- Email: [email protected]
Gravity
David Brutin and Florian Carle Mechanical Engineering Department, Aix-Marseille University, Marseille, France
Chapter 25
GRAVITY
The formation of droplets happens constantly on Earth, whether it is a natural phenomenon or the result of human activity. However, creating a droplet under reduced gravity conditions is different. How can the droplet be deposited onto the substrate when the fluid floats in the test cell and when the scientist floats around his experiment? This chapter discusses how to bypass the disadvantages of weightlessness and use the advantages of microgravity; it also present a few studies performed under hypergravity using a centrifuge.
25.1 Access to reduced gravity conditions Nature is governed by four fundamental interactions: strong nuclear interactions, weak nuclear interactions, electromagnetism, and gravitational forces. This last interaction, despite being the weakest of all, makes all physical bodies attract one another in proportion to their mass. The first consequence of this interaction is the weight P that can be directly felt from Earth. Here, we Droplet Wetting and Evaporation. DOI: http://dx.doi.org/10.1016/B978-0-12-800722-8.00025-4 © 2015 Elsevier Inc. All rights reserved.
383
384 Droplet Wetting and Evaporation disregard all interactions from other astronomical objects—the sun, the moon— and objects on Earth: mearth Um P 5 mUg 5 GC 2 ð25:1Þ Rearth GC 5 6.67 10211 N m2 kg22 is Cavendish’s constant, m is the object/Earth mass, and Rearth is Earth’s radius (approximately 6370 km). Microgravity, also misleadingly called zero-gravity, is a state in which a body (object or human) is no longer under the influence of contact forces, only body forces. The notion of weightlessness comes from the fact that mass is not a parameter that influences the fall. As shown by Galileo in his legendary experiment from the top of the Leaning Tower of Pisa around 1604, two objects with different masses will fall at the same speed if the air friction is similar for the two bodies. This experiment has been reproduced by David Scott in 1971 on the moon surface with a feather and a hammer during the Apollo 15 mission in the vacuum of space, which lacks air friction. After a fall of 1.2 s, the two objects touched the floor at the exact same time, confirming Galileo’s theory that bodies fall with a uniform acceleration without any influence of mass. The more obvious way to experience a microgravity state is to go to the International Space Station (ISS) as it orbits around Earth. However, microgravity is often misunderstood. This state does not mean that the object has no weight. At the orbit apogee, the 450,000 kg payload of the ISS is 426 km from Earth’s surface. From Eq. (25.1), one can derive Eq. (25.2), where mearth UmISS PISS 5 GC ð25:2Þ ðRearth 1DISS Þ2 Therefore, the ISS weight is only reduced by 6.2%; it still weighs 421,700 kg at its farthest point from Earth. Earth’s gravity is constantly pulling objects toward the surface, causing them to fall. If an object is thrown into the gravity field, its trajectory will be curved, and the object will hit the surface rather quickly. However, if the initial speed is great enough to fall into a trajectory that matches Earth’s curvature, the fall is perpetual, and the microgravity state can theoretically last forever. The ISS speed is approximately 7.66 km s21, or 27,600 km h21, and a fall of only 4.9 m for each 8000 m traversed horizontally can be perpetual. All of the objects and the crew inside the station fall at the same speed, and they therefore appear to be floating relative to one another in the ISS frame of reference. Although critics of microgravity science argue that the experiments are extremely costly, microgravity experiments are a unique way to study phenomena that are usually hidden under normal gravity conditions. Microgravity environments are obviously particularly suited for space applications such as astronaut training, antenna deployment, or ISS experiment preparation. It is absolutely essential to test and validate all of the technical solutions before launching the experiments on satellites or on the space station. This work is done by all space agencies (ESA, NASA, CNES, JAXA, DLR, CNSA) that finance research
Gravity 385 activities onboard the ISS, rockets, scientific satellites, and so on. But space science starts on Earth with ground-based research to prepare space experiments. All of this preparation is a great way to conduct high-quality fundamental research that cannot be done on Earth. Biomedical experiments are performed on future astronauts and human guinea pigs to learn how microgravity affects concentration and reaction time, blood flow, vision, displacement, and orientation, because top and bottom notions are not relevant under reduced gravity levels. These experiments allow us to have a better understanding of the human body and its mechanisms of adaptation to new conditions. Most of the time, the results are used to develop techniques and medications for the general public (McGuckin et al., 2005). The microgravity state in droplets is also interesting because of the flow motion and instabilities that appear during evaporation. Hydrodynamic instabilities correspond to bifurcations that develop when a controlled parameter such as temperature gradient or geometry deviates from the threshold value. Several parameters can induce instabilities, so the flow motion inside the droplet is the result of several instabilities happening at the same time. Microgravity is useful for separating several phenomena and observing only one type of instability, such as the hydrothermal waves that appear due to surface tension gradients but are usually hidden by thermogravitational flow. All of the technology and knowledge obtained through microgravity