on the basis of the results obtained by the sessile drop method and calculations. In the case of PO2 ≤ PO2,sat (the saturated oxygen partial pressure in the Si(l)−O2(g)−SiO2(s) system), the surface tension first remains almost constant and then decreases remarkably with the increase of PO2, the temperature coefficient of surface tension (∂σ/∂T) is negative and increases with the oxygen partial pressure, and the molten silicon drop is very sensitive to outside vibrations. However, in the case of PO2 > PO2,sat, the surface tension increases slightly with the oxygen partial pressure, ∂σ/∂T is higher and also increases with PO2, the molten silicon drop is not influenced by environmental disturbances and remains stable, and EPMA (electron probe microanalyzer) analysis indicates the formation of a thin SiO2(s) film on the surface of the molten silicon drop which might account for the surface tension increase.

Surface Tension and Wettability of Liquid Fe-16 mass%Cr-O Alloy with Alumina

The surface tension and wettability of liquid Fe-16 mass%Cr-S alloy with alumina substrate at 1823 K and the temperature dependence of surface tension of liquid Fe-16 mass% Cr-S alloy in the temperature range of 1808-1883 K were measured using the sessile drop technique. The surface tension and contact angle of liquid Fe-16 mass%Cr-S alloys with alumina substrate decreased markedly with increasing sulphur concentration in the alloys. The variation of surface tension of liquid Fe-16 mass% Cr-S alloys with sulphur activity can be described by the following equation: σ 1g = 1640 - 182 ln(1 + 157a s ) (mass% O=0.0037-0.0075, mass% S ≤ 0.195) (mN/m). The interfacial tension between liquid Fe-16 mass% Cr-S alloys and alumina substrate, calculated using Young's equation, can be expressed by the following equation: σs l = 2170 - 220 ln(1 + 237a S ) (mass% O=0.0037-0.0075, mass% S ≤ 0.195) (mN/m). The work of adhesion between liquid Fe-16 mass% Cr-S alloys and alumina had a tendency to increase with increasing sulphur concentration. The temperature coefficient of surface tension, dσ/dT, for Fe-16 mass% Cr-S system in the temperature range of 1808-1883 K increased with increasing sulphur concentration, and changed from negative to positive value when the sulphur concentration exceeded 20 mass ppm.

Numerical analysis of the competitive influence of Marangoni flow and evaporation on heat surface temperature and molten pool shape in laser surface remelting

A one-domain mixture continuum model is introduced to simulate numerically solid/liquid phase transformation with a mushy region in laser surface remelting process of a type 304 stainless steel. Emphasis is given to the competitive influence of laser-induced alloying element vaporization and Marangoni flow on the heating surface maximum temperature and its distribution as well as the molten pool shapes. The molten pool shapes and fluid flow, the temperature distribution and its peak values on the heating surface have been computed for six calculation cases corresponding to six different pool-surface heat flux balances. The results show that the Langmuir-type vaporization heat loss due to Fe, Mn, Cr, Ni elements can significantly reduce the heating surface peak temperature and the pool profile, while |∂ σ/∂ T| is small or the buoyancy force is considered as one and only driving force. However, when vaporization-type heat loss and Marangoni flow are coexisting, the free surface temperature distribution and its peak value are markedly affected by the magnitude order of surface tension gradient and the nature of the relationship between surface tension temperature coefficient and temperature. When |∂ σ/∂ T|>3.0×10 −4 N/m K, the influence of Langmuir-type vaporization heat loss is very small and can be ignored.

Thermocapillary migration of long bubbles in polygonal tubes. I. Theory

Thermocapillary migration of long gas bubbles in cylinders of regular-polygonal or rectangular cross sections is studied. An imposed axial temperature gradient produces a gradient of surface tension leading to a steady migration of the bubble towards the hotter region. A leading order approximation for the bubble migration speed is found by computing the volume flux of liquid through the corner regions of the cylinder, which provide a parallel channel for the flow of fluid driven by the Marangoni stress. A global mass balance is used to relate the dimensionless bubble speed to the modified capillary number Δσ*=γTβa/σ, where β is the temperature gradient, a the tube length scale, σ the mean surface tension, and γT the temperature coefficient of surface tension. The dimensionless bubble speed is found to be linear in this parameter at leading order. The approximation is improved by accounting for the deposition of a thin film on the cylinder walls at small capillary number. A modified Landau–Levich equation governs the thin film profile, the solution of which allows the calculation of the additional flux so produced. It is found that corrections in the bubble velocity are nonlinear in Δσ*. For regular-polygonal tubes with small numbers of sides or low aspect ratio rectangular cross sections, most of the flux passes through the corner regions, while for larger numbers of sides or large aspect ratios, flow in the thin film regions dominates and the results tend toward those for cylindrical tubes.

