The effect of small vibrations on Marangoni convection and the free surface of a liquid bridge

The effects of small vibrations on Marangoni convection were investigated experimentally using a liquid bridge of 5 cSt silicone oil with a disk diameter of 7.0 mm, and an aspect ratio close to 0.5. Experiments were performed to determine the critical temperature difference data for no vibration case and with small vibrations applied. The experimental results have shown that the effect of small vibrations on the onset of oscillatory flow is small since the critical temperature difference data for different aspect ratios were not affected by the vibrations. To clarify the surface oscillation phenomena induced by external vibrations, a 3-D numerical simulation model was also developed using a level set algorithm to predict the surface oscillations of isothermal silicone oil bridges. By subjecting the liquid bridge to small vibrations, the surface oscillation characteristics were predicted numerically, and the numerical results compared well with the predictions of an analytical model proposed previously. Furthermore, the effect of small vibrations on the surface vibration amplitude of the liquid bridge is also discussed.     

Effect of liquid bridge form on oscillatory thermocapillary convection under 1 g and μg conditions

This study analyses the effect of temperature difference between hot and cool disk (ΔT), and non-dimensional liquid bridge volume (V/V_o) on the transition process from steady thermocapillary convection to periodic or chaotic thermocapillary convection in a liquid bridge modeled after the floating zone method under normal gravity and microgravity conditions. From normal gravity and drop shaft experiments, the difference of the regime of the steady state and the oscillatory state was clarified on the ΔT−V/V_o plane under 1 g and μg conditions. A gap or stability region was observed in the specific V/V_o range under 1 g conditions. In the gap or stable region, after the gravity changed from 1 g to μg conditions, the temperature signals showed oscillation. From these results, the critical temperature difference under the μg conditions appeared to be smaller than that under the 1 g conditions. Temperature signals were defined as 6 different types of states. The various temperature oscillatory state regimes were obtained on a ΔT−V/V_o plane under 1 g and μg conditions. Under μg conditions, in these experimental conditions, all temperature oscillatory states exhibited only the Periodic state.     

Oscillatory Thermocapillary Flows in Simulated Floating-zones with Time-dependent Temperature Boundary Conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier–Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L=20 [mm] and a diameter D=20 (mm) is considered. A temperature difference ΔT=30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave', but after a transient time the instability is described by the dynamic model of a ‘standing wave', with an azimuthal spatial distribution corresponding to m=1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.     

On the onset of the oscillatory regimes in Marangoni flows

Recent experiments in microgravity environment (Texus, Spacelab) have shown that Marangoni Numbers, at the onset of oscillatory flow in floating zones, exceeded by more than one order of magnitude the value previously proposed as critical values. A new criterion is proposed based on the dynamic Weber number prevailing at the surface conditions; the new parameter seems to fit much better all the available experimental findings obtained so far.     

Oscillatory thermocapillary flows in simulated floating-zones with time-dependent temperature boundary conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier-Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L = 20 [mm] and a diameter D = 20 (mm) is considered. A temperature difference ΔT = 30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave’, but after a transient time the instability is described by the dynamic model of a ‘standing wave’, with an azimuthal spatial distribution corresponding to m = 1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.     

A micro-gravity simulation of the Marangoni convection

An experimental verification of Marangoni convection in the liquid inter-space between two-coaxial discs is carried out at reduced gravity effect using small Bond's number obtained by choice of small characteristical diameter. Silicon oil is used as working fluid. The upper or lower disc can be heated electrically. The flow is visualized by illuminating fine powder of Titandioxide in the fluid with a vertical “light cut” of about 0.1 mm thickness, which is produced by a laser with a cylindrical glass rod and a microscope objective. Photographs and moving pictures are taken from a TV monitor. From these the vortex configuration and the velocity distribution can be determined, which would be expected for the Marangoni convection in the zero-g condition, for example in the spacelab.     

Effects of variable transport properties on thermal Marangoni flows

The effects of temperature dependence of the diffusion coefficients on the solution fields of Thermal Marangoni Flows in micro-gravity is analyzed by using an unsteady—variable mesh—two dimensional—finite difference numerical code to solve the full Navier-Stokes equations.A typical cylindrical floating zone geometry is analyzed and the estimation of the deviations caused by considering a temperature-dependent variable viscosity is verified with respect to the most important field parameters (streamlines, isotherms, isobars, Nusselt heating curves, velocity and temperature profiles).Comparison with TEXUS experiment is finally performed.     

Preliminary results of Texus 8 experiments on effects of surface tension minimum

A stable, observable liquid-gas interface was realized in an experimental cell (3 × 2 × 1 cm) under microgravity conditions. The liquid used was an aqueous 6.24 10^?3 molal solution of n-heptanol. A temperature gradient, established at the interface, resulted in the build-up of a Marangoni convection cell with the liquid flowing in an unusual direction (i.e. at the surface the liquid flowed from the cold to the hot side).The same experiment on Earth gives rise to a Marangoni cell superimposed on buoyancy cells. The Marangoni and the buoyancy cells then turn in opposite directions.     