experiments are, in the long run, reused for applications on Earth, such as satellite navigation systems, communication and data transmission, and optics and ophthalmology. In addition to all of these direct applications, the skills and expertise developed during space conquest are reused for applications on Earth, such as the space pen, nonstick coating in frying pans, and UV protection on sunglasses. Launching an experiment in the ISS is extremely costly and time consuming. It takes more than 3 years to design an experiment and bring it onboard. Under the same constraints, scientific satellites provide a microgravity environment that is as good as the space station for periods ranging from 10 to 15 days. However, the chances of getting access to satellite facilities are slim. Fortunately, there are other ways to access microgravity on Earth (Figure 25.1). Halfway to space, sounding rockets are regularly launched from uninhabited areas, and they create 312 min of microgravity in low orbits (below 200 km) before reentering the atmosphere and landing with a parachute for recovery. The small portions of orbits that sounding rockets follow are strongly elliptical due to the initial speed (orbit conjugal diameter can be less than 80 km). The payload in which the experiments run is in constant telemetric link with the researchers, allowing them to monitor the experiments and to collect data so that it is not lost in the case of a crash during the return to Earth. The only way to create a microgravity environment on Earth is to use a drop tower. The experiment is set up in a drag shield and dropped from the top of the tower. The tower height h is directly pffiffiffiffiffiffiffiffiffiffi linked to the duration t of the microgravity phase ðtμg 5 2h=gÞ to the 20 m Brisbane drop tower gives about 2 s, whereas the 146 m ZARM vacuum drop
Gravity level compared to earth gravity
386 Droplet Wetting and Evaporation
Parabolic flight 10–2g 10–3g
Sounding rocket International Space Station
10–4g 10–5g
Drop tower
Satellite
10–6g 10 s
22 s
3 min
12 min
10 days 15 days
6 months
Microgravity duration
FIGURE 25.1 Access to reduced gravity levels through various platforms. Figure inspired from ESA website (Carle, 2014).
tower in Bremen allows up to 5.3 s in free fall and 9.3 s with a catapult phase before the drop. These facilities, among others, have the lowest gravity levels (1025g) and the shortest conception time from design to drop in a few months. However, the phenomena that are studied must have very short transition phases in order to benefit from the microgravity phase. The decelerations during landing (involving an air bag), fine polystyrene pellets, or electromagnetic brakes are strong, and the experiment needs to resist up to 30g for catapulted experiments.
25.2 Droplets under reduced gravity conditions 25.2.1 PARABOLIC FLIGHTS Among the tools just mentioned to access reduced gravity conditions, parabolic flights are the most convenient in terms of project duration, cost, and research manipulation. Several papers have been written about spherical tiny droplets’ evaporation of volatile liquids for combustion experiments. A few papers deal with sessile droplets’ wetting and evaporating. In 2009, Brutin et al. performed experiments on sessile drop creation in microgravity. They focused on the droplets’ contact angle and droplet interface in relation to gravity levels. They observed that under terrestrial gravity and hypergravity, the contact angle increased to reach a constant value from small droplets to big drops; they also evidenced in microgravity a different behavior with almost a constant contact angle that was very sensitive to the gravity level, even for small drops with a diameter smaller than the capillary length. On the drop creation, the authors confirmed the feasibility of creating posed drops under microgravity conditions even with low surface tension fluids such as FC-72 and HFE-7100 (below 10 mN m21). Two different contacts angles were
Gravity 387 evidenced considering water droplet creation: if the drop is created under normal gravity, then put under microgravity, or is created during the microgravity phase. The contact angle can be 10 lower compared to the same drop created in microgravity. The authors explained these differences. Among these explanations was the presence of gas trapped in the substrate roughness below the drop and physicochemical interactions. Also, a possible explanation for the change in drop contact angle can be found in the drop pressure change through the gravitational pressure. The droplet interface equation is given by a pressure balance (Eq. 25.3). At the hydrostatic equilibrium, the overpressure inside the drop is given by the balance of the Laplace pressure and the hydrostatic pressure: 2 dz 1 dz P0 2 ρgz 5 σ 1 ð25:3Þ dx2 x dx qffiffiffiffi σ is the capillary length and P0 is the pressure at the top of the where Lc 5 ρg drop. The equation to obtain the interface profile is solved in polar coordinate. Two parameters are used to solve numerically Eq. (25.3): the pressure at the top of the drop (P0) and the drop contact angle (θ). These two parameters have to be modified to verify the two other physical parameters: the drop base diameter and the drop height. Consequently, a drop contact angle is obtained. Based on the images obtained for three gravity levels during the parabolic flight, we extract the experimental drop interfaces and plot them on Figure 25.2. 1.0 0.9 0.8
θ = 84°
0.7
θ = 83° h/R0
0.6 0.5 0.4
θ = 76° Experiments (μg) Experiments (1g) Experiments (1.8g) Model (μg) Model (1g) Model (1.8g)
0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 R/R0
0.6
0.7
0.8
0.9
1.0
FIGURE 25.2 Normalized droplet height variation for three levels of gravity compared to the Laplace-hydrostatic model (water, Teflon, R0 5 4 mm).
