cSt Silicone Oil Research Articles

Dynamics of a Bouncing Droplet onto a Vertically Vibrated Interface

Low viscosity (<100 cSt) silicon oil droplets are placed on a high viscosity (1000 cSt) oil bath that vibrates vertically. The viscosity difference ensures that the droplet is more deformed than the bath interface. Droplets bounce periodically on the bath when the acceleration of its sinusoidal motion is larger than a threshold value. The threshold is minimum for a particular frequency of excitation: droplet and bath motions are in resonance. The bouncing droplet has been modeled by considering the deformation of the droplet and the lubrication force exerted by the air layer between the droplet and the bath. Threshold values are predicted and found to be in good agreement with our measurements.

A new experimental technique for measuring the dynamical free surface deformation in liquid bridges due to thermal convection

The dynamical free surface deformation due to thermal (Marangoni-buoyant) convection in liquid bridges of 5 cSt silicone oil was studied experimentally using optical imaging. The experiments were conducted under ground-based conditions for a wide range of temperature differences between the solid supports, and for several liquid bridge volumes. Oscillatory motion set in at a critical value of the temperature difference and caused oscillation of the free surface. The amplitude and fundamental frequency characterizing the magnitude and shape of that oscillation were obtained by optical imaging. The procedure allows one to describe the oscillation up to sub-micron order. The temperature oscillations at five points inside the liquid bridge were measured by five thermocouples. Their amplitude and fundamental frequency were compared with the corresponding values of the free surface oscillations. The optical imaging revealed the same dynamics as was obtained from the (more intrusive) temperature measurements. The spatial structure of the free surface oscillations along the liquid bridge axis was also analysed.

Effect of curvature on thermocapillary‐buoyancy convection in a shallow annular pool

AbstractIn order to understand the influence of curvature on thermocapillary‐buoyancy convection in a differentially heated annular pool with an outer heated cylinder ($ro=40 mm$) and an inner cooled cylinder (ri=20 or 10 mm), a series of unsteady two‐dimensional numerical simulations using the finite‐volume method was conducted. The pool was filled with 0.65 cSt silicone oil (Prandtl number Pr=6.7); its depth changed from 0.5 to 1.5 mm. Simulation results show that the flows with different curvature are all stable at small temperature differences. Increasing the temperature difference, the flow transition to an oscillatory flows occurs. The critical temperature difference, depending on the curvature of annulus, is determined. It was found that there is a good agreement between the simulation and the experiment results on the critical temperature difference. ©2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(4): 187– 197, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20157

Three-dimensional thermocapillary–buoyancy flow of silicone oil in a differentially heated annular pool

In order to understand the characteristics of thermocapillary–buoyancy flow, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary–buoyancy flow of 0.65cSt silicone oil (Prandtl number Pr = 6.7) in an annular pool with different depth ( d = 1–11 mm) heated from the outer wall (radius r o = 40 mm) and cooled at the inner cylinder ( r i = 20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions correspond to those in the experiments of Schwabe [D. Schwabe, Buoyant–thermocapillary and pure thermocapillary convective instabilities in Czochralski systems, J. Crystal Growth 237–239 (2002) 1849–1853]. Simulation results with large Marangoni number predict three types three-dimensional flow patterns. In the shallow thin pool ( d = 1 mm), the hydrothermal wave characterized by curved spokes is dominant. In the deep pools ( d ⩾ 5 mm) the three-dimensional stationary flow appears and this flow pattern corresponds to the Rayleigh-Benard instability, which consists of pairs of counter-rotating longitudinal rolls. When 2 mm ⩽ d ⩽ 4 mm, the hydrothermal wave and three-dimensional oscillatory flow coexist in the pool and travel along the same azimuthal direction with the same angular velocity. The critical conditions for the onset of three-dimensional flows were determined and compared with the experimental results. The characteristics of three-dimensional flows were discussed.

Influence of interfacial heat exchange on the flow organization in liquid bridge

The appearance and development of thermoconvective oscillatory flows in a cylindrical column with a free lateral surface (so-called liquid bridge) filled with 5 cSt silicone oil are investigated experimentally. The experiments were carried out under terrestrial conditions for a wide range of volumes of liquid bridges. Heat transfer from the interface changed the threshold of socillatory instabilities. The sensitivity of thermo-convective flows to the interfacial heat exchange was found to be strongly depending on the liquid bridge volume. Slender liquid bridges (under filled zone with respect to the straight cylinder) are rather stable to external disturbances. On the contrary, fat liquid bridges are extremely sensitive to the thermal environment in the gas phase.

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.

