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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Symbolic Computational Approach to the Marangoni Convection Problem With Soret Diffusion

A recently reported solution for stationary stability of a thermosolutal system with Soret diffusion is re-derived and examined using a symbolic computational package. Symbolic computational languages are well suited for such an analysis and facilitate a pragmatic approach that is adaptable to similar problems. Linearization of the equations, normal mode analysis, and extraction of the final solution are performed in a Mathematica notebook format. An exact solution is obtained for stationary stability in the limit of zero gravity. A closed form expression is also obtained for the location of asymptotes in relevant parameter, (Sm(sub c), Mac(sub c)), space. The stationary stability behavior is conveniently examined within the symbolic language environment. An abbreviated version of the Mathematica notebook is given in the Appendix.

Skarda, J. Raymond↗
NASA NTRS1993

Marangoni effect induced convection in material processing under microgravity (M-18)

On the ground the upper layer of the liquid in a vessel heated from below becomes hotter than the lower layer. This well-known phenomenon results from buoyancy-induced convection. Though this means that the buoyancy-induced convection is not dominant under microgravity conditions in space, another convection called Marangoni convection may possibly occur. This convection results from an intermolecular force which acts on a free surface, that is surface tension. Since it is stronger at lower temperatures, the liquid surface near the heated wall is pulled to the cooled side as shown. This surface movement causes the inner convection. Marangoni convection, however, may be negligible on the Earth, for the molecular force is generally smaller than buoyancy. Various tests on material processing were recently conducted in space and some high quality crystals free from buoyancy convection were obtained. But, at the same time, others proved to be less uniform than expected in the components' distribution. This nonuniformity seems to be mainly caused by Marangoni convection. It is, therefore, very important to know how to control the convection by studying its characteristics, but the problem is that on the ground it is impossible to carry out the experiment without gravity. That is what a space experiment aboard the space shuttle is planned as the First Material Processing Tests (FMPT) of Japan. The experiment on Marangoni flow visualization is being performed in order to investigate the characteristics of convection in uni-dimensional melt growth under microgravity conditions.

Enya, S.↗
NASA NTRS1999

Measurement of Temperature Fluctuations and Microscopic Growth Rates in a Silicon Floating Zone and Microgravity

A silicon crystal growth experiment has been accomplished using the floating-zone technique under microgravity on a sounding rocket (TEXUS 36). Measurements of temperature fluctuations in the silicon melt zone due to time dependent thermocapillary convection (Marangoni convection) and an observation of the microscopic growth rate were simultaneously performed during the experiment. Temperature fluctuations of about 0.5 - 0.7 C with a frequency range < 0.5Hz were detectable. The microscopic growth rate fluctuates considerably around the average growth rate of 1 mm/min: Growth rates up to 3 to 4mm/min, close to zero mm/min, as well as negative values (backmelting) were observed. Dopant striations are clearly visible in the Sb-doped crystal. They were characterized by Spreading Resistance measurements and Differential Interference Contrast microscopy. The frequencies of temperature fluctuations, microscopic growth rates, and the dopant inhomogeneities correspond quite well, with main frequencies between 0.1 and 0.3 Hz. 3D numerical simulations were performed to predict the optimum position of the temperature sensor, and the characteristic temperature amplitudes and frequencies. At a position 3.4mm above the interface and 1.4mm inside the melt, equivalent to the sensor tip position in the experiment, temperature fluctuations up to 1.8 C and frequencies ? 0.25Hz were found in the simulations.

Schweizer, Markus↗
NASA NTRS1999

Design of Ceramic Springs for Use in Semiconductor Crystal Growth in Microgravity

Segregation studies can be done in microgravity to reduce buoyancy driven convection and investigate diffusion-controlled growth during the growth of semiconductor crystals. During these experiments, it is necessary to prevent free surface formation in order to avoid surface tension driven convection (Marangoni convection). Semiconductor materials such as gallium arsenide and germanium shrink upon melting, so a spring is necessary to reduce the volume of the growth chamber and prevent the formation of a free surface when the sample melts. A spring used in this application must be able to withstand both the high temperature and the processing atmosphere. During the growth of gallium arsenide crystals during the GTE Labs/USAF/NASA GaAs GAS Program and during the CWRU GaAs programs aboard the First and Second United States microgravity Laboratories, springs made of pyrolytic boron nitride (PBN) leaves were used. The mechanical properties of these PBN springs have been investigated and springs having spring constants ranging from 0.25 N/mm to 25 N/mm were measured. With this improved understanding comes the ability to design springs for more general applications, and guidelines are given for optimizing the design of PBN springs for crystal growth applications.

