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Marangoni convection is induced by the variation of surface tension along a free surface, which depends not only on temperature but also concentration. However, the onset of thermo-solutal Marangoni convection in a liquid bridge system is still unknown. Here, we perform a global linear stability analysis to determine the theoretical onset of the Marangoni convection occurring in the half-zone liquid bridge of the floating zone method of SixGe1−x crystal growth. The cylindrical liquid bridge is heated from the bottom and the highest Silicon concentration is on the top. The thermal and solutal Marangoni forces are in the same direction in this configuration. The stability diagram of the axisymmetric base flow is obtained by solving the large-scale eigenvalue problem using a Jacobian-free Arnoldi method. Oscillatory disturbance patterns appear with different azimuthal wavenumbers for unstable eigenmodes. The present linear stability analysis results explain our previous numerical simulation results.

The growth of high-quality InGaSb crystals by Vertical Gradient Freezing (VGF) under microgravity was numerically simulated. Machine learning tools were used to optimize the growth conditions. The study focuses on controlling growth interface shape which directly affects the quality and homogeneity of the grown crystals. Initially, Bayesian optimization was utilized to search for the most favorable growth conditions that promote a desirable flatter growth interface shape. Afterward, a reinforcement learning model was developed. The system was subjected to a lower temperature gradient near the feed crystal and to crucible rotation with a rate ranging according to the obtained optimal strategy. Results showed that the interface deformation is considerably reduced, and a flatter growth interface could be maintained. The growth rate and solute concentration uniformity were also improved. This adaptive control recipe proves to hold great potential in the continuous and rapid optimization of other crystal growth processes.

A three-dimensional numerical simulation study has been carried for the Top-Seeded Solution Growth (TSSG) process of single crystal SiC. During growth, Marangoni and forced convections (flows) develop in the growth solution due to free surface tension gradient and seed rotation, respectively. Relative contributions of such flows were numerically examined. Since supersaturation in the growth solution near the crystal surface is a key factor affecting the stability of crystal morphology, our study has focused on the influence of these flows on the distributions of spatial and temporal flow velocity and solution supersaturation. Simulation results show that the contribution of Marangoni convection gives rise to the development of spoke-like flow patterns and a downward flow below the seed crystal that leads to a non-uniform supersaturation distribution at the center and at the edge near the seed crystal surface. Additionally, a characteristic frequency associated with the supersaturation oscillation appears to be due to the Marangoni instability. Results also show that, although the forced convection induced by seed rotation may weaken such supersaturation non-uniformity in the center and suppress the development of such spoke-like patterns, its effect near the edge is not significant.

Previous numerical simulations carried out for the TSSG process of SiC crystal have shown that the downward flow developing in the melt under the seed crystal induces radial growth rate non-uniformity. In order to minimize the adverse effect of this flow, an adjoint-based sensitivity analysis was performed and an optimal crucible temperature condition was determined. The analysis at the initial state showed that the middle region of the crucible sidewall is the most sensitive region for the optimization of the objective functional. At the optimized state, growth rate uniformity is significantly improved without any reduction in growth rate. Furthermore, this optimized state is stable within a range of crucible temperature perturbations.

Marangoni convection driven by surface tension gradient plays an important role in nano-scale processes and also the processes under microgravity in space, where the effect of surface tension may become significant compared with that of the gravitational body force. For a better understanding of Marangoni convection occurring in a nano-scale process, Molecular Dynamics (MD) and Computational Fluid Dynamics (CFD) simulations were carried out for a thin liquid film with concentration gradient. The computed flow structures by these methods were compared. The results show quantitative differences in the magnitudes of the flow velocity and the deformation of the liquid film. It was also found that a stronger driving force would be needed to generate nano-scale flows compared with that required for macro-scale flows. This is due to the fact that a stronger surface force may be needed to overcome the random movements of molecules.