Hydrothermal waves in a liquid bridge with aspect ratio near the Rayleigh limit under microgravity

A 2 cSt silicone oil (Pr=28) liquid bridge of 15.0mm length L and 3.0mm radius r (aspect ratio A=L∕r=5) was established under microgravity during the flight of the sounding rocket MAXUS-4. Four different temperature differences ΔT=7, 9, 10, and 12K were applied between the ends, each for sufficient time to reach steady-state thermocapillary flow conditions. The aim of the experiment—to observe the onset of hydrothermal waves and to measure their features such as the wave phase speed and the angle between the wave vector and the applied temperature gradient—was reached. We used microgravity in this experiment in a twofold manner: (1) a liquid bridge with A=5 can be established only under microgravity; (2) it was possible to study hydrothermal waves without the influence of gravity and without the aspect ratio restrictions at normal gravity.

Hydrodynamic instabilities under microgravity in a differentially heated long liquid bridge with aspect ratio near the Rayleigh-limit: Experimental results

A liquid bridge of 15.0 mm length L and 3.0 mm radius r (aspect ratio A = L/r = 5) from 2 cSt silicone oil ( Pr = 28) was established under microgravity during the flight of the sounding rocket MAXUS-4. Four different temperature differences Δ T = 7, 9, 10, 12 K have been applied between the ends for sufficient time to reach steady state thermocapillary flow conditions. The aim of the experiment – to observe the onset of hydrothermal waves and to measure their features, like the waves phase speed and the angle between the wave vector and the applied temperature gradient – was reached. Moreover, we can report about the occurrence of a further hydrodynamic structure or instability occurring at the same time in this experiment, namely convection cells of the type of the Bénard–Marangoni instability, drifting in the surface flow from the hot towards the cold side. The latter instability has not been observed in the liquid bridges with A = 1 investigated normally, because of geometric restrictions. The Bénard–Marangoni instability is due to the cooling of the free liquid surface in our experiment.

Thermocapillary convection in a differentially heated annular pool for moderate Prandtl number fluid

In order to understand the nature of thermocapillary convection under microgravity in a differentially heated annular pool with the outer heated container of radius r o =40 mm and the inner cooled cylinder of r i =20 mm, and an adjustable depth d=3–14 mm, we conducted a series of unsteady two-dimensional numerical simulations with the finite volume method. The pool was filled with the 0.65cSt silicone oil (Prandtl number Pr=6.7). With a large enough temperature difference in the radial direction, the simulation can predict oscillatory thermocapillary flows. Hopf bifurcation neutral curve is delineated in the thermocapillary Reynolds number ( Re)-aspect ratio ( A=( r o − r i )/ d) plane. It is found that time-dependent motion is only possible if A exceeds a critical value A cri which is around 2.29. Streamline and isotherm patterns are presented at different thermocapillary Reynolds number and the aspect ratio corresponding to stationary and oscillatory states.

Three-dimensional numerical simulation of thermocapillary flow of moderate Prandtl number fluid in an annular pool

A series of unsteady three-dimensional numerical simulations were conducted for thermocapillary flow of 0.65 cSt silicone oil (Prandtl number Pr=6.7) in annular pools with different depths ( d=1–17 mm) heated from the outer wall (radius r o=40 mm) and cooled at the inner cylinder ( r i=20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions corresponded to those in the microgravity experiments of Schwabe and Benz (Adv. Space Res. 29 (2002) 629). A temperature difference between the outer and inner walls (Δ T) generates roll-cell thermocapillary flow. Simulations with large Δ T predicted two types of oscillatory thermocapillary flows. One is the hydrothermal wave with curved spokes, which is dominant only in shallow pools ( d=1–3 mm). The second one is dominant in deep pools ( d>3 mm) and is characterized by traveling straight spoke patterns in the azimuthal direction. Critical conditions for the onset of the oscillatory flow in liquid pools of different depths were determined. Details of the flow and temperature fields were discussed. Oscillation frequencies were compared with the experimental results as functions of Δ T and pool depth d. Quantitative agreements were obtained for small Δ T and shallow pools.

Effect of ambient conditions near the interface on flow instability

The appearance and the development of thermoconvective oscillatory flows are investigated experimentally and numerically in a liquid bridge (LB) filled by 10 cSt silicone oil ( Pr ≈ 108). The experiments were carried out under terrestrial conditions using the shielding of a liquid bridge. It allows to create different temperature distributions in the ambient gas near the interface. The 3-D numerical simulations have been done using parameters as close as possible to the experimental conditions. The dependence of viscosity upon temperature is taken into account. Both results are in an excellent agreement for the determination of the critical temperature difference. The different heat transfer possibilities at the free surface are analyzed.