Kaforey, M. F.↗
NASA NTRS1988

Future MAUS payload and the TWIN-MAUS configuration

The German MAUS project (materials science autonomous experiments in weightlessness) was initiated in 1979 for optimum utilization of NASA's Get Away Special (GAS) program. The standard MAUS system was developed to meet GAS requirements and can accommodate a wide variety of GAS-type experiments. The system offers a range of services to experimenters within the framework of standardized interfaces. Four MAUS payloads being prepared for future space shuttle flight opportunities are described. The experiments include critical Marangoni convection, oscillatory Marangoni convection, pool boiling, and gas bubbles in glass melts. Scientific objectives as well as equipment hardware are presented together with recent improvements to the MAUS standard system, e.g., a new experiment control and data management unit and a semiconductor memory. A promising means of increasing resources in the field of GAS experiments is the interconnection of GAS containers. This important feature has been studied to meet the challenge of future advanced payloads. In the TWIN-MAUS configuration, electrical power and data will be transferred between two containers mounted adjacent to each other.

Staniek, S.↗
NASA NTRS1996

Marangoni-Benard Convection in a Evaporating Liquid Thin Layer

Marangoni-Benard convection in evaporating liquid thin layers has been investigated through flow visualization and temperature profile measurement. Twelve liquids, namely ethyl alcohol, methanol, chloroform, acetone, cyclohexane, benzine, methylene chloride, carbon tetrachloride, ethyl acetate, n-pentane, silicone oil (0.65 cSt.), and freon-113, were tested and convection patterns in thin layers of these samples were observed. Comparison among these tested samples shows that some liquids are sensitive to surface contamination from aluminum powder but some are not. The latter is excellent to be used for the investigation of surface-tension driven convection through visualization using the tracer. Two sample liquids, alcohol and freon-113 were particularly selected for systematic study. It was found that the wavelength of Benard cells would not change with thickness of the layer when it evaporates at room temperature. Special attention was focused on cases in which a liquid layer was cooled from below, and some interesting results were obtained. Convection patterns were recorded during the evaporation process and the patterns at certain time frame were compared. Benard cells were observed in thin layers with a nonlinear temperature profile and even with a zero or positive temperature gradient. Wavelength of the cells was found to increase as the evaporation progressed.

Chai, An-Ti↗
NASA NTRS1999

The Influence of Static and Rotating Magnetic Fields on Heat and Mass Transfer in Silicon Floating Zones

Hear and mass transfer in float-zone processing are strongly influenced by convective flows in the zone. They are caused by buoyancy convection, thermocapillary (Marangoni) convection, or artificial sources such as rotation and radio frequency heating. Flows in conducting melts can be controlled by the use of magnetic fields, either by damping fluid motion with static fields or by generating a def@ned flow with rotating fields. The possibilities of using static and rotating magnetic fields in silicon floating-zone growth have been investigated by experiments in axial static fields up to ST and in transverse rotating magnetic fields up to 7.S mT. Static fields of a few 100 MT already suppress most striations but are detrimental to the radial segregation by introducing a coring effect. A complete suppression of dopant striations caused by time-dependent thermocapillary convection and a reduction of the coring to insignificant values, combined with a shift of the axial segregation profile towards a more diffusion-limited case, is possible with static fields ? 1T. However, under certain conditions the use of high axial magnetic fields can lead to the appearance of a new type of pronounced dopant striations, caused by thermoelec:romagnetic convection. The use of a transverse rotating magnetic field influences the microscopic segregation at quite low inductions, of the order of a few mT. The field shifts time-dependent flows and the resulting striation patterns from a broad range of low frequencies at high amplitudes to a few high frequencies at low amplitudes

