Star Formation in Magnetized, Turbulent and Rotating Molecular Cloud: The Critical Mass

In this paper, we present the critical mass of magnetized, turbulent and rotating star-forming molecular cloud core (MCc) in the presence of magnetic tension. The critical mass of star-forming magnetized cloud is influenced by the magnetic tension, magnetic pressure and other pressures. Applying the method of theoretical modelling by taking into account the basic equations and assumptions, we formulate the critical mass of magnetized MCc in different cases. Accordingly, the minimum critical masses we find in both cases are different. Energy due to magnetic tension significantly triggers the collapse at relatively larger radius of the core. The model shows that when the initial radius of the parent cloud (Ro) is larger than that of collapsing core radius (Rcore) the magnetic tension also has the larger radius of curvature, so it plays a significant role in supporting gravity to collapse the core. The results indicate gravity without magnetic tension may not overcome magnetic pressure, turbulence pressure and pressure due to rotation. This shows the critical mass of MCc for the collapse depends on the tension force that magnetic field lines apply on the envelope. We conclude that if there is magnetic pressure in star-forming MCc, there is also unavoidable magnetic tension, which triggers the collapse of the core. If there is no magnetic tension, the magnetized MCc needs relatively larger mass and higher density within the small size to collapse.

Calculation Model for Surface Tension of Slag Melt

Based on the coexistence theory of slag melt structure and Butler’s equation,a new calculation model has been proposed for the calculation of surface tension of slag melt.This model establishes a specific correlation between surface tension and mass action concentrations(activities) in the melt and on its surface on the basis of inner and surficial structures of slag melt.Calculated surface tensions of CaO-SiOand MnO-SiOslag melts are consistent with those measured.Furthermore,iso-surface tension lines of CaO-MnO-SiOslag melt have also been calculated.

Modeling bubble column reactor with the volume of fluid approach:Comparison of surface tension models

This work aims at comparing surface tension models in VOF(Volume of Fluid) modeling and investigating the effects of gas distributor and gas velocity. Hydrodynamics of a continuous chain of bubbles inside a bubble column reactor was simulated. The grid independence study was first conducted and a grid size of 1.0 mm was adopted in order to minimize the computing time without compromising the accuracy of the results. The predictions were validated by comparing the experimental studies reported in the literature. It was found that all surface tension models can describe the bubble rise and bubble plume in a column with slight deviations.

Prediction of surface and interfacial tension based on thermodynamic data and CALPHAD approach

In this article, following a brief introduction concerning experimental measurements of surface and interfacial tensions, methods for calculating surface tension and surface segregation for binary, ternary, and multicomponent high-temperature melts based on Bulter＇s original treatment [ 1] and on available physical properties and thermodynamic data, especially excess Gibbs free energies of bulk phase and surface phase versus temperature obtained from thermodynamic databases using the calculation of phase diagram （CALPHAD） approach, with special attention to the model parameter β, have been described. In addition, the geometric models can be extended to predict surface tensions of multicom- ponent systems from those of sub-binary systems. For illustration, some calculated examples, including Pb-free soldering systems and phase-diagram evaluation of binary alloys in nanoparticle systems are given. On the basis of surface tensions of high-temperature melts, interracial tensions between liquid alloy and molten slag as well as molten slag and molten matter can be calculated using the Girifalco-Good equation [2]. Modifications are suggested in the Nishizawa＇s model [3] for estimation of interracial tension in liquid metal （A）/ceramics （MX） systems so that the calculations can be carried out based on the sublattice model and thermodynamic data, without deliberately differentiating the phase of MX at high temperature. Finally, the derivation of an approximate expression for predicting interfacial tension between the high-temperature multicomponent melts, employing Becker＇s model [4] in conjunction with Bulter＇s equation and inteffacial tension data of the simple systems is described, and some examples concerning pyrometallurgical systems are given for better understanding.