388 Droplet Wetting and Evaporation The contact angles obtained for these 8-mm diameter droplets are 85.3 in microgravity, 93.4 under normal gravity, and 89.5 under hypergravity. On the same figure, we plot the drop interface modeled using the Laplace-hydrostatic equation. We successfully predict all three drop interfaces within the error margin, and we obtain for the contact angle 84.0 in microgravity, 83.0 under normal gravity, and 76.0 under hypergravity. This increasing variation in the contact angle with decreasing gravity level is in accordance with the Laplace-hydrostatic equilibrium. We obtain a good agreement for the contact angle only in microgravity. When gravity exists, a gap of more than 10 exists. This is attributed to the difficult repeatability of contact angle experiments with gravity fluctuation and plane vibrations. After the experiments on wetting, the same team studied the evaporation stage. Brutin et al. (2010) and Carle et al. (2012) presented results obtained during a parabolic flight campaign observing ethanol sessile drop evaporation under microgravity conditions. Droplets were created using a syringe pump by injection through a substrate. The droplets were recorded using both a video camera and an infrared camera. The experimental setup enables the simultaneous visualization in the infrared and the visible wavelengths and also allows access to the heat-flux density transferred to the droplet using a heat-flux meter. The authors evidenced the different stages observed in reduced gravity when the droplets evaporate. The first phase (a) of the experiment is a phase of hypergravity at 1.8g. The substrate is dry at the set temperature. The flux measured by the heat-flux meter during this phase corresponds to the loss by natural convection from a horizontal flat plate at 1.8g (approximately 200 W m22). A microgravity phase follows this hypergravity phase. At t 5 0 s, a droplet is created by the injection of the fluid, and a transition regime is observed. The substrate temperature decreases rapidly by approximately 2 C, and the heat flux increases to 1500 W m22. These changes are caused by the warming of the droplet coupled with the spreading of the liquid on the substrate. This transitional phase lasts between 5 and 8 s. After the quasistationary regime is reached (phase c), we observe that these two variables (temperature and heat-flux) remain constant. The limiting phenomenon of evaporation, for a conductive substrate, is the vapor diffusion into the atmosphere (David et al., 2007). The evolution of the evaporation mass flow rate is consistent with the theoretical model of quasi-steady diffusion-driven evaporation implemented with the temperature variation. During the evaporation, thermo-capillary instabilities develop. Figure 25.3 shows the hydrothermal waves (HTWs) on two droplets with similar diameters (R1g 5 2.81 mm and Rμg 5 2.77 mm) that are evaporating on equally heated substrates (TS 5 35 C) under two levels of gravity. In both cases, the droplets of ethanol are hemispherical, and the initial contact angles (θi) are less than 40 . Utilizing the work of Garnier et al. (2006), the two cases can be compared using
Gravity 389 (A)
(B) 5 mm
5 mm
HTWs Apex HTWs
Triple line
FIGURE 25.3 Infrared visualization of ethanol droplets under normal gravity (A) and reduced gravity (B) (normal gravity (TS 5 35 C; P 5 1013: 25 mbar; R1g 5 2.81 mm), and reduced gravity (TS 5 35 C; P 5 835 mbar; Rμg 5 2.77 mm)).
