Effect of Marangoni Convection on Mass Transfer in Liquid Phase

Marangoni convection and its influence on the mass transter in the liquid phase were investigated. Marangoni convection was visualized using laser Schlieren technique, Orderly polygonal convection patterns and random interfacial turbulence were observed. The effect of Marangoni convection on the mass transfer rate was studied by desorbing ethanol from aqneous solution in the falling film. The experimental results show that Marangoni convection can speed up the surface real and enhance the mass transfer rate in the liquid phase.The liquid mass transfer coefficient can be enhanced by as much as 3 folds. The corresponding empirical correlations are given in terms of the mass transfer enhancement factor. Furthermore, in considering the Marangoni effect, the conventional mass transfer correlation was modified, The differences between the values predicted by the correlation and the experimental data are within ±8.2% and the average difference is 4.2%.

Buoyant Marangoni convection of nanofluids in square cavity

The buoyant Marangoni convection heat transfer in a differentially heated cavity is numerically studied. The cavity is filled with water-Ag, water-Cu, water-Al2O3, and water-TiO2 nanofiuids. The governing equations are based on the equations involving the stream function, vorticity, and temperature. The dimensionless forms of the governing equations are solved by the finite difference （FD） scheme consisting of the alternating direction implicit （ADI） method and the tri-diagonal matrix algorithm （TDMA）. It is found that the increase in the nanoparticle concentration leads to the decrease in the flow rates in the secondary cells when the convective thermocapillary and the buoyancy force have similar strength. A critical Marangoni number exists, below which increasing the Marangoni number decreases the average Nusselt number, and above which increasing the Marangoni number increases the average Nusselt number. The nanoparticles play a crucial role in the critical Marangoni number.

Bio-Marangoni convection flow of Casson nanoliquid through a porous medium in the presence of chemically reactive activation energy

Bioconvection research is primarily focused on the augmentation of energy and mass species,which has implications in the processes intensification,mechanical,civil,electronics,and chemical engineering branches.Advanced bioconvection technology sectors include cooling systems for electronic devices,building insulation,and geothermal nuclear waste disposal.Hence,the present investigation is mainly discoursing the impact of Marangoni convention Casson nanoliquid flow under gyrotactic microorganisms over the porous sheet.The partial differential equations(PDEs)are re-structured into ordinary differential equations(ODEs)via suitable similar variables.These ODEs are numerically solved with the help of the spectral relaxation method(SRM).The numerical outcomes are illustrated graphically for various parameters over velocity,temperature,concentration,and bioconvection profiles.Three-dimensional(3 D)views of important engineering parameters are illustrated for various parameters.The velocity of the Casson nanoliquid increases with increasing the Marangoni parameter but decreases against higher porosity parameter.The surface drag force enhances for enhancement in the Marangoni number.The rate of mass transmission is higher for reaction rate constraint but diminishes for activation energy parameter.The higher radiative values augment the rate of heat transmission.

Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.

3D multiphase flow simulation of Marangoni convection on reactive absorption of CO_(2) by monoethanolamine in microchannel

A multiphase flow 3D numerical simulation method employing the coupled volume of fluid(VOF)and level set model is established to study the reactive absorption of CO_(2)by the monoethanolamine(MEA)aqueous solution in a falling film microchannel.Based on the flow-reaction-mass transfer model of the MEA-CO_(2)system in the falling film microchannel,the enhancement effect of the Marangoni convection in this reactive absorption process is analyzed.The enhancement factor of the Marangoni convection obtained in this work is in good agreement with experimental results in the literature.With consideration of the absorption ratio as well as the enhancement effect of the Marangoni convection,the influence of different MEA concentrations on absorption of CO_(2)is investigated.Furthermore,the appropriate MEA concentration for absorption enhanced by the Marangoni convection is acquired.

Heat transfer for Marangoni convection over a vapor-liquid interface due to an imposed temperature gradient

A similarity analysis for Marangoni convection induced flow over a vapor-liquid interface due to an imposed temperature gradient was carried out. The analysis assumes that the surface tension varies linearly with temperature but the temperature variation is a power law function of the location. The similarity solutions are presented numerically and the associated transfer characteristics are discussed.