Croell, Arne↗
NASA NTRS1999

Static Magnetic Fields in Semiconductor Floating-Zone Growth

Heat and mass transfer in semiconductor float-zone processing are strongly influenced by convective flows in the zone, originating from sources such as buoyancy convection, thermocapillary (Marangoni) convection, differential rotation, or radio frequency heating. Because semiconductor melts are conducting, flows can be damped by the use of static magnetic fields to influence the interface shape and the segregation of dopants and impurities. An important objective is often the suppression of time-dependent flows and the ensuing dopant striations. In RF-heated Si-FZ - crystals, fields up to O.STesla show some flattening of the interface curvature and a reduction of striation amplitudes. In radiation-heated (small-scale) SI-FZ crystals, fields of 0.2 - 0.5 Tesla already suppress the majority of the dopant striations. The uniformity of the radial segregation is often compromised by using a magnetic field, due to the directional nature of the damping. Transverse fields lead to an asymmetric interface shape and thus require crystal rotation (resulting in rotational dopant striations) to achieve a radially symmetric interface, whereas axial fields introduce a coring effect. A complete suppression of dopant striations and a reduction of the coring to insignificant values, combined with a shift of the axial segregation profile towards a more diffusion-limited case, are possible with axial static fields in excess of 1 Tesla. Strong static magnetic fields, however, can also lead to the appearance of thermoelectromagnetic convection, caused by the interaction of thermoelectric currents with the magnetic field.

Croll, Arne↗
NASA NTRS1999

The Influence of Static and Rotating Magnetic Fields on Heat and Mass Transfer in Silicon Floating Zones

Heat and mass transfer in float-zone processing are strongly influenced by convective flows in the zone. They are caused by buoyancy convection, thermocapillary (Marangoni) convection, or artificial sources such as rotation and radio-frequency heating. Flows in conducting melts can be controlled by the use of magnetic fields, either by damping fluid motion with static fields or by generating a defined flow with rotating fields. The possibilities of using static and rotating magnetic fields in silicon floating-zone growth have been investigated by experiments in axial static fields up to 5 T and in transverse rotating magnetic fields up to 7.5 mT. Static fields of a few 100 mT already suppress most striations but are detrimental to the radial segregation by introducing a coring effect. A complete suppression of dopant striations caused by time-dependent thermocapillary convection and a reduction of the coring to insignificant values, combined with a shift of the axial segregation profile toward a more diffusion-limited case, is possible with static fields greater than or equal to 1 T. However, under certain conditions the use of high axial magnetic fields can lead to the appearance of a new type of pronounced dopant striations, caused by thermoelectromagnetic convection. The use of a transverse rotating magnetic field influences the microscopic segregation at quite low inductions, of the order of a few millitesla. The field shifts time- dependent flows and the resulting striation patterns from a broad range of low frequencies at high amplitudes to a few high frequencies at low amplitudes.

Croll, A.↗
NASA NTRS1996

Three-Dimensional Simulations of Marangoni-Benard Convection in Small Containers by the Least-Squares Finite Element Method

This paper reports a numerical study of the Marangoni-Benard (MB) convection in a planar fluid layer. The least-squares finite element method (LSFEM) is employed to solve the three-dimensional Stokes equations and the energy equation. First, the governing equations are reduced to be first-order by introducing variables such as vorticity and heat fluxes. The resultant first-order system is then cast into a div-curl-grad formulation, and its ellipticity and permissible boundary conditions are readily proved. This numerical approach provides an equal-order discretization for velocity, pressure, vorticity, temperature, and heat conduction fluxes, and therefore can provide high fidelity solutions for the complex flow physics of the MB convection. Numerical results reported include the critical Marangoni numbers (M(sub ac)) for the onset of the convection in containers with various aspect ratios, and the planforms of supercritical MB flows. The numerical solutions compared favorably with the experimental results reported by Koschmieder et al..

Yu, Sheng-Tao↗
NASA NTRS2000

Float-Zone Growth of Gel-xSix (x ? 10 at .%) Single Crystals: Influence of Thermocapillary and Solutocapillary Convection

Gel-xSix (x ? 10 at.%) single crystals have been grown with the float-zone technique applied within a monoellipsoid mirror furnace. The feed crystal consisted of synthesized GeO.95siO.05 polycrystalline material. Two Boron-doped (much much more than 1-2 (raised dot) 1017 at/cm3) crystals were grown under identical conditions using <100> Ge seeds. One Ge:Ga-doped (much much more than 1018 at/cm3) reference crystal was also grown in the same furnace. Compositional profiles were measured with an energy dispersive analysis by X-ray (EDAX). The maximum silicon concentration attained was 10 at.%. Micrographs of the etched crystals show sharp changes in interface curvature at the crystal edges. These are considered to be caused by solutal Marangoni convection, whose strength is assumed to be a direct function of silicon concentration, Theoretical considerations show that the flow direction, velocity, and strength varies significantly from a solutal Marangoni convection regime directly in front of the solid-liquid interface to a thermal Marangoni convection regime within the bulk melt.