The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios A_s has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model of a liquid bridge between a cold (top plane) and a hot (bottom plane) disks. The highest Si concentration is on the top of the liquid bridge. The aspect ratio (A_s) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (Ma_TA_s, 論文

We have developed a reinforcement learning (RL) model to control the melt flow in the radio frequency (RF) top-seeded solution growth (TSSG) process for growing more uniform SiC crystals with a higher growth rate. In the study, the electromagnetic field (EM) strength is controlled by the RL model to weaken the influence of Marangoni convection. The RL model is trained through a two-dimensional (2D) numerical simulation of the TSSG process. As a result, the growth rate under the control of the RL model is improved significantly. The optimized RF-coil parameters based on the control strategy for the 2D melt flow are used in a three-dimensional (3D) numerical simulation for model validation, which predicts a higher and more uniform growth rate. It is shown that the present RL model can significantly reduce the development cost and offers a useful means of finding the optimal RF-coil parameters.

A series of three-dimensional numerical simulations considering the effect of radiative heat transfer on the free surface has been carried out to examine the characteristics of thermal-solutal Marangoni convection in a shallow rectangular cavity that is subjected to mutually perpendicular temperature and concentration gradients. In the simulation, the overall contributions of thermal and solutal Marangoni flows are in the same order (Marangoni ratio M a σ = 1 ) for all the cases considered, and the ambient temperature Θ a ranges from − 1.5 to 1.5, representing the transition from heat loss to heat gain in the whole system. Results show that with the increase of ambient temperature in the case of steady flow, the intensity of the thermal Marangoni effect decreases first, and then increases; furthermore, the flow structure, temperature, and concentration fields in the cavity are significantly affected by the radiative heat transfer on the free surface. When the Marangoni number exceeds a critical value, the flow stability is lost, and a three-dimensional oscillatory flow develops. The critical Marangoni number at which the flow destabilizes highly depends on thermal radiation and exhibits different variation tendencies on the stages of heat loss and gain. For the oscillatory flow, the observed wave patterns of temperature and concentration fluctuations are caused by the coupling effect of thermal-solutal Marangoni flow and radiative heat transfer. Two new types of oscillatory modes with different propagation directions appear in the cases of larger heat loss and gain due to the effect of thermal radiation. In addition, a sudden drop in the frequency is observed at a higher thermal Marangoni number.

A set of numerical simulations were conducted to investigate the effect of applied static magnetic field on the convective flows and carbon concentration in the Top-Seeded Solution Growth (TSSG) process of SiC. The applied magnetic field is considered as vertical and cusp in an axisymmetric configuration. Seed rotation was also included in the simulations. The numerical results show that the applications of VMF (vertical magnetic field) and weak CMF (cusp magnetic field) are effective in suppressing Marangoni convection. The application of VMF slows down growth rate but reduces the variation of growth rate towards a more constant rate. Seed rotation appears to be not beneficial in the presence of CMF alone. However, the combined effect of seed rotation with VMF enhances growth and makes the growth rate variation smaller.

The diffusion coefficient of GaSb in InSb melt was estimated by using the microgravity experimental results performed onboard the International Space Station (ISS), where the effect of natural convection is minimized. We numerically investigated the transport phenomena during InGaSb crystals growth via a vertical gradient freezing method and it was deduced that the growth rate is dominated by the solute diffusion in the melt. Furthermore, the crystal growth rate was well explained by adopting a diffusion coefficient with function of GaSb concentration, obtained by analyzing the available experimental results and utilizing machine learning and Bayesian optimization methods. These results also contribute to further understanding of crystal growth on the ground.

A series of three-dimensional numerical simulations have been carried out to examine the characteristics of Marangoni convection in a shallow rectangular cavity that is subjected to a linear solutal boundary condition. For the working fluid, two Schmidt number values (moderate and high) ( S c = 10 and 100) are chosen. The computed flow velocity and concentration distributions show more unique and complex characteristics compared with those of previous studies used a constant solutal boundary condition. Results also indicate that the flow is steady at a relatively small solutal Marangoni number. The secondary vortices embedded in the liquid layer appear. Number of vortices develop greatly depends on the levels of selected solutal Marangoni and Schmidt numbers. When the solutal Marangoni number exceeds a critical value, the Marangoni flow losses its stability, and a three-dimensional oscillatory flow develops. For the oscillatory flow, compared with the case of constant boundary condition, although a backward transition from chaotic to oscillatory is observed with the use of linear boundary condition at a moderate Schmidt number, the disturbance energy of that is always weaker at the same Marangoni number levels. The evolution sequences of flow instabilities are related to the Schmidt number due to the occurrence of a secondary wave at a higher Schmidt number. In addition, the wave patterns undergo a series of evolutions, namely, expansion, separation, squeezing, and merging during propagation due to the effect of cavity boundaries. As a result, since the waves are confined within the rectangular cavity, the wave patterns of spline-like, horseshoe-like, and wedge-like develop in the domain.