Simulation of interfacial Marangoni convection in gas-liquid mass transfer by lattice Boltzmann method

Interfacial Marangoni convection has signifi-cant effect on gas-liquid and/or liquid-liquid mass transfer processes.In this paper,an approach based on lattice Boltzmann method is established and two perturbation models,fixed perturbation model and self-renewable interface model,are proposed for the simulation of interfacial Marangoni convection in gas-liquid mass transfer process.The simulation results show that the concentration contours are well consistent with the typical roll cell convection patterns obtained experimentally in previous studies.

硅酸铋(Bi_(12)SiO_(20))熔体中Marangoni对流的实时观察研究

The convection in melt crystal growth influences the crystal integrity deeply.During space crystal growth,the buoyancy driven convection has been eliminated for the microgravity environment,therefroe,surface tension driven convection (Marangoni Convection) become the main convection form.But the Marangoni convection forms,starting condition,development process and its influence on crystal growth are still unclear now.At the present time,Many studies focused on simulating liquid Marangoni convection or numerical simulation.However,few studies concerned on real melt,especially on oxide melt. In this paper,an in situ observation is carried out to study the start and development of Marangoni convection of Bi 12 SiO 20 melt in a 2mm diameter loop like platinum crucible.The different states of steady convection and the transition from steady to oscillatory convection are observed.The critical Marangoni number is obtained as 22433 and it agreed with a dependence Ma c=2884Pr 0.638 for high Prandtl number melt.The authors also obtained a dependence of convection oscillatory frequency on melt temperature.It increases with temperature rising.

Orientation-dependent Hydrodynamic Instabilities from Chemo-Marangoni Cells to Large Scale Interfacial Deformations

The interplay between chemistry and interfacial-tension-driven hydrodynamic instabilities has been studied experimentally. The system on hand consists of two immiscible liquids separated along an initially plane interface at which an interfacial reaction takes place to produce in situ a surfactant. It is identified that the dynamics of the system depends on the orientation of the Hele-Shaw cell with respect to the vector of gravity. If the nele-Shaw cell is placed vertically, Marangoni cells with vigorous convection develop in both phases along a nearly planar interface. However, if the Hele-Shaw cell is tilted off the gravity, the instabilities in the system are characterized by the large scale interracial deformation with a spatio-temporal periodicity together with the chemo-Marangoni convection. The focus is on the exploration of the transition from the cellular mode to the large scale interfacial deformation.

Numerical Simulation of the Marangoni Effect with Interphase Mass Transfer Between Two Planar Liquid Layers

The Marangoni effect induced by mass transfer at the interface between two immiscible liquids displays important influence on laboratory and industrial operation of solvent extraction. A systematic numerical study of the two-dimensional Marangoni effect in a two liquid layer system was conducted. The linear relationship of the inter- facial tension versus the solute concentration was incorporated into a mathematical model accounting for liquid flow and mass transfer in both phases. The typical cases analyzed by Sternling ＆ Scriven （AIChE J., 1959） using the linear instability theory were simulated bv the finite difference method and good agreement between the theory and the numerical simulation was observed. The simulation suggests that the Marangoni convection needs certain time to develop sufficiently in strength and scale to enhance the interphase mass transfer, the Marangoni effect is dynamic and transient, and remains at some stabilized level as long as the mass transfer driving force is kept con- stant. When certain level of shear is imposed at the interface as in most cases of practical significance, the Maran- goni effect is suppressed slightly but progressively as the shear is increased gradually. The present two-dimensional simulation of the Marangoni effect provides some insight into the underlying mechanism and also the basis for further theoretical study of the three-dimensional Marangoni effect in the real world and in chemical engineering applications.