Campbell, Tom A.↗
NASA NTRS1994

Marangoni-Benard convection in a low-aspect-ratio liquid layer

This paper presents the results of a study on the variation of the critical Marangoni number (Ma(sub c)) for the onset of Benard convection in a finite liquid layer bounded horizontally as well as from below. A direct-numerical-simulation procedure is devised to determine the Ma(sub c) for aspect ratios (Ar) ranging from 0.8 to 10. The results predict a strong increase of Ma(sub c) as Ar decreases to below 2. A dip of Ma(sub c) occurs between Ar = 1.45 and 1.3, which is accompanied by a pattern transition from a two-cell convection to a unicellular flow. For Ar above 4, the calculated Ma(sub c) shows little change and asymptotically approach a value of 116.15, with Biot number (Bi) equal to 1.

Duh, J. C.↗
NASA NTRS1985

High Marangoni number convection in a square cavity

Steady thermocapillary flows in a square cavity are computed using a finite difference procedure. Accurate numerical solutions are obtained for as high a Reynolds number as possible, in order to characterize the nature of strongly convective flows of this general class. Only the case of capillary number going to zero is considered, so that the free surface is assumed flat at the leading order. Surface deflections are computed by domain perturbation. Boundary layer formation at different values of the Prandtl number is observed at large values of the Marangoni number and Re. The numerical results are used to infer the relevant scalings of a consistent boundary layer picture of the flow, valid asymptotically as Re goes to infinity.

Zebib, A.↗
NASA NTRS1999

Identification of Gravity-Related Effects on Crystal Growth From Melts With an Immiscibility Gap

This work involves an experimental-numerical approach to study the effects of natural and Marangoni convections on solidification of single crystals from a silicate melt with a liquid-liquid immiscibility gap. Industrial use of crystals grown from silicate melts is becoming increasingly important in electronic, optical, and high temperature structural applications. Even the simplest silicate systems like Al203-SiO2 have had, and will continue to have, a significant role in the development of traditional and advanced ceramics. A unique feature of crystals grown from the silicate systems is their outstanding linear electro-optic properties. They also exhibit exceptionally high optical rotativity. As a result, these crystals are attractive materials for dielectric, optical, and microwave applications. Experimental work in our laboratory has indicated that directional solidification of a single crystal mullite appears to be preceded by liquid-liquid phase separation in the melt. Disruption of the immiscible state results in crystallization of a two phase structure. There is also evidence that mixing in the melt caused by density-driven convection can significantly affect the stability of the immiscible liquid layers and result in poly-crystalline growth. On earth, the immiscible state has only been observed for small diameter crystals grown in float zone systems where natural convection is almost negligible. Therefore, it is anticipated that growth of large single crystals from silicate melts would benefit from microgravity conditions because of the reduction of the natural convective mixing. The main objective of this research is to determine the effects of transport processes on the phase separation in the melt during growth of a single crystal while addressing the following issues: (1) When do the immiscible layers form and are they real?; (2) What are the main physical characteristics of the immiscible liquids?; and (3) How mixing by natural or Marangoni convection affects the stability of the phase separated melt.

Kassemi, M.↗
DOE OSTI2025

A fluctuating hydrodynamics model for nanoscale surfactant-laden interfaces

A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a Cahn-Hilliard free energy density combined with incompressible, isothermal fluctuating hydrodynamics where dissipative fluxes include both deterministic and stochastic terms. The intermolecular parameters in the free energy are chosen such that one species acts as a partially miscible surfactant. From Laplace pressure measurements, we show that in this model the surface tension decreases linearly with surfactant concentration, leading to Marangoni convection for interfaces with concentration gradients. In the capillary wave spectrum for interfaces with and without surfactant, we find that for the former, the spectrum deviates significantly from classical capillary wave theory, presumably due to Gibbs elasticity. In non-equilibrium simulations of the Rayleigh-Plateau instability, deterministic simulations showed that the surfactant delays pinching of a fluid cylinder into droplets. However, stochastic simulations indicate that thermal fluctuations disrupt the surfactant's stabilizing effect. Similarly, the spreading of a patch of surfactant, driven by Marangoni convection, was found to be partially suppressed by thermal fluctuations.