characteristic dimensionless numbers. The Rayleigh number, representing the buoyancy forces, is compared to the Marangoni number, representing the thermocapillary forces. In both cases shown, buoyancy forces are quite small, allowing the thermo-capillarity effect to dominate. In this configuration, the instabilities that develop are of type hydrothermal waves 2 (HTW2). The use of a microgravity environment induces a 113-fold decrease in the static Bond number and a 74-fold decrease in the dynamic Bond number. Under normal gravity, the thermo-convective effects are dominated by the thermo-capillary ones but are not negligible (Bd1g 5 Ra 5 Ma 0.08), whereas under microgravity, only the thermocapillary effects exist (Bdµg 5 0.001). Under normal gravity, a temperature gradient develops during the evaporation from the apex of the droplet and the contact line, resulting in a gradient of surface tension. This gradient then generates the thermo-capillary instabilities. These HTWs propagate radially around the apex, where most of the evaporation occurs. The HTWs are spaced by an almost constant angle along the axial symmetry of the triple line. Two different spatial dynamics were observed. The HTWs were found to run orthoradially around the edge of the droplet, either from a source point where they are established to a well where they collapse or all in the same direction but with no preferred direction (clockwise or counterclockwise), depending on the temperature of the substrate and the height of the droplet (Sobac and Brutin, 2011). Under microgravity, the temperature gradient is not as well defined as it is under normal gravity, but the apex maintains a temperature below the temperature of the triple line. In this configuration, HTWs have the same trend, but their movements are not as systematic as they are under normal gravity. The instabilities develop during the transitional phase. During the quasi-stationary regime, the HTWs propagate from a
390 Droplet Wetting and Evaporation source point to a well. These instabilities also propagate on the edge of the droplet, but the angle of propagation is not as constant as it is under normal gravity. This change in propagation could be caused by the vibrations of the aircraft, which cause significant fluctuations in the level of microgravity. Despite this lack of stability, the evolution of the number of HTWs is similar under both gravitational conditions.
25.2.2 DROP TOWER Several drop towers exist over the world (including Germany, Australia, Japan, and Spain). The one used here is in Brisbane, Australia, at the Queensland University of Technology (QUT). The QUT drop tower facility enables testing for 2 s in reduced gravity. The experimental rack is contained inside a drag shield, and both are raised to the top of the tower and suspended by a single thin metal wire. The facility incorporates a simple wire cutting release mechanism to initiate the drop of the experimental rack independently from the drag shield at the same instance. The drag shield and experiment are caught by an airbag mechanism, where release vents allow for high-pressure air release during impact in order to reduce peak deceleration levels. A network of bungee cords and ropes are used to provide horizontal stability to the drag shield during deceleration. The experimental rack experiences typical levels of reduced gravity around 1025g. Diana et al. (2012) observed that the droplet shape is adequately described by the YoungLaplace equation in using the drop tower facility, whereby a variation occurred in the diameter and height upon the surface energy to obtain the lowest free energy shape (sphere-like). The dimensional variations showed that an increase in the Bond number correlated well with the change in the wetted diameter and the height of the droplet (Figure 25.4). The triple-line perimeters of the drops were observed to be lower in reduced gravity than in normal gravity, and differences in contact angle were observed between these two different gravity environments and do not seem well described by theory. The YoungLaplace equation, therefore, can be used to determine the contact angle in reduced gravity
FIGURE 25.4 Digital image of sessile drops of water in normal gravity exhibiting various diameters (different Bond numbers). (A) corresponds to a Bond number of less than 1 (diameter less than capillary length), (B) corresponds to a Bond number of about 1 that is equal to the capillary length), and (C) corresponds to a Bond number greater than 1 (diameter greater than the capillary length). Images from Diana et al. (2012).
Gravity 391 for small droplets, but it was not optimal for describing the contact angle for larger drops (above the drops’ associated capillary length). Because hysteresis is the result of the drop pinning due to roughness, one could consider whether the hysteresis is affected by the microgravity conditions. The way in which the roughness affects the contact angle also could be gravitydependent. In fact, weightlessness could promote the droplet liftoff (Wenzel versus CassieBaxter behavior) in the case where one assumes some air pockets are trapped at the rough solidliquid surface.