MHD and Viscous Dissipation Effects in Marangoni Mixed Flow of a Nanofluid over an Inclined Plate in the Presence of Ohmic Heating

The problem of Marangoni mixed convection in the presence of an inclined magnetic field with uniform strength in a nanofluid(formed by the dispersion of two metallic nanoparticles,i.e.,Copper(Cu),and alumina(Al_(2)O_(3))in water)is addressed numerically.The effects of viscous dissipation and Ohmic heating are also considered.The original set of governing partial differential equations is reduced to a set of non-linear coupled ordinary differential equations employing the similarity transformation technique.The simplified equations are numerically solved through MATLAB‘bvp4c’algorithm.The results are presented in terms of graphs for several parameters.It is found that enhancing the stratification parameter leads to a decrease in the fluid temperature,and an increase in the aligned magnetic field angle reduces the flow velocity.Moreover,mixed convection tends to enhance both the Nusselt and Sherwood numbers.If the angle of inclination is made higher,the fluid velocity is reduced and the thickness of the thermal and concentration boundary layer grows.

Time Dependant Weld Shape in Ar-O_2 Shielded Stationary GTA Welding

The stationary gas tungsten arc welding （GTA） is carried out on SUS304 stainless steel under Ar-0.1%O2 and Ar-0.3%O2 mixed shielding to observe the evolution of the molten pool and investigate the role of Marangoni convection on the weld shape. After welding, the oxygen content in the weld metal was measured by using an oxygen/nitrogen analyzer. Small addition of oxygen to the argon based shielding gas can effectively adjust the weld pool oxygen content. Oxygen plays an important role as an surface active element in determining the pattern of Marangoni convection in the stainless steel weld pool. When the weld metal oxygen content is over the critical value, 0.01 wt pct, corresponding to the Ar-0.3%O2 mixed shielding gas, the Marangoni convection changes from outward to inward direction and the weld shape dramatically changes from wide shallow shape to narrow deep shape.

Local corrosion mechanism of SiO2-based refractories caused by slag movement near solid–liquid–gas interface in different slag systems

Slag movement on SiO2-based prism refractories in different slag systems was observed. The cross section shape evolution mechanism was discussed. Two types of shape evolution appear. For PbO-SiO2 slag whose surface tension improves with SiO2 concentration, slag film flows up along four edges under axial Marangoni shear force and wettability. Then, it flows down along four lateral faces under gravity. Corrosion rate at edges is larger than that on lateral faces due to different SiO2 solubilities of ascending and descending flow. Prism cross section shape changes from square to round. For FetO-SiO2 slag whose surface tension reduces with the increase of SiO2 concentration, slag film flows up under the inflence of wettability. Then, it flows down under Marangoni shear force and gravity. Compared to four edges, slag is mainly up and down on four lateral faces due to larger surface tension and size. So, prism cross section shape keeps square.

Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations

A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a genera/analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.

Effect of Welding Parameters on GTA Weld Shape for Pure Iron Plate under Ar-O_2 Mixed Shielding

Weld shape variation for different welding parameters is investigated on pure iron plate under gas tungsten arc （GTA） welding with argon-oxygen mixed shielding. Results showed that small addition of oxygen to the argon base shielding gas can effectively adjust the oxygen adsorption to the molten pool. An inward Marangoni convection occurs on the pool surface when the oxygen content in the weld pool is over the critical value, 80×10^-6, for pure iron plate under Ar-0.3%O2 mixed shielding. Low oxygen content in the weld pool changes the inward Marangoni to an outward direction under the Ar-0.1%O2 shielding. The GTA weld shape depends to a large extent on the pattern and strength of the Marangoni convection on the pool surface, which is determined by the content of surface active element, oxygen, in the weld pool and the welding parameters. The strength of the Marangoni convection on the liquid pool is a product of the temperature coefficient of the surface tension （dσ/dT） and the temperature gradient （dT/dr） on the pool surface. Different welding parameters will change the temperature distribution and gradient on the pool surface, and therefore, affect the strength of Marangoni convection and the weld shape.

Similarity Solution for Convection Heat Transfer Due to Marangoni Flow over a Flat Surface

Marangoni convection occurs along any liquid vapor interface that has a surface tension gradient. The surface tension gradient can result from either temperature or concentration gradients along the surface. Marangoni convection is of importance in crystal growth melts and during boiling as it influences the flow around the vapor bubbles. The influence of Marangoni induced convection is more obvious under microgravity but also occurs in earth gravity. This paper presents a similarity solution for Marangoni induced flow for both the velocity and temperature profiles, assuming developing boundary layer flow along a surface with various imposed temperature profiles. The surface velocity, the total flow rate, and the heat transfer characteristics are given for various temperature profiles and various Prandtl numbers. Since the predicted boundary layer thickness would be much less than the diameter of vapor bubbles during nucleate boiling, the bubble surface curvature effects can be neglected and this analysis can also be used as a first estimate of the effect of Marangoni flow around a vapor bubble.