A numerical simulation study of thermo-solutal Marangoni convection has been carried out in a full floating zone with radiative heat transfer under zero gravity. In this system, the thermal and solutal Marangoni flows develop in the same direction and/or opposite directions along the free surface depending on the location in the zone. In the model, the ambient temperature distribution along the zone is taken as a Gaussian profile, and the radiative heat transfer is considered dominant. The characteristics of the concentration pattern in the zone vary due to the varying thermal and solutal Marangoni numbers, as well as the characteristic azimuthal wave. The flow velocity field exhibits two or four main vortices along the free surface. These vortices get stronger at higher thermal Marangoni number values.

A numerical simulation study was carried out to examine the transport phenomena occurring during the Top-Seeded Solution Growth (TSSG) process of SiC. The simulation model includes the contributions of radiative and conductive heat transfer in the furnace, mass transfer and fluid flow in the melt, and the induced electric and magnetic fields. Results show that the induced Lorentz force is dominant in the melt compared with that of buoyancy. At the relatively low coil frequencies, the effect of the Lorentz force on the melt flow is significant, and the corresponding flow patterns loose their axisymmetry and become almost fully disturbed. However, at the relatively higher frequency values, the flow is steady and the flow patterns remain axisymmetric.

A global numerical simulation was performed for the induction heating Top-Seeded Solution Growth (TSSG) process of SiC. Analysis included the furnace and growth melt. The effects of interfacial force due to free surface tension gradient, the RF coil-induced electromagnetic body force, buoyancy, melt free surface deformation, and seed rotation were examined. The simulation results showed that the contributions of free surface tension gradient and the electromagnetic body force to the melt flow are significant. Marangoni convection affects the growth process adversely by making the melt flow downward in the region under the seed crystal. This downward flow reduces carbon flux into the seed and consequently lowers growth rate. The effects of free surface deformation and seed rotation, although positive, are not so significant compared with those of free surface tension gradient and the electromagnetic body force. Due to the small size of the melt the contribution of buoyancy is also small.

A numerical simulation study was carried out to investigate the effect of thermo-solutal Marangoni convection on the flow patterns and the azimuthal wave number ( m ) in a liquid bridge under zero-gravity. The liquid bridge in the model represents a three dimensional half-zone configuration of the Floating Zone (FZ) growth system. Three dimensional field equations of the liquid zone, i.e. continuity, momentum, energy, and diffusion equations, were solved by the PISO algorithm. The physical properties of the silicon-germanium melt were used ( Pr =6.37×10 −3 and Sc =14.0, where Pr and Sc stand for the Prandtl number and the Schmidt number). The aspect ratio Asp was set to 0.5 ( Asp = L / a , where L and a stand for the length of free surface and the radius of liquid bridge). Computations were performed using the open source software OpenFOAM. The numerical simulation results show that the co-existence of thermal and solutal Marangoni convections significantly affects the azimuthal wave number m in the liquid bridge.

Gas-liquid stirred tanks are widely used in various chemical engineering processes such as fermentation and pharmaceutical production. In the mixing process for fermentation, aerobic microbes produce high polymer compounds from oxygen and carbon sources which need to be supplied by agitation and aeration in a tank. It is essential to supply a sufficient and uniform amount of nutrients to provide high quality and quantity products, and hence, it is necessary to optimize the shape and operating conditions of the stirring tank to mix gas and materials in the liquid sufficiently and uniformly. However, it is difficult to obtain a guideline for the design of plant-scale tanks from laboratory-scale experiments because experimental measurements cannot provide the detailed distribution of materials. The present study aims to obtain a guideline for an optimized design by developing computational fluid dynamics (CFD) simulation of the gas-liquid two-phase flow in the stirred tank and investigating the mass transfer inside the stirred tank in detail. Applying k-ω shear stress transport (SST) model, we calculate the gas-liquid flow in the stirred tank and estimate overall gas hold-up in comparison with experimental data.