Influence of Aspect Ratio on the Onset of ThermocapillaryOscillatory Convection in a Floating Half Zone of Large Prandtl NumberFluid

The onset of oscillatory thermocapillary convection in afloating half zone of 10 cst silicon oil (Prandtl number 105.6) isstudied by the three-dimensional and unsteady numerical simulation inmicrogravity environment (g = 10-4gearth). The results showthat the steady and axi-symmetric convection, for a fixed liquid bridgevolume ratio Vℓ/V0 = 1, transits directly to theoscillatory convection if geometrical aspect ratio A is largerthan the critical value Ac = 1.25, but transits to theoscillatory convection via the steady and non-axisymmetric flow ifA is smaller than the critical value Ac. The result means thatthere are two bifurcation transitions in a liquid bridge of the largePrandtl number fluid with a smaller aspect ratio A.

Protein separation and surfactant control of electroosmotic flow in poly(dimethylsiloxane)-coated capillaries and microchips

A thermally pyrolyzed poly(dimethylsiloxane) (PDMS) coating intended to prevent surface adsorption during capillary electrophoretic (CE) [Science 222 (1983) 266] separation of proteins, and to provide a substrate for surfactant adsorption for electroosmotic mobility control was prepared and evaluated. Coating fused-silica capillaries or glass microchip CE devices with a 1% solution of 100 cSt silicone oil in CH 2Cl 2, followed by forced N 2 drying and thermal curing at 400 °C for 30 min produced a cross-linked PDMS layer. Addition of 0.01 to 0.02% Brij 35 to a 0.020 M phosphate buffer gave separations of lysozyme, cytochrome c, RNase, and fluorescein-labeled goat anti-human IgG Fab fragment. Respective plates/m typically obtained at 20 kV (740 V cm −1) were 2, 1.5, 1.25, and 9.4·10 5. In 50 m M ionic strength phosphate, 0.01% Brij 35 running buffer, the electroosmotic flow observed was about 25% of that in a bare capillary, and showed no pH dependence between pH 6.3–8.2. Addition of sodium dodecylsulfate (SDS) or cetyltrimethylammonium bromide (CTAB) to this running buffer allowed ready control of electroosmotic mobility, μ eo. Concentrations of SDS between 0.005 to 0.1% resulted in μ eo ranging from 3 to 5·10 −4 cm 2 V −1 s −1. Addition of 1 to 2.3·10 −4% (2.7–6.3 μ M) CTAB caused flow reversal. CTAB concentrations between 3.5·10 −4 and 0.05% (0.0014–1.37 m M) allowed control of μ eo between −1·10 −4 and −5.0·10 −4 cm 2 V −1 s −1. For both surfactants the added presence of 0.01% Brij 35 provided slowly varying changes in μ eo with charged surfactant concentration.

Thermocapillary flow instabilities in an annulus under microgravity — results of the experiment magia

We investigated thermocapillary flow in an annular gap with outer heater container of radius R 1 = 40 mm and inner cooled cylinder of R 2 = 20 mm and with an adjustable height h, 2.5 ≤ h ≤ 20 mm. The gap was filled flat up to the rim with the 0.65 cSt silicone oil hexamethyldisiloxane (Prandtl number Pr = 6.7). The temperature differences ΔT, 0 K ≤ ΔT ≤ 40 K between outer and inner wall generated thermocapillary flow in the free upper surface and various flow structures have been observed under microgravity. We identified hydrothermal waves for small h and more complicated oscillations for larger h. For small h and small ΔT the multiroll structure was visible via IR-images of the free surface: concentric steady convection rolls with the same sense of rotation, embedded into the main thermocapillary roll. We measured the critical Marangoni number Ma c for the transition to time-dependent flow in the aspect ratio range A = h/(R 1 − R 2), 0.125 ≤ A ≤ 1, where it was virtually constant Ma c ≈ 5 · 10 4. We report and discuss a steady temperature asymmetry, changing its direction from time to time, as recorded by the IR-camera. This symmetry breaking is most probably due to slowly changing residual acceleration in the satellite.

Droplet sizing using silicone oils

The ISO standard protocol for determining size of droplets suspended between two layers of silicone oils of differing viscosity was evaluated in experiments using a monosize droplet generator. Cross-sectional areas of 0.27-nl droplets captured in silicone oils decreased linearly with time until droplets disappeared at 26 min after application. Rates of decrease in cross-sectional area of droplets were independent of droplet size (range 0.27–269 nl), but decreased as the gradient in water vapour concentration between droplet and ambient atmosphere decreased. Saturating silicone oils with water reduced rates of decrease in cross-sectional areas of droplets (−37%). Diffusion studies established that the amount of water diffusing through silicone oil increased linearly with time. Permeance to water vapour was inversely related to thickness of the oil layer. Permeability coefficients averaged 45.8×10 −9 and 29.5×10 −9 m 2 s −1 for low- (9.6 cSt) and high-viscosity (10 350 cSt) silicone oil and were up to 52-fold higher than for mineral oils of comparable viscosity. Our data suggest that the high water vapour permeability of silicone oil and the solubility of water in silicone oil accounted for the decrease in size of droplets captured in silicone oil. Based on our findings, the ISO standard protocol should be modified to correct for these effects.