25.3 Increased gravity conditions Increased gravity conditions are investigated using centrifuge. Experimental results on the dynamics of sessile water drops are presented by Kabov and Zaitsev (2013) and Kabov et al. (2014). They performed experiments under normal gravity (1g), microgravity (μg), and hypergravity (up to 20g). The microgravity experiments were conducted during the parabolic flights of the European Space Agency (ESA). The hypergravity experiments were carried out on the ESA large diameter centrifuge. The objective was to study the effect of the gravity on (i) the shape of a static sessile drop and (ii) the dynamic advancing contact angle in a growing sessile drop (Figure 25.5). Different smooth and rough surfaces were used, with different contact angles and different contact angle hysteresis. Water was used for the working liquid. The main variable parameters were gravity (μg20g); drop volume (1 µL5 mL); liquid flow rate (0.0616 mL min21); and contact angle (30 130 ). The drop shape was visualized from the top with the help of the Phase Schlieren System and from the side with the help of the shadow technique with resolution of 6 µm pix21. The spreading of a sessile liquid drop under the influence of gravity was observed experimentally on surfaces with relatively low contact angle hysteresis (,15 ) (A) 1 mm
1g
(B) μg
1 mm
μg
1g
1.8g 1.8g
FIGURE 25.5 Parabolic flight experiments, static drop gravity effect on drop shape. (A) 0.146 mL water drop on Teflon surface (contact angle hysteresis is 12.6 ). (B) 0.313 mL water drop on polyvinylacetate (contact angle hysteresis is 34.5 ). From Kabov et al. (2014).
392 Droplet Wetting and Evaporation 120 1.8g Advancing contact angle (°)
100 μg
80
μg
1.8g
60 40 20 0 0
0.5
1
1.5
2 Time (s)
2.5
3
3.5
4
FIGURE 25.6 Parabolic flights experiments, dynamic drop. Dynamic advancing contact angle versus time in growing water drop on copper surface under different gravity levels. Flow rate is 1 mL min21. Shown are 16 µL drops. From Kabov et al. (2014).
(Figure 25.6). In this case good agreement is obtained between the experiment data and modeling (Picknett and Bexon, 1977) with assumption of constant contact angle. For surfaces with relatively high contact angle hysteresis (.30 ), the contact line is pinned while the contact angle adjusts for different gravity levels (Figure 25.6). The dynamic advancing contact angle was found to increase with the gravity.
References Bartashevich, M.V., Kuznetsov, V.V., Kabov, O.A., 2010. Gravity effect on the axisymmetric drop spreading. Microgravity Sci. Technol. 22 (1), 107114. Brutin, D., Zhu, Z.Q., Rahli, O., Xie, J.-C., Liu, Q.-S., Tadrist, L., 2009. Sessile drop in microgravity: creation, contact angle and interface. Microgravity Sci. Technol. 21 (Suppl. 1), 6776. Brutin, D., Zhu, Z.Q., Rahli, O., Xie, J.-C., Liu, Q.-S., Tadrist, L., 2010. Evaporation of ethanol drops on a heated substrate under microgravity conditions. Microgravity Sci. Technol. 22, 387395. Carle F., 2014. Flow Motion in Sessile Droplets: Evaporation and Nanoparticles Assembly (Ph.D. thesis). Aix-Marseille University. Carle, F., Sobac, B., Brutin, D., 2012. Hydrothermal waves on ethanol droplets evaporating under terrestrial and reduced gravity levels. J. Fluid Mech. 712, 614623. David, S., Sefiane, K., Tadrist, L., 2007. Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids and Surfaces A 298, 108114.
