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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

The Role of Marangoni Convection for the FZ-Growth of Silicon

In growing crystals by the floating zone (FZ) technique under microgravity, the size restriction we have under earth conditions because of the hydrostatic pressure are avoided. Further, buoyancy related convection is eliminated to a high degree. But in the case of silicon, the gravity independent thermocapillary (Marangoni) convection is time-dependent even for small zone geometries. This has been demonstrated in several Technische Experimente unter Schwerelosigkeit (TEXUS) - technical experiments under reduced gravity) flights. Thus, to really take advantage of microgravity with respect to improve crystal quality, tools are required to control Marangoni convection in space facilities. Applying magnetic fields, convection can be influenced; fluid flow can either be damped (static magnetic fields) or overlaid by a regular flow regime (rotating magnetic fields). In floating zones of 8-10mm diameter and height (Ma approximately equals 6 x 10(exp 3)), a static magnetic field of about 2OOmT is sufficient to suppress time-dependent Marangoni convection to a high degree, but in dependence on the kind and the concentration of the added dopant, a new type of strongly pronounced dopant inhomogeneities have been detected. They are originated by thermoelectromagnetic convection. This can be avoided as well as detrimental effects on the radial dopant distribution by using rotating magnetic fields instead of static ones. Applying 75mT/50Hz to the FZ, the intensity of the dopant fluctuations is reduced to a high degree. Considering the rather low power consumption of rotating magnetic fields, this will be a useful tool for control or elimination of time-dependent Marangoni convection under microgravity. The strong time dependent character of thermocapillary flow and its influence on the temperature field has been measured in silicon half-zones for Marangoni numbers of Ma is approximately equal to 1-1.5 x 10(exp 4): temperature fluctuations up to 4C have been determined. Their frequency range was 0.1 and 0.4 Hz. Between certain thermocouple or sensor pairs, strong correlation has been detected.

Dold, P.↗
NASA NTRS1999

The Role of Marangoni Convection for the FZ-Growth of Silicon

Growing crystals by the floating zone (FZ) technique under microgravity avoids the size restriction we have under earth conditions due to hydrostatic pressure. Further, buoyancy related convection is eliminated to a great degree. But in the case of silicon, the gravity independent thermocapillary (Marangoni) convection is time-dependent even for small zone geometries. This has been demonstrated in several Technische Experimente unter Schwerelosigkeit (TEXUS) technical experiments under reduced gravity flights. Thus, to really take advantage of microgravity with respect to improved crystal quality, tools are required to control Marangoni convection in space facilities. With the application of magnetic fields, convection can be influenced; fluid flow can either be damped (static magnetic fields) or overlaid by a regular flow regime (rotating magnetic fields). In floating zones of 8-10 mm diameter and height (i.e., Ma is much greater than 6X 10(exp 3), a static magnetic field of about 2OOmT is sufficient to suppress time-dependent Marangoni convection to a high degree, but in dependence on the kind and the concentration of the added dopant, a new type of strongly pronounced dopant inhomogeneities have been detected. They are originated by thermoelectromagnetic convection. This can be avoided as well as detrimental effects on the radial dopant distribution by using rotating magnetic fields instead of static ones. Applying 7.5mT/5OHz to the FZ, the intensity of the dopant fluctuations is reduced to a high degree. Considering the rather low power consumption of rotating magnetic fields, this will be a useful tool for control or elimination of time-dependent Marangoni convection under microgravity. The strong time-dependent character of thermocapillary flow and its influence on the temperature field has been measured in silicon half-zones for Marangoni numbers of Ma is much greater than l - 1.5 X 10(exp 4): temperature fluctuations up to 4C have been determined, their frequency range was 0.4 and 0.4Hz. Between certain thermocouple or sensor pairs, strong correlation has been detected.

Dold, P.↗
NASA NTRS1999

A New Approach to Measure Contact Angle and Evaporation Rate with Flow Visualization in a Sessile Drop