Phase field investigation on the initial planar instability with surface tension anisotropy during directional solidification of binary alloys

Phase field investigation reveals that the stability of the planar interface is related to the anisotropic intensity of surface tension and the misorientation of preferred crystallographic orientation with respect to the heat flow direction. The large anisotropic intensity may compete to determine the stability of the planar interface. The destabilizing effect or the stabilizing effect depends on the misorientation. Moreover, the interface morphology of initial instability is also affected by the surface tension anisotropy.

Surface tension of lithium bromide aqueous solution/ammonia with additives and nano-particles

In order to investigate the effect of additives and nano-particle on the surface tensions of lithium bromide(Li Br) aqueous solution/ammonia, many experiments were carried out based on Wilhelmy plate method. Firstly, the surface tension of Li Br aqueous solution with 1-octanol was measured and then the comparison between the measured results and previous experimental results was given to verify the measuring accuracy. Some new additives, such as cationic surfactants cetyltrimethyl ammonium chloride(CTAC), and cetyltrimethyl ammonium bromide(CTAB) were chosen in the experiments. The experimental results show that CTAC and CTAB can obviously reduce the surface tension of Li Br aqueous solution/ammonia. In addition, it is found that nano-particles cannot remarkably decrease the surface tension of Li Br aqueous solution/ammonia. However, the mixed addition of additives and nano-particles can remarkably affect the surface tension of Li Br aqueous solution/ammonia. That is to say, additives play more important role in reducing the surface tension of Li Br aqueous solution/ammonia. But nano-particles may enhance the heat transfer in the absorption refrigeration process.

CALCULATION MODEL OF SURFACE TENSION FOR ALLOY MELTS

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SURFACE TENSION OF MOLTEN IF STEEL CONTAINING Ti AND ITS INTERFACIAL PROPERTIES WITH SOLID ALUMINA

Surface tension of molten IF steel containing Ti and contact angle between the liquid steel and solid alumina were measured with sessile droplet method under Ar gas atmosphere at 1500, 1575 and 1600°C. The results show that titanium decreases the surface tension of the molten IF steel and the contact angle. The interfacial tension between the molten IF steel containing Ti and solid alumina decreases with increase in titanium content. The work of adhesion between molten IF steel containing Ti and solid alumina decreases slightly at 1550°C, but increases at 1600°C with increasing titanium content. It can be deduced that fine bubbles and fine alumina inclusions are easily entrapped in solidifying interface for IF steel containing Ti.

Blast furnace ironmaking process with super high TiO_(2) in the slag:Density and surface tension of the slag

Aiming at the process of smelting ultra-high(>80%)or even full vanadium titanomagnetite in blast furnace,we are conducting a series of works on physics character of high TiO_(2) bearing blast furnace slag(BFS)for slag optimization.This work discussed the density and surface tension of high TiO_(2) bearing BFS using the Archimedean principle and the maximum bubble pressure method,respectively.The influence of TiO_(2) content and the MgO/CaO mass ratio on the density and surface tension of CaO-SiO_(2)-TiO_(2)-MgO-Al_(2)O_(3)slags were investigated Results indicated that the density of slags decreased with the TiO_(2) content increasing from 20wt%to 30wt%,but it increased slightly with the MgO/CaO mass ratio increasing from 0.32 to 0.73.In view of silicate network structure,the density and the degree of polymerization(DOP)of network structure have a consistent trend.The addition of TiO_(2) reduced(Q^(3))^(2)/(Q^(2)) ratio(Q^(2) and Q^(3) represent structural unit with bridge oxygen number of 2 and 3,respectively)and then decreased DOP,which led to the decrease of slag density.The surface tension of CaO-SiO_(2)-TiO_(2)-MgO-Al_(2)O_(3) slags decreased dramatically with the TiO_(2) content increasing from 20wt%to 30wt%.Conversely,it increased with the MgO/CaO mass ratio increasing from 0.32 to 0.73.Furthermore,the iso-surface tension lines were obtained under 1723 K using the Tanaka developed model in view of Butler formula.It may be useful for slag optimization of ultra-high proportion(>80%)or even full vanadium titanomagnetite under BF smelting.