Gravity 393 Diana, A., Castillo, M., Brutin, D., Steinberg, T., 2012. Sessile drop wettability in normal and reduced gravity. Microgravity Sci. Technol. 24, 195202. Garnier, N., Chiffaudel, A., Daviaud, F., 2006. Hydrothermal waves in a disk of fluid. In: Mutabazi, I., Wesfreid, J.E., Guyon, E. (Eds.), Dynamics of spatio-temporal cellular structures: Henri Be´nard centenary review, vol. 207. Springer, pp. 147161. Kabov, O.A., Zaitsev, D.V., 2013. The effect of wetting hysteresis on drop spreading under gravity. Doklady Phys. 58 (7), 292295. Kabov, O., Zaitsev, D., Gatapova, E., Semenov, A., Bykovskaya, E., Karnauhova, E., et al. (2014). Drop spreading and evaporation on a heated substrate under variable gravity conditions. In: Proceedings of the 15th International Heat Transfer Conference, IHTC-15, August 1015, 2014, Kyoto, Japan. Paper # IHTC15-9504. McGuckin, C.P., Forraz, N., Baradez, M.-O., Navran, S., Zhao, J., Urban, R., Tilton, R., Denner, L., 2005. Production of stem cells with embryonic characteristics from human umbilical cord blood. Cell Prolif. 38 (4), 245255. Picknett, R.G., Bexon, R., 1977. The evaporation of sessile or pendant drops in still air. Journal Colloid Interface Science 61, 336350. Sobac, B., Brutin, D., 2011. Triple-line behavior and wettability controlled by nano-coated substrates: Influence on sessile drop evaporation. Langmuir 27, 1499915007.
Chapter 25
GRAVITY
The formation of droplets happens constantly on Earth, whether it is a natural phenomenon or the result of human activity. However, creating a droplet under reduced gravity conditions is different. How can the droplet be deposited onto the substrate when the fluid floats in the test cell and when the scientist floats around his experiment? This chapter discusses how to bypass the disadvantages of weightlessness and use the advantages of microgravity; it also present a few studies performed under hypergravity using a centrifuge.
25.1 Access to reduced gravity conditions Nature is governed by four fundamental interactions: strong nuclear interactions, weak nuclear interactions, electromagnetism, and gravitational forces. This last interaction, despite being the weakest of all, makes all physical bodies attract one another in proportion to their mass. The first consequence of this interaction is the weight P that can be directly felt from Earth. Here, we Droplet Wetting and Evaporation. DOI: http://dx.doi.org/10.1016/B978-0-12-800722-8.00025-4 © 2015 Elsevier Inc. All rights reserved.
383
384 Droplet Wetting and Evaporation disregard all interactions from other astronomical objects—the sun, the moon— and objects on Earth: mearth Um P 5 mUg 5 GC 2 ð25:1Þ Rearth GC 5 6.67 10211 N m2 kg22 is Cavendish’s constant, m is the object/Earth mass, and Rearth is Earth’s radius (approximately 6370 km). Microgravity, also misleadingly called zero-gravity, is a state in which a body (object or human) is no longer under the influence of contact forces, only body forces. The notion of weightlessness comes from the fact that mass is not a parameter that influences the fall. As shown by Galileo in his legendary experiment from the top of the Leaning Tower of Pisa around 1604, two objects with different masses will fall at the same speed if the air friction is similar for the two bodies. This experiment has been reproduced by David Scott in 1971 on the moon surface with a feather and a hammer during the Apollo 15 mission in the vacuum of space, which lacks air friction. After a fall of 1.2 s, the two objects touched the floor at the exact same time, confirming Galileo’s theory that bodies fall with a uniform acceleration without any influence of mass. The more obvious way to experience a microgravity state is to go to the International Space Station (ISS) as it orbits around Earth. However, microgravity is often misunderstood. This state does not mean that the object has no weight. At the orbit apogee, the 450,000 kg payload of the ISS is 426 km from Earth’s surface. From Eq. (25.1), one can derive Eq. (25.2), where mearth UmISS PISS 5 GC ð25:2Þ ðRearth 1DISS Þ2 Therefore, the ISS weight is only reduced by 6.2%; it still weighs 421,700 kg at its farthest point from Earth. Earth’s gravity is constantly pulling objects toward the surface, causing them to fall. If an object is thrown into the gravity field, its trajectory will be curved, and the object will hit the surface rather quickly. However, if the initial speed is great enough to fall into a trajectory that matches Earth’s curvature, the fall is perpetual, and the microgravity state can theoretically last forever. The ISS speed is approximately 7.66 km s21, or 27,600 km h21, and a fall of only 4.9 m for each 8000 m traversed horizontally can be perpetual. All of the objects and the crew inside the station fall at the same speed, and they therefore appear to be floating relative to one another in the ISS frame of reference. Although critics of microgravity science argue that the experiments are extremely costly, microgravity experiments are a unique way to study phenomena that are usually hidden under normal gravity conditions. Microgravity environments are obviously particularly suited for space applications such as astronaut training, antenna deployment, or ISS experiment preparation. It is absolutely essential to test and validate all of the technical solutions before launching the experiments on satellites or on the space station. This work is done by all space agencies (ESA, NASA, CNES, JAXA, DLR, CNSA) that finance research