The contact angle and the spreading process of sessile droplet are very crucial in many technological processes, such as painting and coating, material processing, film-cooling applications, lubrication, and boiling. Additionally, as it is well known that the surface free energy of polymers cannot be directly, measured for their elastic and viscous restraints. The measurements of liquid contact angle on the polymer surfaces become extremely important to evaluate the surface free energy of polymers through indirect methods linked with the contact angle data. Due to the occurrence of liquid evaporation is inevitable, the effects of evaporation on the contact angle and the spreading become very important for more complete understanding of these processes. It is of interest to note that evaporation can induce Marangoni-Benard convection in sessile drops. However, the impacts of the inside convection on the wetting and spreading processes are not clear. The experimental methods used by previous investigators cannot simultaneously measure the spreading process and visualize the convection inside. Based on the laser shadowgraphic system used by the present author, a very simple optical procedure has been developed to measure the contact angle, the spreading speed, the evaporation rate, and to visualize inside convection of a sessile drop simultaneously. Two CCD cameras were used to synchronously record the real-time diameter of the sessile drop, which is essential for determination of both spreading speed and evaporation rate, and the shadowgraphic image magnified by the sessile drop acting as a thin plano-convex lens. From the shadowgraph, the inside convection of the drop can be observed if any and the image outer diameter, which linked to the drop profile, can be measured. Simple equations have been derived to calculate the drop profile, including the instantaneous contact angle, height, and volume of the sessile drop, as well as the evaporation rate. The influence of the inside convection on the wetting and spreading processes can be figured out through comparison of the drop profiles with and without inside convection when the sessile drop is placed at different evaporation conditions.

Zhang, Nengli↗
NASA NTRS2006

Heat Transfer of Thermocapillary Convection in a Two-Layered Fluid System Under the Influence of Magnetic Field

Heat transfer of a two-layer fluid system has been of great importance in a variety of industrial applications. For example, the phenomena of immiscible fluids can be found in materials processing and heat exchangers. Typically in solidification from a melt, the convective motion is the dominant factor that affects the uniformity of material properties. In the layered flow, thermocapillary forces can come into an important play, which was first emphasized by a previous investigator in 1958. Under extraterrestrial environments without gravity, thermocapillary effects can be a more dominant factor, which alters material properties in processing. Control and optimization of heat transfer in an immiscible fluid system need complete understanding of the flow phenomena that can be induced by surface tension at a fluid interface. The present work is focused on understanding of the magnetic field effects on thermocapillary convection, in order to optimize material processing. That is, it involves the study of the complicated phenomena to alter the flow motion in crystal growth. In this effort, the Marangoni convection in a cavity with differentially heated sidewalls is investigated with and without the influence of a magnetic field. As a first step, numerical analyses are performed, by thoroughly investigating influences of all pertinent physical parameters. Experiments are then conducted, with preliminary results, for comparison with the numerical analyses.

Ramachandran, N.↗
NASA NTRS1998

Thin Film Mediated Phase Change Phenomena: Crystallization, Evaporation and Wetting

We focus on two distinct materials science problems that arise in two distinct microgravity environments: In space and within the space of a polymeric network. In the former environment, we consider a near eutectic alloy film in contact with its vapor which, when evaporating on earth, will experience compositionally induced buoyancy driven convection. The latter will significantly influence the morphology of the crystallized end member. In the absence of gravity, the morphology will be dominated by molecular diffusion and Marangoni driven viscous flow, and we study these phenomena theoretically and experimentally. The second microgravity environment exists in liquids, gels, and other soft materials where the small mass of individual molecules makes the effect of gravity negligible next to the relatively strong forces of intermolecular collisions. In such materials, an essential question concerns how to relate the molecular dynamics to the bulk rheological behavior. Here, we observe experimentally the diffusive motion of a single molecule in a single polymer filament, embedded within a polymer network and find anomalous diffusive behavior.

Wettlaufer, John S.↗
NASA NTRS2003

Thermocapillary Convection Due to a Stationary Bubble - A Paradox

We analyze the velocity and temperature fields at steady state due to thermocapillary convection around a gas bubble that is stationary in a liquid. A linear temperature field is imposed in the undisturbed liquid. Our interest is in investigating the effect of convective transport of momentum and energy on the velocity and temperature fields. We assume the pertinent physical properties to be constant, and that buoyant convection is negligible. Suitably defined Reynolds and Marangoni numbers are assumed to be small compared with unity. When both the Reynolds and Marangoni numbers are set equal to zero, a solution can be found. In this solution, far from the bubble, the velocity field decays as the inverse of the distance from the bubble, and the disturbance temperature field decays as the inverse of the square of this distance. We now attempt to obtain a solution when the Reynolds number is zero, but the Marangoni number is small, but non-zero, by a perturbation expansion in the Marangoni number. When the temperature field is expanded in a regular perturbation series in the Marangoni number, we show that the problem for the first correction field is ill-posed. The governing equation for this perturbation field contains an inhomogeneity, and the corresponding particular solution neither decays far from the bubble, nor can be canceled by a homogeneous solution. Additional information is included in the original extended abstract.