Effect of Oxygen on Thermocapillary Convection in a Molten Silicon Column under Microgravity

X-ray flow visualization in a half-zone molten silicon bridge was carried out under microgravity at a variety of oxygen partial pressures in an ambient atmosphere. The flow velocity of thermocapillary convection was found to decrease with increased oxygen partial pressure. Thermocapillary flow stabilized when the oxygen partial pressure at the inlet was increased to MPa. The dependence of the flow velocity and flow mode on can be explained in terms of the decrease in the temperature coefficient of surface tension due to the increase in oxygen partial pressure. © 2001 The Electrochemical Society. All rights reserved.

Surface effects and flow conditions in small volume melts with varying sulphur content

The surface effects and flow behaviour in melts with a volume of a few cubic millimetres were investigated using 1 mm thick X5CrNi18‐9 (AISI 304) stainless steel strips after partial remelting by a TIG (tungsten inert gas) burner. In the industrially produced material the S mass content was varied between 20 and 100 ppm. The surface excess of sulphur indicates that the surface saturation was not achieved compared to the values in the Fe‐S system. The thickness of the layer with high sulphur enrichment depends on the S activity and varied between approximately 260 and 460 nm and achieves the bulk S content at a distance of approximately 1.2 μm from the surface. This layer is noticeably thinner than the diffusion boundary layer and considerably thinner than the flow boundary layer. The topography of the rapidly solidified liquid pool makes it possible, taking previously estimated temperature coefficients of surface tension into account, to explain the flow behaviour in the melt with regard to the S content and to the temperature gradients. The results obtained indicate that the shearing force caused by surface tension gradients (Marangoni effect) controls the flow conditions in small volume melts.

The effect of oxygen on the temperature fluctuation of Marangoni convection in a molten silicon bridge

Temperature fluctuations in a half-zone liquid bridge of molten silicon were measured under precisely controlled oxygen partial pressure in the ambient atmosphere. A transition from a mode with non-periodic fluctuations in temperature to one with periodic fluctuations occurred when the oxygen partial pressure at the inlet was increased from 3.5×10 −7 to 1.8×10 −5 MPa. The transition indicates that the absolute temperature coefficient of surface tension decreases with increasing oxygen partial pressure at the silicon surface.

A Monte Carlo simulation on surface tension of liquid nickel

Surface tensions of liquid metals are of particular importance in analysing and understanding many of metallurgical and processing operations. With the development of powerful computer simulation techniques, molecular simulation method provides a possible way to obtain reliable thermophysical properties of metals. In the present contribution, we concern ourselves with the application of the Monte Carlo (MC) method and the embedded-atom method (EAM) to calculate the surface tension and temperature coefficient of surface tension of a liquid transition metal, namely nickel. The simulation of surface tension is performed through the calculation of cohesive work of the metal. The results are compared with some of the existing experimental data. It shows that the Monte Carlo simulation in conjunction with an effective potential function derived from EAM provide a possible way of obtaining surface tension of transition metals.

Thermocapillary migration of long bubbles in cylindrical capillary tubes

We consider the problem of the migration of a long bubble in a tube with a prescribed axial temperature gradient. The resulting thermocapillary stress moves the bubble toward hotter regions and we are interested in determining the speed of the bubble. Assuming small Peclet, Reynolds, Bond, and capillary numbers, Ca allows the uncoupling of the temperature field from the flow field, the use of creeping flow and lubrication theory, the assumption of axisymmetry, and the use of matched expansions in Ca, respectively. The structure of the solution is that of a constant thickness film bounded by constant curvature cap regions, with transition layers in between. A modified Landau–Levich equation governing the film profile in the transition regions is solved numerically, establishing the relationship between the unknown film thickness and the unknown bubble speed. A global mass conservation relation is then used to complete the solution and relate the bubble speed to the thermophysical properties. The solution is a function of a single dimensionless parameter, Δσ*=γTβa/σ where β is the temperature gradient, a the tube radius, σ the mean surface tension, and γT the temperature coefficient of surface tension. It is found that the speed increases with the temperature gradient as expected, and has a nonlinear dependence on Δσ* that is ultimately connected with the nonlinearity of the fluid dynamics in the transition regions.

EFFECTS OF THERMOCAPILLARY CONVECTION ON MELTING WITHIN DROPLETS

A computational study of the effects of thermocapillary convection on melting of spherical droplets as a result of an incident uniform heat flux under zero gravity conditions is presented. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables, whereby the time-dependent continuity, momentum, and energy equations in the spherical coordinate system are solved. During the early periods of the melting process, conduction mode of heat transfer is dominant. As the thermocapillary convection strengthens due to the growth of the melt zone, faster melting on the side of the droplet is observed compared with the conduction-only case. Because of the slanted shape of the interface caused by the preferred melting on the surface, a new recirculating vortex is created that promotes melting within the droplet. For moderate Pr-number fluids, the molten zone increases rapidly along the surface and reaches the unheated side, thus producing a solid inner core. The effects of the Biot number and the change in the sign of the surface-tension temperature coefficient (partialdiff sigma/ partialdiff T) on the melting pattern are also investigated.