Gravity 385 activities onboard the ISS, rockets, scientific satellites, and so on. But space science starts on Earth with ground-based research to prepare space experiments. All of this preparation is a great way to conduct high-quality fundamental research that cannot be done on Earth. Biomedical experiments are performed on future astronauts and human guinea pigs to learn how microgravity affects concentration and reaction time, blood flow, vision, displacement, and orientation, because top and bottom notions are not relevant under reduced gravity levels. These experiments allow us to have a better understanding of the human body and its mechanisms of adaptation to new conditions. Most of the time, the results are used to develop techniques and medications for the general public (McGuckin et al., 2005). The microgravity state in droplets is also interesting because of the flow motion and instabilities that appear during evaporation. Hydrodynamic instabilities correspond to bifurcations that develop when a controlled parameter such as temperature gradient or geometry deviates from the threshold value. Several parameters can induce instabilities, so the flow motion inside the droplet is the result of several instabilities happening at the same time. Microgravity is useful for separating several phenomena and observing only one type of instability, such as the hydrothermal waves that appear due to surface tension gradients but are usually hidden by thermogravitational flow. All of the technology and knowledge obtained through microgravity experiments are, in the long run, reused for applications on Earth, such as satellite navigation systems, communication and data transmission, and optics and ophthalmology. In addition to all of these direct applications, the skills and expertise developed during space conquest are reused for applications on Earth, such as the space pen, nonstick coating in frying pans, and UV protection on sunglasses. Launching an experiment in the ISS is extremely costly and time consuming. It takes more than 3 years to design an experiment and bring it onboard. Under the same constraints, scientific satellites provide a microgravity environment that is as good as the space station for periods ranging from 10 to 15 days. However, the chances of getting access to satellite facilities are slim. Fortunately, there are other ways to access microgravity on Earth (Figure 25.1). Halfway to space, sounding rockets are regularly launched from uninhabited areas, and they create 312 min of microgravity in low orbits (below 200 km) before reentering the atmosphere and landing with a parachute for recovery. The small portions of orbits that sounding rockets follow are strongly elliptical due to the initial speed (orbit conjugal diameter can be less than 80 km). The payload in which the experiments run is in constant telemetric link with the researchers, allowing them to monitor the experiments and to collect data so that it is not lost in the case of a crash during the return to Earth. The only way to create a microgravity environment on Earth is to use a drop tower. The experiment is set up in a drag shield and dropped from the top of the tower. The tower height h is directly pffiffiffiffiffiffiffiffiffiffi linked to the duration t of the microgravity phase ðtμg 5 2h=gÞ to the 20 m Brisbane drop tower gives about 2 s, whereas the 146 m ZARM vacuum drop
Gravity level compared to earth gravity
386 Droplet Wetting and Evaporation
Parabolic flight 10–2g 10–3g
Sounding rocket International Space Station
10–4g 10–5g
Drop tower
Satellite
10–6g 10 s
22 s
3 min
12 min
10 days 15 days
6 months
Microgravity duration
FIGURE 25.1 Access to reduced gravity levels through various platforms. Figure inspired from ESA website (Carle, 2014).
tower in Bremen allows up to 5.3 s in free fall and 9.3 s with a catapult phase before the drop. These facilities, among others, have the lowest gravity levels (1025g) and the shortest conception time from design to drop in a few months. However, the phenomena that are studied must have very short transition phases in order to benefit from the microgravity phase. The decelerations during landing (involving an air bag), fine polystyrene pellets, or electromagnetic brakes are strong, and the experiment needs to resist up to 30g for catapulted experiments.