Balasubramaniam, R.↗
NASA NTRS1994

Effects of thermocapillarity on an evaporating extended meniscus in microgravity

An analytical investigation of the effects of thermocapillarity on the flow field within and heat transfer from the extended meniscus region of a heated meniscus which is re-supplied by capillarity is presented. Microgravity conditions are considered. The analysis shows that even for extremely small temperature differences between the wall and the vapor (less than 1 mK) thermocapillary stresses at the liquid-vapor interface due to a non-uniform interfacial temperature drastically alters the flow field. At the same time, these stresses were shown to have only a slight effect on the heat transfer from the extended meniscus but increasing with an increasing temperature difference. Additionally, thermocapillary effects were shown to be sensitive to pore size. A criterion was established from a scaling analysis identifying the conditions necessary for thermocapillarity to affect the operation of capillary-pumped heat transport devices in microgravity. A critical Marangoni number and corresponding critical temperature difference between wall and vapor were identified.

Hallinan, Kevin P.↗
NASA NTRS1998

The Role of Marangoni Convection for the FZ-Growth of Silicon

Fluctuations of the electrical resistivity due to inhomogeneous dopant distribution are still a serious problem for the industrial processing yield of doped silicon crystals. In the case of silicon floating-zone growth, the main sources of these inhomogeneities are time- dependent flows in the liquid phase during the growth process. Excluding radio frequency (RF) induced convection, buoyancy and thermocapillary (Marangoni) convection are the two natural reasons for fluid flow. Both originate from temperature/concentration gradients in the melt, buoyancy convection through thermal/concentrational volume expansion, and thermocapillary convection through the temperature/concentration dependence of the surface tension. To improve the properties of grown crystals, knowledge of the strength, the characteristic, and the relation of these two flow mechanisms is essential. By the use of microgravity, the effect and the strength of buoyancy (gravity dependent) and thermocapillary (gravity independent) convection can be separated and clarified. Applying magnetic fields, both convective modes can be influenced: fluid flow can either be damped (static magnetic fields) or overlaid by a regular flow regime (rotating magnetic fields). Two complementary approaches have been pursued: Silicon full zones (experiments on the German sounding rockets TEXUS 7, 12, 22, 29, and 36) with the maximum temperature at half of the zone height and silicon half zones (experiments on the Japanese sounding rockets TR-IA4 and 6) with the maximum temperature at the top of the melt. With the full zone arrangement, the intensity and the frequency of the dopant striations could be determined and the critical Marangoni number could be identified. The half zone configuration is suited to classify the flow pattern and to measure the amplitude and the frequency of temperature fluctuations in the melt by inserting thermocouples or temperature sensors into the melt. All experiments have been carried out in monoellipsoid mirror furnaces. Typical zone geometries are approx. 8 to 14 mm in diameter and height. The crystals grown under microgravity are compared to crystals grown in static axial magnetic fields (B<5 tesla) and in transversal rotating magnetic fields (B<7.5 mT / f=50 Hz). Experimental results are completed by 3D numerical simulations: the obtained temperature and concentration distribution in the melt confirm the damping effect of rotating magnetic fields and explain the change in the radial segregation under static magnetic fields.

Dold, P.↗
NASA NTRS1990

Salt-finger convection under reduced gravity

Salt-finger convection in a double-diffusive system is a motion driven by the release of gravitational potential due to differential diffusion rates. Because of the fact that the destabilizing effect of the concentration gradient is amplified by the Lewis number (the ratio of thermal diffusivity to solute diffusivity) salt-finger convection can be generated at very much reduced gravity levels. This effect may be of importance in the directional solidification of binary alloys carried out in space. The transport of solute and heat by salt-finger convection at microgravity conditions is considered; instability arising from surface tension gradients, the Marangoni instability, is discussed, and the possible consequences of combined salt-finger and Marangoni instability are considered.

Chen, C. F.↗
NASA NTRS1991

Thermocapillary flow and natural convection in a melt column with an unknown melt/solid interface

A vertical melt column set up between an upper heating rod and a lower sample rod, i.e., the so-called half-zone system, is a convenient experimental tool for studying convection in the melt in floating-zone crystal growth. In order to help understand the convection observed in the melt column, a computer model has been developed to describe steady state, axisymmetrical thermocapillary flow and natural convection in the melt. The governing equations and boundary conditions are expressed in general non-orthogonal curvilinear coordinates in order to accurately treat the unknown melt/solid interface as well as all other physical boundaries in the system. The effects of key dimensionless variables on the following items are discussed: (1) convection and temperature distribution in the melt; (2) the shape of the melt/solid interface; (3) the height of the melt column. These dimensionless variables are the Grashof, Marangoni and Prandtl numbers.