Floating zone experiments with germanium crystals in sounding rockets

A floating zone experiment with a coated surface was performed in a sounding rocket. Analysis of the segregation showed that elimination of free surfaces decreased the convection in the liquid zone. Analysis of radial segregation during floating zone crystal growth under different experimental conditions demonstrated high sensitivity to interface shape and to convection. Under conditions of very weak convection, microgravity and coated surfaces, dopant concentration fields giving severe radial segregation were built up.     

不同尺度下相变材料熔化过程自然对流影响分析

为了解自然对流对固液相变传热的影响,采用有限容积法对重力条件下矩形腔内相变材料熔化过程进行了数值模拟。通过改变矩形腔的尺寸,分析了不同尺度对高温壁面平均Nu数(Nu数)及相变材料温度场、速度场的影响。结果表明:随着尺度增加,自然对流作用增强,Nu数逐步增大,液相区流动从稳定向周期振荡过渡,且流线越来越不规则。     

The study of Marangoni convection and the solid/liquid interface shape on a germanium float zone in microgravity

The study of the instability of the float zone in microgravity is necessary in order to produce pure and homogeneous crystals. Three types of instabilities may be present in a float zone. The first two, the static and dynamic instabilities, have been investigated by many authors. The third, onset of Marangoni convection is investigated in this study. The Navier-Stokes equations and the energy equation, in cylindrical coordinates, were solved using the finite element method. These pure and homogeneous germanium crystals will find application as integral components of sensitive γ radiation measuring equipment.     

The loss of stability in ground based experiments in liquid bridges

In this study our primary goal is to investigate the loss of stability of the steady convection in deformable liquid bridges. Definitely, the deformation plays an important role in the transition process from the steady axi-symmetric 2-D basic state to the 3-D periodical one. As it was shown experimentally by many researchers, the critical Marangoni number is very sensitive to the volume of liquid.

It seems to be proved^1–4, that the critical wave number for high Prandtl fluids (for example, silicone oil of different viscosities. Pr > 50) is m = 1 for aspect ratios Γ = height/radius ≥ 1.0 regardless of the free surface shape. But the data from our last experiments show, that by changing surrounding conditions around the liquid bridge we can change the critical wave number. Particularly, by placing the liquid bridge of diameter 2r = 6mm into another cylindrical volume of the diameter 2R = 12mm kept at constant temperature, the critical mode is switched from m = 1 to m = 2.     

On the structure of the floating zone in melting

Floating zone melting is used in crystal growth and purification of high melting materials. The use of a reduced gravity environment will remove the constraint imposed on the length of the zone by the hydrostatic pressure. The equilibrium of the floating zone may involve, (1) Hydrostatic forces, when the zone rotates as a whole. (2) Convective driving forces, when the zone is stationary but fluid property gradients appear. (3) Hydrodynamic forces, when some parts of the zone are set into motion with respect to others. The last effects are considered in this paper. The flow pattern of a floating zone held between two discs in relative motion is complicated, and thence the solution of the problem is difficult even assuming a constant property-newtonian liquid. Nevertheless, when a small parameter appears in the problem, the complete flow field can be split into zones where simple solutions are found. To illustrate this approach, the spin-up from rest of an initially cylindrical floating zone is considered with detail. Here the small parameter is the time elapsed from the impulsive starting of motion. Since the problem which has been considered, as well as some others which can be tackled by use of similar methods, concern the viscous layer close to either plate, they can be simulated experimentally in the ground laboratory with short floating zones. Procedures to produce these zones are indicated.     

Transition of Planar Rotational Motion of an Asymmetric Spacecraft into Oscillatory Motion at Its Reentry into the Atmosphere

The motion of a spacecraft with small asymmetry relative to its center of mass is considered. The restoring aerodynamic moment of the spacecraft is described by the Fourier series in terms of the angle of attack with the two first sinusoidal and the first cosinusoidal terms. A solution for the angle of attack in the undisturbed rotational motion is found. The analytical expression is obtained for the integral of action taken along the separatrices that separate the rotational and oscillatory regions of the phase portrait of a system. The transition of the spacecraft's motion from planar rotational to oscillatory is investigated. This transition is caused by a slow variation of moment characteristic coefficients, as well as by the presence of small asymmetry and damping and slow variation of their coefficients. Analytical formulas are obtained for determining the times of transition from rotational to oscillatory motion, as well as for the critical angular velocity of beyond-the-atmosphere rotation. When this critical velocity is exceeded, body rotation proceeds for a long time interval (planar autorotation arises).     

Influence of a surface tension minimum as a function of temperature on the marangoni convection

Aqueous long chain alcohol solutions have a surface tension which presents a minimum as a function of the temperature. At this particular temperature, the dimensionless Marangoni number is vanishing. It is thus expected that around the temperature of the minimum, Marangoni Convection would be slowered with a convective pattern deeply modified. An experiment to be performed in microgravity during the Texus 8 flight is described.     