Surface tension of liquid Au-Bi-Sn alloys

The surface tension of a promising lead-free solder Au-Bi-Sn alloys was investigated both by the sessile-drop method and calculation. Experimental measurements were carried out for two cross-sections with the constant gold to bismuth ration of 1:1 and 1:2. For all the investigated compositions, decrease of the surface tension is observed with increasing temperature. Meanwhile, the surface tension values were also calculated based on Butler’s equation, with using the newest research on thermodynamics data of Au-Bi-Sn ternary system. Compared with the experimental results, a good agreement was obtained.

Surface Tension Calculation of Undercooled Alloys

Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (x(Ni)=0.42) and Ni-Fe (x(Ni)=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys.

Surfactant Surface Tension Effects on Promoting Hydrate Formation: An Experimental Study Using Fluorocarbon Surfactant (Intechem-01) + SDS Composite Surfactant

The investigation of surface tension is a very important task for gas hydrate studying. Surfactants can effectively reduce the surface tension, improve the gas storage capability of hydrate and increase the formation rate, shorten the induction time. The objective of this study were to obtain a better understanding of the role of surface tension on hydrate formation and build gas hydrate models involve surfactant. In this study it was highlighted that the surface tension of Intechem-01 + SDS composite surfactants in natural gas hydrate promotion system and the change rules at different temperatures, concentration and proportion. According to the results of experiment, the surface tension of composite surfactants decreased with the increase of Intechem-01. The best cooperating effect was observed in proportion (Intechem-01 content) of 0.6 - 0.7, where the surface tension was the lowest. In this proportion range, the composite surfactants showed the same effect to pure fluorine carbon surfactant. The study shown the surface tension of composite surfactants decreased with the rise of temperature, and they were in a linear relationship within a certain range. Surface tension of composite surfactants decreased with the increase of surfactant concentration, however, it was no longer decreased above critical micelle concentration (CMC). The fitting equation of surface tension with various factors has been obtained.

A Simple Weighted Integration Method for Calculating Surface Tension Force to Suppress Parasitic Flow in the Level Set Approach

Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved method for calculating the surface tension based on the level set approach is proposed, in which the contribution of not only the center node but also the rest area of a control volume to the calculation of surface tension is considered in a balanced manner. The weighted integration method (WIM) is more consistent with the concept of a banded in- terface in the level set method. It is applied to the temporal evolution of a two-dimensional neutrally buoyant liquid drop and a buoyancy driven deformable bubble in an immiscible fluid for the validation of WIM. The results show that the parasitic flows are evidently suppressed by the weighted integration method. The weight factors for WIM in 3-D cases are also suggested.

The effect of anisotropic surface tension on the morphological stability of planar interface during directional solidification

This paper considers the effect of the anisotropic surface tension on the morphological stability of the planar interface during directional solidification. When the expression exhibiting the four-fold symmetry is included, the modified absolute stability criterion is obtained by employing the multi-variable expansion method. The linear stability analysis reveals that for the given temperature gradient, as the anisotropic surface tension parameter increases, the stability zone tends to decrease.

Surface Tension of Molten Ni and Ni-Co Alloys

Surface tension of molten Ni and Ni-Co (5 and 10 mass fraction) alloys was measured at the temperature range of 1773-1873 K using an improved sessile drop method with an alumina substrate in an Ar+3%H2 atmosphere. The error of the data obtained was analyzed. The surface tension of molten Ni and Ni-Co (5 and 10 mass fraction) alloys decreases with increasing temperature. The influence of Co on the surface tension of Ni-Co alloys is little in the studied Co concentration range.