Lan, C. W.↗
NASA NTRS2000

Onset of Convection Due to Surface Tension Variations in Multicomponent and Binary Fluid Layers

Under certain conditions, such as in thin liquid films or microgravity, surface tension variations along a free surface can induce convection. Convection onset due to surface tension variation is important to many terrestrial technological processes in addition to microgravity materials processing applications. Examples include coating, drying crystallization, solidification, liquid surface contamination, and containerless processing. In double-diffusive and multicomponent systems, the spatial variations of surface tension are associated with two or more stratifying agencies, respectively. For example, both temperature and species (concentration) gradients are associated with convection in the solidification of binary alloys or salt ponds. The direction of the two (or more) gradients has a profound effect on the nature of the flow at or slightly beyond the onset of convection. Our recent work at the NASA Lewis Research Center focused on characterizing surface-tension-induced onset of convection, often referred to as Marangoni-Benard convection. Exact solutions for the stationary neutral stability of multicomponent fluid layers with interfacial deformation were derived. These solutions also permit the computation of a boundary curve that separates the long and finite wavelength instabilities. Computing points along this boundary using the exact solution (when possible) is more efficient than the typical numerical approaches, such as finite difference or spectral methods. Above the curve, a long wavelength instability was predicted, suggesting that convection would occur principally through one large flow cell in the layer, whereas below the curve, finite wavelength instabilities occur which suggest multiple finite-sized circulation cells. For many common liquids with layer depths greater than 100 mm, finite wave instability is predicted under terrestrial conditions; however, with little exception, long wavelength instability is predicted in microgravity for the identical fluid systems.

Skarda, J. Raymond Lee↗
NASA NTRS1987

Thermocapillary migration of a gas bubble in an arbitrary direction with respect to a plane surface

The thermocapillary migration of a gas bubble in an unbounded fluid in the presence of a neighboring rigid plane surface is considered in the limit of negligible Reynolds and Marangoni numbers. Results are given for a scalar interaction parameter defined as the ratio of the speed of the bubble in the presence of the plane surface to the speed in its absence. It is suggested that the weaker interaction effects noted for the case of thermocapillary migration relative to the case of motion due to a body force such as that caused by a gravitational field is attributable to the more rapid decay, away from the bubble, of the disturbance velocity and temperature gradient fields. The surface is found to exert the greatest influence in the case of motion normal to it, and the weakest influence in the case of parallel motion.

Meyyappan, M.↗
NASA NTRS1990

Thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity

Computer simulation of steady-state axisymmetrical heat transfer and fluid flow was conducted to study thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity. The effects of key variables on the extent of thermocapillary flow in the melt zone, the shapes of melt/solid interfaces and the length of the melt zone were discussed. These variables are: (1) the temperature coefficient of surface tension (or the Marangoni number), (2) the pulling speed (or the Peclet number), (3) the feed rod radius, (4) the ambient temperature distribution, (5) the heat transfer coefficient (or the Biot number), and (6) the thermal diffusivity of the material (or the Prandtl number).

Lan, C. W.↗
NASA NTRS2013

Effect of Residual Noncondensables on Pressurization and Pressure Control of a Zero-Boil-Off Tank in Microgravity

The Zero-Boil-Off Tank (ZBOT) Experiment is a small-scale experiment that uses a transparent ventless Dewar and a transparent simulant phase-change fluid to study sealed tank pressurization and pressure control with applications to on-surface and in-orbit storage of propellant cryogens. The experiment will be carried out under microgravity conditions aboard the International Space Station in the 2014 timeframe. This paper presents preliminary results from ZBOT's ground-based research that focuses on the effects of residual noncondensable gases in the ullage on both pressurization and pressure reduction trends in the sealed Dewar. Tank pressurization is accomplished through heating of the test cell wall in the wetted and un-wetted regions simultaneously or separately. Pressure control is established through mixing and destratification of the bulk liquid using a temperature controlled forced jet flow with different degrees of liquid jet subcooling. A Two-Dimensional axisymmetric two-phase CFD model for tank pressurization and pressure control is also presented. Numerical prediction of the model are compared to experimental 1g results to both validate the model and also indicate the effect of the noncondensable gas on evolution of pressure and temperature distributions in the ullage during pressurization and pressure control. Microgravity simulations case studies are also performed using the validated model to underscore and delineate the profound effect of the noncondensables on condensation rates and interfacial temperature distributions with serious implications for tank pressure control in reduced gravity.