Thermocapillary simulation of single bubble dynamics in zero gravity

The lack of significant buoyancy effects in zero gravity conditions poses an issue with fluid transfer in a stagnant liquid. In this paper bubble movement in a stagnant liquid is analysed and presented numerically using a computational fluid dynamics (CFD) approach. The governing continuum conservation equations for two phase flow are solved using the commercial software package Ansys-Fluent v.13 and the Volume of Fluid (VOF) method is used to track the liquid/gas interface in 2D and 3D domains. The simulation results are in reasonable agreement with the earlier experimental observations, the VOF algorithm is found to be a valuable tool for studying the phenomena of gas–liquid interaction. The flow is driven via Marangoni influence induced by the temperature difference which in turn drives the bubble from the cold to the hot region. A range of thermal Reynolds (Re_T) and Marangoni numbers (Ma_T) are selected for the numerical simulations, specifically Re_T=13–658 and Ma_T=214–10,721 respectively. The results indicate that the inherent velocity of bubbles decreases with an increase of the Marangoni number, a result that is line with the results of previous space experiments (Kang et al., 2008) [1]. An expression for predicting the scaled velocity of bubble has been derived based on the data obtained in the present numerical study. Some three-dimensional simulations are also performed to compare and examine the results with two-dimensional simulations.     

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

The surface temperature distributions due to thermocapillary convections in a thin liquid layer with heat fluxes imposed on the free surface are investigated. The nondimensional analysis predicts that, when convection is important, the characteristic length scale in the flow direction L, and the characteristic temperature difference ΔT₀, can be represented by and , respectively, where L_R and ΔT_T are the reference scales used in the conduction-dominant situations with A denoting the aspect ratio and Ma the Marangoni number. Having had L and ΔT₀ defined, the global surface-temperature gradient ( ), the global thermocapillary driving-force, and other interesting features can then be readily determined. Finally, numerical calculations involving a Gaussian heat flux distribution are presented to justify these two relations.     

Influence of freezing rate oscillations and convection on eutectic microstructure

As discussed in our review paper (Wilcox, W. R. and Regel, L. L., Microgravity Quarterly, 1994, 4, 147–156), the influence of microgravity on eutectic microstructure has been rather erratic and largely unexplained. Directional solidification in microgravity sometimes coarsened the structure, sometimes made it finer, and sometimes, even on the same system, had no measurable effect. Theoretical models predicted no influence of the weak buoyancy-driven convection that occurs in the vertical Bridgman technique on earth. Thus, we hypothesized that freezing rate fluctuations due to irregular convection might be responsible. For example, with a fibrous microstructure an increase in freezing rate must cause new fibers to form, either by branching or by nucleation. A decrease in freezing rate would cause fibers to terminate by overgrowth of the matrix phase. If the kinetics of fiber formation differs from that for fiber termination, an oscillatory freezing rate would cause the average fiber spacing to deviate from that at a steady freezing rate. We have been investigating this hypothesis both experimentally and theoretically. Vertical Bridgman experiments were performed on the MnBi–Bi eutectic with freezing rate oscillations caused by periodic electric current pulses passed through the material. With increased current amplitude, more and more grains exhibited irregular microstructures. Of the grains with continued quasi-regular rod structure, the microstructure became finer. This result was contrary to that expected from our hypothesis for this system. Numerical modeling also predicted that an oscillatory freezing rate should yield a finer microstructure. It was also predicted that freezing interface oscillations should cause the average melt composition at the freezing rate to deviate from the eutectic. This results in the formation of a composition boundary layer of sufficient thickness that it would become sensitive to convection. Hence we have arrived at a revised hypothesis. On earth, irregular convection causes freezing rate fluctuations that change the interfacial melt composition, leading to a thick composition boundary layer. Convection interacts with this boundary layer to change the interfacial melt composition, thereby altering the response of the system to freezing rate fluctuations.     

The effect of surfactant redistribution on combined gravitational and thermocapillary interactions of deformable drops

Trajectories are calculated by the boundary-integral method for two contaminated deformable drops under the combined influence of buoyancy and a constant temperature gradient at low Reynolds number and with negligible thermal convection. The surfactant is bulk-insoluble, and its coverage is determined by solution of the time-dependent convective-diffusion equation. Two limits are considered. For small drops, the deformation is small, and thermocapillary and buoyant effects are of the same order of magnitude. In this case, comparison is made with incompressible surfactant results to determine when surfactant redistribution becomes important. Convection of surfactant can lead to elimination of interesting features, such as the possibility of two different-sized drops migrating with fixed separation and orientation, and can increase the difference between the drops' velocities. For larger drops, deformation can be significant, leading to smaller or larger drop breakup, and buoyant motion dominates thermocapillarity. In this case, convection of surfactant can increase deformation and offset previously observed inhibition of breakup for clean drops when the driving forces are opposed. This effect is less pronounced for larger size ratios. By extension, redistribution of surfactant can enhance deformation-increasing tendencies seen with driving forces aligned in the same direction.