Convection in a Czochralski crucible – Part 1: non-rotating crystal

A Czochralski melt is simulated in a model experiment and by numerical analysis. We use a transparent fluid (0.65 cSt silicone oil with Pr=6.8) which is contained in a transparent sapphire crucible (40 mm inner diameter, 40 mm height, crystalline material). A copper rod (e.g. 14 mm diameter) is used to simulate the growing crystal. An imposed temperature difference between the crucible and the crystal dummy gives rise to convective flow in the fluid. Forced convection by crystal rotation has also been applied but will be treated in part 2 of this paper. Our experiment models to a good degree the growth of oxide and fluoride crystals from noble metal crucibles. Flow visualization and flow velocity measurements are performed. We report the flow patterns observed in the fluid for different parameters (temperature difference, fluid depth, meniscus, free surface cooling). We observe a separated surface tension driven convection roll at the free surface and a “cold jet” beneath the crystal dummy. The flow is strongly affected by thermocapillary forces. The experimental results can be used as benchmarks to test numerical simulation programs for Czochralski growth. Numerical simulations are performed (2D, steady, axisymmetric). The simulation results compare favorably with the experimental data. In a parametric numerical study the relative importance of thermocapillary and buoyant forces is investigated.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection: III. Three-dimensional model

An unsteady and three-dimensional model of the floating-half-zone convection on the ground is studied by the direct numerical simulation for the medium of 10 cSt silicon oil, and the influence of the liquid bridge volume on the critical applied temperature difference is especially discussed. The marginal curves for the onset of oscillation are separated into two branches related, respectively, to the slender liquid bridge and the fat liquid bridge. The oscillatory features of the floating-half-zone convection are also discussed.

The Bénard-Marangoni-Instability in small circular containers under microgravity: Experimental results

During the 12-minute microgravity-phase of the sounding rocket MAXUS 2 a 3.0-mm-thick layer of 10 cSt silicone oil was heated from below to generate the Bénard-Marangoni-Instability (BMI) due to surface tension forces in the free oil surface. The layer was partly covered with a solid lid from Polycarbonate (LEXAN) with circular openings with diameter D for a flat free oil surface with aspect ratio A= D/d= 1.0, 1.5, 2.0, 3.0, 4.0, 8.0, 10.0. The flow structure in these 7 “containers” with liquid lateral walls was visualized by aluminum flakes which orient parallel to the flow direction. The BMI was clearly observed under microgravity, and the onset of convection as function of A was measured and compared to theory and ground-based experiments, of which the latter suffer under the additional action of buoyancy. Beautiful and sharp convection patterns have been observed in the containers A = 4, 8, and 10. At the end of the microgravity time an instability of the boundary between two convection cells in the container with A= 4 was observed (switching between modes (2,1) and (1,1)).

A Thermocapillary Convection Experiment in Microgravity

Results are reported of the Surface Tension Driven Convection Experiment (STDCE) aboard the USML-1 Spacelab, which was launched on June 25, 1992. In the experiment, 10 cSt silicone oil was placed in an open 10-cm-dia circular container, which was 5 cm deep. The fluid was heated either by a cylinderical heater (1.11 cm diameter) located along the container centerline or by a CO2 laser beam to induce thermocapillary flow. Several thermistor probes were placed in the fluid to measure the temperature distribution. The temperature distribution along the liquid-free surface was measured by an infrared imager. Tests were conducted over a range of heating powers, laser-beam diameters, and free surface shapes. An extensive numerical modeling of the flow was conducted in conjunction with the experiments. Some results of the temperature measurements with flat free surfaces are presented in this paper and they are shown to agree well with the numerical predictions.

Analysis of velocity data taken in Surface Tension Driven Convection Experiment in microgravity

Some velocity field results from the Surface Tension Driven Convection Experiment (STDCE) that was conducted aboard the USML-1 Spacelab in 1992 are reported. 10 cSt silicone oil was placed in an open circular container (10 cm wide×5 cm deep) and heated either by a cylindrical heater (1.11 cm diam) placed along the centerline or by a CO2 laser to induce thermocapillary flow. Tests were conducted under varieties of powers, laser beam diameters, and free-surface shapes. The flow field was studied by flow visualization and the data were analyzed by a PIV technique. The results from the velocity measurement are presented and the effects of heating mode and free-surface shape on the flow are discussed. The results are also compared with a numerical analysis conducted in conjunction with the experiment. Good agreement is shown.