Marangoni and Natural Convection↗
NASA NTRS1993

Study of bubble behavior in weightlessness (effects of thermal gradient and acoustic stationary wave) (M-16)

The aim of this experiment is to understand how bubbles behave in a thermal gradient and acoustic stationary wave under microgravity. In microgravity, bubble or bubbles in a liquid will not rise upward as they do on Earth but will rest where they are formed because there exists no gravity-induced buoyancy. We are interested in how bubbles move and in the mechanisms which support the movement. We will try two ways to make bubbles migrate. The first experiment concerns behavior of bubbles in a thermal gradient. It is well known than an effect of surface tension which is masked by gravity on the ground becomes dominant in microgravity. The surface tension on the side of the bubble at a lower temperature is stronger than at a higher temperature. The bubble migrates toward the higher temperature side due to the surface tension difference. The migration speed depends on the so-called Marangoni number, which is a function of the temperature difference, the bubble diameter, liquid viscosity, and thermal diffusivity. At present, some experimental data about migration speeds in liquids with very small Marangoni numbers were obtained in space experiments, but cases of large Marangoni number are rarely obtained. In our experiment a couple of bubbles are to be injected into a cell filled with silicon oil, and the temperature gradient is to be made gradually in the cell by a heater and a cooler. We will be able to determine migration speeds in a very wide range of Marangoni numbers, as well as study interactions between the bubbles. We will observe bubble movements affected by hydrodynamical and thermal interactions, the two kinds of interactions which occur simultaneously. These observation data will be useful for analyzing the interactions as well as understanding the behavior of particles or drops in materials processing. The second experiment concerns bubble movement in an acoustic stationary wave. It is known that a bubble in a stationary wave moves toward the node or the loop according to whether its diameter is larger or smaller than that of the main resonant radius. In our experiment fine bubbles will be observed to move according to an acoustic field formed in a cylindrical cell. The existence of bubbles varies the acoustic speed, and the interactive force between bubbles will make the bubble behavior collective and complicated. This experiment will be very useful to development of bubble removable technology as well as to the understanding of bubble behavior.

Azuma, H.↗
NASA NTRS1991

Numerical investigation on Benard instability in a finite liquid layer

A numerical procedure for directly simulating the Benard-Marangoni instabilities (B-M-I) in a bounded liquid layer is presented in this paper. The procedure consists of applying a finite amplitude disturbance to the basic static state, and then integrating the Navier-Stokes equations to determine whether the disturbance will die down or will reach a state of finite-strength steady convection. The critical Marangoni number (Mac) for the onset of B-M-I can thus be determined and can be correlated as a function of the aspect ratio (Ar), Prandtl number (Pr), and Rayleigh number (Ra). The Biot number (B) between the liquid and the air is analyzed to approximate the heat transfer condition along the free surface. A 2D calculation is performed to investigate the effect of various initial disturbances, and the Mac is determined for Ar = 2, Ra = 0, and Pr = 0.7. Current results show that disturbances of different nature and amplitude have little effect on Mac. The Mac determined in this study also clearly demonstrates the dominant effect of the sidewalls.

Duh, J. C.↗
NASA NTRS1992

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Dijkstra, Henk A.↗
NASA NTRS1990

Thermal buoyancy and Marangoni convection in a two fluid layered system - A numerical study

Thermal buoyancy and surface tension driven convection is numerically investigated in a system with two, immiscible fluids. The geometry investigated, has an open cavity configuration with the lighter fluid situated on top of the heavier fluid, forming a stable layered system. The upper fluid meniscus and the interface are assumed to be flat and undeformable in the calculations. The governing equations and boundary/interface conditions are solved by a control volume based finite difference scheme for two pairs of immiscible fluids; the water-hexadecane system and a so called generic system. The steady state calculations show, that dramatically different flows are predicted when the interfacial tension effects are included or excluded from the system model. These differences are particularly appreciable in surface tension dominated flows, that are typical of microgravity situations. Complex flow patterns, with induced secondary flows are noticed in both the fluids. In general, the overall system heat transfer is found to increase with increases in the thermal buoyancy and surface tension effects, but the behavior of the system flow and thermal fields is not easy to characterize, when different combinations of these forces are considered.

Ramachandran, N.↗