Interactions of ferro-nanoparticles(hematite and magnetite) with reservoir sandstone: implications for surface adsorption and interfacial tension reduction

There are a few studies on the use of ferro-nanofluids for enhanced oil recovery,despite their magnetic properties;hence,it is needed to study the adsorption of iron oxide(Fe2 O3 and Fe3 O4) nanoparticles(NPs) on rock surfaces.This is important as the colloidal transport of NPs through the reservoir is subject to particle adsorption on the rock surface.Molecular dynamics simulation was used to determine the interfacial energy(strength) and adsorption of Fe2 O3 and Fe3 O4 nanofluids infused in reservoir sandstones.Fourier transform infrared spectroscopy and X-ray photon spectroscopy(XPS) were used to monitor interaction of silicate species with Fe2 O3 and Fe3 O4.The spectral changes show the variation of dominating silicate anions in the solution.Also,the XPS peaks for Si,C and Fe at 190,285 and 700 eV,respectively,are less distinct in the spectra of sandstone aged in the Fe3 O4 nanofluid,suggesting the intense adsorption of the Fe3 O4 with the crude oil.The measured IFT for brine/oil,Fe2 O3/oil and Fe3 O4/oil are 40,36.17 and 31 mN/m,respectively.Fe3 O4 infused with reservoir sandstone exhibits a higher silicate sorption capacity than Fe2 O3,due to their larger number of active surface sites and saturation magnetization,which accounts for the effectiveness of Fe3 O4 in reducing IFT.

Lattice Boltzmann simulation of liquid vapor system by incorporating a surface tension term

In this study, we investigate the pseudopotential multiphase model of lattice Boltzmann method（LBM） and incorporate a surface tension term to implement the particle interaction force. By using the Carnahan–Starling（CS） equation of state（EOS） with a proper critical pressure–density ratio, a density ratio over 160000 is obtained with satisfactory numerical stability. The added surface tension term offers a flexible choice to adjust the surface tension strength. Numerical tests of the Laplace rule are conducted, proving that smaller spurious velocity and better numerical stability can be acquired as the surface tension becomes stronger. Moreover, by wall adhesion and heterogeneous cavitation tests, the surface tension term shows its practical application in dealing with problems in which the surface tension plays an important role.

Modified surface tension model for free surface flow with single-phase lattice Boltzmann method

A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow.The computational efficiency and accuracy are both enhanced.The restriction to the relaxation factor （which needs to be smaller than 1） is circumvented by the new surface tension algebra,due to its rational physical nature compared with the treatment of Xing,Buther and Yang in their paper （Comp.Mater.Sci.,2007,39（2）：282-290）.The proposed stable surface tension scheme is applied to simulate the free deformation of a square droplet with surface tension effect and the process of a droplet impinging on a liquid film.The numerical solution for free deformation of a droplet agrees well with thermodynamic principles,and also achieves high accuracy in comparison with Xing,et al.＇s model.Three typical impinging modes are successfully obtained with the new scheme,and another particular mode found by Wang and Chen is also successfully simulated.The evolutions of liquid crown agree well with the power law related to time.

Size-dependent surface tension of a cylindrical nanobubble in liquid Ar

In view of the continued disputes on the fundamental question of whether the surface tension of a vapour bubble in liquid argon increases, or decreases, or remains unchanged with the increase of curvature radius, a cylindrical vapour bubble of argon is studied by molecular dynamics simulation in this paper instead of spherical vapour bubble so as to reduce the statistical error. So far, the surface tension of the cylindrical vapour bubble has not been studied by molecular dynamics simulation in the literature. Our results show that the surface tension decreases with radius increasing. By fitting the Tolman equation with our data, the Tolman length σ = -0.6225 sigma is given under cut-off radius 2.5σ, where σ = 0.3405 nm is the diameter of an argon atom. The Tolman length of Ar being negative is affirmed and the Tolman length of Ar being approximately zero given in the literature is negated, and it is pointed out that this error is attributed to the application of the inapplicable empirical equation of state and the neglect of the difference between surface tension and an equimolar surface.