Accepted: 2018-04-27, 資料番号: SA1180029000

Summary Three numerical methods, namely, volume of fluid (VOF), simple coupled volume of fluid with level set (S-CLSVOF), and S-CLSVOF with the density-scaled balanced continuum surface force (CSF) model, have been incorporated into OpenFOAM source code and were validated for their accuracy for three cases: (i) an isothermal static case, (ii) isothermal dynamic cases, and (iii) non-isothermal dynamic cases with thermocapillary flow including dynamic interface deformation. Results have shown that the S-CLSVOF method gives accurate results in the test cases with mild computation conditions, and the S-CLSVOF technique with the density-scaled balanced CSF model leads to accurate results in the cases of large interface deformations and large density and viscosity ratios. These show that these high accuracy methods would be appropriate to obtain accurate predictions in multiphase flow systems with thermocapillary flows. Copyright © 2016 John Wiley & Sons, Ltd.

A series of three-dimensional numerical simulations have been carried out to examine the characteristics of thermal-solutal Marangoni convection in a rectangular cavity that is subjected to mutually perpendicular temperature and concentration gradients. In the simulations, the thermal Marangoni number MaT is selected as 0, 1, 3, and 7 × 104, but the solutal Marangoni number MaC is varied in order to be able to investigate the complex flow patterns and flow transitions. Results show that the flow is steady at relatively small MaC. Then, at this MaC value, we observe three types of steady flows as MaT increases, namely, a longitudinal surface flow, an oblique stripe flow, and a lateral surface flow. When MaC exceeds a critical value, the stability of the Marangoni flow is destroyed, and a three-dimensional oscillatory flow appears. For the oscillatory flow, the wave patterns of temperature and concentration fluctuations are highly dependent on the coupling of the thermal and solutal Marangoni effect. Two different propagation directions of wave patterns coexist on the free surface when the contributions of thermal and solutal flows are in the same order (i.e., MaC is approximately equal to MaT). In addition, a sudden drop in the wave frequency and a backward transition phenomenon from chaotic to oscillatory are also observed. For all the cases of the thermal Marangoni numbers, thermal-solutal Marangoni convection becomes chaotic at higher MaC values. The present study would provide more physical insights into industrial processes such as painting and drying.

In order to practically apply induced pluripotent stem (iPS) cells to regenerative medicine, a large amount of undifferentiated iPS cells should be produced by using an automated/scaled-up suspension culture system. However, in large-scale culture, oxygen supply to iPS cells away from the gas-liquid interface can be insufficient. In this numerical study, the oxygen supply performance is quantitatively evaluated by estimating the volumetric mass transfer coefficient of oxygen in the suspension culture of iPS cells. And, focusing on shaking culture, where shear stress that causes death or differentiation of iPS cells is relatively reduced, we compare two different shaking methods: one direction rotation (ODR) and periodic alternate rotation (PAR). The validity of the volumetric mass transfer coefficient calculation is confirmed by comparison with the experiment. The PAR method is superior to the ODR method in terms of oxygen supply because of higher turbulence intensities, but it is much less energy efficient than the ODR method. In the ODR method, the cell size is thought to be non-uniform since iPS cells are aggregated due to cell sedimentation. On the other hand, in the PAR method, cell sedimentation is suppressed by controlling the Froude number (Fr).

In x Ga1− x Sb is a ternary alloy with tunable properties. The wavelength of In x Ga1− x Sb can be varied in the range of 1.7– 6.8 μm, which is in the infrared (IR) region and makes that In x Ga1− x Sb can be used as a substrate for IR detector and thermophotovoltaic (TPV). The phase diagram reveals that there is a large temperature gap between liquidus and solidus lines, which leads to constitutional supercooling and the formation of crystal defects during the solidification process of InGaSb crystal. Moreover, convection caused by gravity will increase the inhomogeneity of transport in the liquid region near the crystal growth interface, which makes it quite difficult to grow In x Ga1− x Sb crystal. The convection will be restrained in microgravity environment, and thus, it is very beneficial for crystal growth. This article introduces the effect of microgravity on the growth of In x Ga1− x Sb crystal and the results of the space growth experiment of In x Ga1− x Sb ternary crystal with a high concentration of In in SJ10 recoverable scientific experimental satellite.