Capillary waves↗
NASA NTRS1995

USML-1 Glovebox experiments

This report covers the development of and results from three experiments that were flown in the Materials Science Glovebox on USML-1: Marangoni convection in Closed Containers (MCCC), Double Float Zone (DFZ), and Fiber Pulling in Microgravity (FPM). The Glovebox provided a convenient, low cost method for doing simple 'try and see' experiments that could test new concepts or elucidate microgravity phenomena. Since the Glovebox provided essentially one (or possibly two levels of confinement, many of the stringent verification and test requirements on the experiment apparatus could be relaxed and a streamlined test and verification plan for flight qualification could be implemented. Furthermore, the experiments were contained in their own carrying cases whose external configurations could be identified early in the integration sequence for stowage considerations while delivery of the actual experiment apparatus could be postponed until only a few months before flight. This minimized the time fluids must be contained and reduced the possibility of corrosive reactions that could ruin the experiment. In many respects, this exercise was as much about developing a simpler, cheaper way of doing crew-assisted science as it was about the actual scientific accomplishments of the individual experiments. The Marangoni Convection in Closed Containers experiment was designed to study the effects of a void space in a simulated Bridgman crystal growth configuration and to determine if surface tension driven convective flows that may result from thermal gradients along any free surfaces could affect the solidification process. The Fiber Pulling in Microgravity experiment sought to separate the role of gravity drainage from capillarity effects in the break-up of slender cylindrical liquid columns. The Stability of a Double Float Zone experiment explored the feasibility of a quasi-containerless process in which a solidifying material is suspended by two liquid bridges of its own melt.

Naumann, Robert J.↗
NASA NTRS1999

Measurement of Temperature Fluctuations and Microscopic Growth Rates in a Silicon Floating Zone Under Microgravity

USA Several microgravity experiments on sounding rockets and the Space Shuttle have shown that time-dependent thermocapillary (Marangoni) convection is the major cause for the formation of dopant striations in floating-zone grown semiconductor crystals, at least in small-scale systems not employing RF heating. To quantify this correlation, a silicon floating-zone experiment was performed during the TEXUS36 flight (February 7, 1998) in the monoellipsoid mirror furnace TEM02-ELLI. During the experiment, temperature fluctuations in the silicon melt zone and the microscopic growth rate were simultaneously measured. Temperature fluctuations of 0.5 C - 0.7 C with main frequencies between 0.1 Hz and 0.3 Hz were detectable. The microscopic growth rate fluctuated considerably around the average growth rate of 1 mm/min: rates from 4 mm/min to negative values (backmelting) were observed. Dopant striations are clearly visible in the Sb-doped crystal. They were characterized by Spreading Resistance measurements and Differential Interference Contrast microscopy. The frequencies associated with the dopant inhomogeneities correspond quite well with those of the temperature fluctuations and microscopic growth rates. 3D numerical simulations were performed to predict the optimum position of the temperature sensor, to evaluate characteristic temperature amplitudes and frequencies, and to give insight into the instability mechanisms of Marangoni convection in this configuration. The simulations were in good agreement with the experimental values, showing temperature fluctuations with frequencies ? 0.25 Hz and amplitudes up to 1.8 C at a position equivalent to that of the sensor tip in the experiment.

Croell, Arne↗
NASA NTRS1999

Measurement of Temperature Fluctuations and Microscopic Growth Rates in a Silicon Floating Zone on TEXUS36

Several pg experiments on sounding rockets and the Space Shuttle have shown that time-dependent thermocapillary (Marangoni) convection is the major cause for the formation of dopant striations in floating-zone grown semiconductor crystals, at least in small-scale systems not employing RF heating. To quantify this correlation, a silicon floating-zone experiment was performed during the TEXUS36 flight (February 7, 1 998) in the monoellipsoid mirror furnace TEM02-ELLI. During the experiment, temperature fluctuations in the silicon melt zone and the microscopic growth rate were simultaneously measured. Temperature fluctuations of 0.5 C - 0.7 C with main frequencies between 0.1 Hz and 0.3Hz were detectable. The microscopic growth rate fluctuated considerably around the average growth rate of 1 mm/min: rates from 4mm/min to negative values (backmelting) were observed. Dopant striations are clearly visible in the Sb-doped crystal. They were characterized by Spreading Resistance measurements and Differential Interference Contrast microscopy. The frequencies associated with the dopant inhomogeneities correspond quite well with those of the temperature fluctuations and microscopic growth rates. 3D numerical simulations were performed to predict the optimum position of the temperature sensor, to evaluate characteristic temperature amplitudes and frequencies, and to give insight into the instability mechanisms of Marangoni convection in this configuration. The simulations were in good agreement with the experimental values, showing temperature fluctuations with frequencies? 0.25 Hz and amplitudes up to 1.8 C at a position equivalent to that of the sensor tip in the experiment.

Croell, Arne↗