Principles Giving High Penetration under the Double Shielded TIG Process

A new welding method named double shielded tungsten inert gas （TIG） has been developed to improve the TIG weld penetration. The main principles to increase the weld depth have been discussed. Results show that the critical oxygen content in the weld pool is around 100 × 10 -6 as the temperature coefficient of surface tension changes from negative to positive. The tracer test using pure silver shows that the direction of Marangoni convection changes as the oxygen content increases in the weld pool. The effect of arc constriction on the weld depth has been evaluated on a water-cooled copper plate, and the result indicates that the torch of double shielded can give a more powerful arc. Heavy oxide on the pool surface has undesirable impacts on the increasing of weld depth as the oxygen excessively accumulates in weld pool. It is possible to form chromium oxide in the weld process, while the iron oxide may form as the weld surface exposes to the air after the shielded gas moving away.

Weld Shape Variation and Electrode Oxidation Behavior under Ar-(Ar-CO_2) Double Shielded GTA Welding

Double shielded gas tungsten arc welding （GTAW, also known as tungsten inert gas （TIG） welding） of an SUS304 stainless steel with pure inert argon as the inner layer shielding and the At-CO2 or CO2 active gas as the out layer shielding was proposed in this study to investigate its effect on the tungsten electrode protection and the weld shape variation. The experimental results showed that the inner inert argon gas can successfully prevent the outer layer active gas from contacting and oxidizing the tungsten electrode during the welding process. Active gas, carbon dioxide, in the outer layer shielding is decomposed in the arc and dissolves in the liquid pool, which effectively adjusts the active element, oxygen, content in the weld metal. When the weld metal oxygen content is over 70×10-6, the surface-tension induced Marangoni convection changes from outward into inward, and the weld shape varies from a wide shallow one to a narrow deep one. The effect of the inner layer gas flow rate on the weld bead morphology and the weld shape was investigated systematically. The results show that when the flow rate of the inner argon shielding gas is too low, the weld bead is easily oxidized and the weld shape is wide and shallow. A heavy continuous oxide layer on the liquid pool is a barrier to the liquid pool movement.

Growth of Czochralski silicon under magnetic field

Growth of Czochralski (CZ) silicon crystals under the magnetic field induced by a cusp-shaped permanent magnet of NdFeB has been investigated. It is found that the mass transport in silicon melt was controlled by its diffusion while the magnetic intensity at the edge of a crucible was over 0.15 T. In comparison with the growth of conventional CZ silicon without magnetic field, the resistivity homogeneity of the CZ silicon under the magnetic field was improved. Furthermore, the Marangoni convection which has a significant influence on the control of oxygen concentration was observed on the surface of silicon melt. It is suggested that the crystal growth mechanism in magnetic field was similar to that in micro-gravity if a critical value was reached, named the growth of equivalent micro-gravity. The relationship of the equivalent micro-gravity and the magnetic intensity was derived as g=(v0/veff)g0. Finally, the orders of the equivalent micro-gravity corresponding to two crucibles with characteristic sizes were calculated.

Effect of Active Gas on Weld Shape and Microstructure of Advanced A-TIG-Welded Stainless Steel

Advanced A-TIG method was conducted to increase the weld penetration and compared with the conventional TIG welding process.A two-pipeline setup was designed to apply Ar ＋ CO_2 mixed gas as the outer layer,while pure argon was applied as the inner layer to prevent any consumption of the tungsten electrode.The results indicate that the presence of active gas in the molten pool led to the change in the temperature coefficient of surface tension so that the Marangoni convection turns inward and forms a deep weld zone.The increase in gas flow rate causes a decrease in the weld efficiency which is attributed to the increase in oxygen content in the weld pool and the formation o f a thicker oxide layer on the weld surface.Moreover,the stir and the temperature fluctuation,led by double shielding gas,create more homogeneous nucleation sites in the molten pool so that a fine grain micros true ture was obtained.