Numerical simulations of the thermo-solutal Marangoni convection developing in a Si–Ge liquid bridge of a floating-zone system have been performed under zero gravity. Half of the liquid bridge was considered as the three-dimensional (3D) computational domain. In this system, the solutal Marangoni convection develops in the direction opposite to the thermal Marangoni convection along the free surface in the bridge, i.e., the thermal Marangoni number, MaT, is negative and the solutal Marangoni number, MaC, is positive. Since the SiGe melt is a low-Prandtl number (Pr = 6.37 × 10−3) and high-Schmidt number (Sc = 14.0) liquid, the temperature field is almost independent of the convective flow and the concentration field determines the transport structures. When MaC is larger than −MaT, the concentration pattern is steady and two-dimensional (2D) axisymmetric. When MaC is smaller than −MaT, we predict two kinds of flow transitions with the increase in |MaT|. If MaC is sufficiently large (MaC ≳ 530), as |MaT| increases, the flow changes from a 2D-steady pattern to a 3D-chaotic behavior at moderate |MaT| (1050 ≲ |MaT| ≲ 2800). We also predict that a second transition and an oscillatory rotating flow occur as |MaT| increases further. The flow becomes 3D-steady at smaller MaC (MaC ≲ 360) with no transition, and the azimuthal wavenumber (m) decreases with increasing |MaT|. Furthermore, the thermo-solutal Marangoni convection in this system can be suppressed almost completely when MaC is approximately equal to −MaT (MaC ≈ −MaT) and the flow becomes periodically stable with weak fluctuations.

The Top-Seeded Solution Growth (TSSG) method is a promising technique for the production of high-quality SiC single crystal. To achieve a high- and uniform-growth rate in the TSSG process of SiC, the fluid flows developing in the growth solution (melt), due to the applied and induced electromagnetic fields, buoyancy, seed rotation, and free surface tension gradient, need to be controlled. Previous numerical analysis has shown that such complex flows in the TSSG melt can be controlled by the applications of a static magnetic field and seed rotation. However, the requirement of significant computational resources prevented us from carrying out the needed optimization for the process parameters involved. In order to resolve the computational demand issue, in this study, we utilized the Bayesian optimization algorithm for an efficient optimization of the associated control parameters of the TSSG process of SiC. It was shown that the Bayesian algorithm determines the optimal state at about roughly 1/4 of the computational cost of a conventional optimization, and accurately predicts the growth-rate evaluation function around the optimal state. The optimal state obtained by the present optimization process predicts a high- and uniform-growth rate in the TSSG system of SiC considered in this work.

Research on induced Pluripotent Stem (iPS) cell has attracted attention due to their remarkable progress in regenerative medicine. Cost and quality are two main factors to be considered when using iPS cells in biological applications in a large scale. In this study, the suspension culture of iPS cells was numerically simulated in a cylindrical tank under the two-different shaking methods; one-direction rotation and periodic alternate rotation. The two shaking methods exhibited a significant difference in the average number of cells accumulated in the bottom. Even though the one direction rotation method suppressed the shear stress acting on iPS cells, after eight seconds it accumulated more cells in the bottom than the periodic alternate rotation method.

Marangoni convection is a flow along the interface between two fluids due to the variation of surface tension, which is mainly caused by temperature and/or concentration gradients, namely thermal and/or solutal Marangoni convection(s). During the crystal growth by the floating zone method, Marangoni convection may induce the striation and affect the quality of growing crystal. Therefore, it is necessary to understand the convective phenomenon and control it. In this study, a three-dimensional configuration of the half-zone liquid bridge in the crystal growth of SixGe1-x was selected by establishing the temperature and concentration differences. The equations of continuity, momentum, energy and mass transfer were solved by the PISO algorithm in the OpenFOAM. Thermal and solutal Marangoni convections were set to flow in the opposite direction under zero gravity in the melt with different Marangoni numbers. Results have shown that when MaC is larger than −MaT, the flow is steady and axisymmetric, while MaC is smaller than −MaT, the flow is unsteady and irregular. As for the control of Marangoni convection, rotation of top and bottom plane in the liquid bridge was applied during the crystal growth. With different rotation speeds and directions, the suppression of Marangoni convection can be effectively realized by the appropriate forced rotation.