25.2 Droplets under reduced gravity conditions 25.2.1 PARABOLIC FLIGHTS Among the tools just mentioned to access reduced gravity conditions, parabolic flights are the most convenient in terms of project duration, cost, and research manipulation. Several papers have been written about spherical tiny droplets’ evaporation of volatile liquids for combustion experiments. A few papers deal with sessile droplets’ wetting and evaporating. In 2009, Brutin et al. performed experiments on sessile drop creation in microgravity. They focused on the droplets’ contact angle and droplet interface in relation to gravity levels. They observed that under terrestrial gravity and hypergravity, the contact angle increased to reach a constant value from small droplets to big drops; they also evidenced in microgravity a different behavior with almost a constant contact angle that was very sensitive to the gravity level, even for small drops with a diameter smaller than the capillary length. On the drop creation, the authors confirmed the feasibility of creating posed drops under microgravity conditions even with low surface tension fluids such as FC-72 and HFE-7100 (below 10 mN m21). Two different contacts angles were
Gravity 387 evidenced considering water droplet creation: if the drop is created under normal gravity, then put under microgravity, or is created during the microgravity phase. The contact angle can be 10 lower compared to the same drop created in microgravity. The authors explained these differences. Among these explanations was the presence of gas trapped in the substrate roughness below the drop and physicochemical interactions. Also, a possible explanation for the change in drop contact angle can be found in the drop pressure change through the gravitational pressure. The droplet interface equation is given by a pressure balance (Eq. 25.3). At the hydrostatic equilibrium, the overpressure inside the drop is given by the balance of the Laplace pressure and the hydrostatic pressure: 2 dz 1 dz P0 2 ρgz 5 σ 1 ð25:3Þ dx2 x dx qffiffiffiffi σ is the capillary length and P0 is the pressure at the top of the where Lc 5 ρg drop. The equation to obtain the interface profile is solved in polar coordinate. Two parameters are used to solve numerically Eq. (25.3): the pressure at the top of the drop (P0) and the drop contact angle (θ). These two parameters have to be modified to verify the two other physical parameters: the drop base diameter and the drop height. Consequently, a drop contact angle is obtained. Based on the images obtained for three gravity levels during the parabolic flight, we extract the experimental drop interfaces and plot them on Figure 25.2. 1.0 0.9 0.8
θ = 84°
0.7
θ = 83° h/R0
0.6 0.5 0.4
θ = 76° Experiments (μg) Experiments (1g) Experiments (1.8g) Model (μg) Model (1g) Model (1.8g)
0.3 0.2 0.1 0.0 0.0
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FIGURE 25.2 Normalized droplet height variation for three levels of gravity compared to the Laplace-hydrostatic model (water, Teflon, R0 5 4 mm).
388 Droplet Wetting and Evaporation The contact angles obtained for these 8-mm diameter droplets are 85.3 in microgravity, 93.4 under normal gravity, and 89.5 under hypergravity. On the same figure, we plot the drop interface modeled using the Laplace-hydrostatic equation. We successfully predict all three drop interfaces within the error margin, and we obtain for the contact angle 84.0 in microgravity, 83.0 under normal gravity, and 76.0 under hypergravity. This increasing variation in the contact angle with decreasing gravity level is in accordance with the Laplace-hydrostatic equilibrium. We obtain a good agreement for the contact angle only in microgravity. When gravity exists, a gap of more than 10 exists. This is attributed to the difficult repeatability of contact angle experiments with gravity fluctuation and plane vibrations. After the experiments on wetting, the same team studied the evaporation stage. Brutin et al. (2010) and Carle et al. (2012) presented results obtained during a parabolic flight campaign observing ethanol sessile drop evaporation under microgravity conditions. Droplets were created using a syringe pump by injection through a substrate. The droplets were recorded using both a video camera and an infrared camera. The experimental setup enables the simultaneous visualization in the infrared and the visible wavelengths and also allows access to the heat-flux density transferred to the droplet using a heat-flux meter. The authors evidenced the different stages observed in reduced gravity when the droplets evaporate. The first phase (a) of the experiment is a phase of hypergravity at 1.8g. The substrate is dry at the set temperature. The flux measured by the heat-flux meter during this phase corresponds to the loss by natural convection from a horizontal flat plate at 1.8g (approximately 200 W m22). A microgravity phase follows this hypergravity phase. At t 5 0 s, a droplet is created by the injection of the fluid, and a transition regime is observed. The substrate temperature decreases rapidly by approximately 2 C, and the heat flux increases to 1500 W m22. These changes are caused by the warming of the droplet coupled with the spreading of the liquid on the substrate. This transitional phase lasts between 5 and 8 s. After the quasistationary regime is reached (phase c), we observe that these two variables (temperature and heat-flux) remain constant. The limiting phenomenon of evaporation, for a conductive substrate, is the vapor diffusion into the atmosphere (David et al., 2007). The evolution of the evaporation mass flow rate is consistent with the theoretical model of quasi-steady diffusion-driven evaporation implemented with the temperature variation. During the evaporation, thermo-capillary instabilities develop. Figure 25.3 shows the hydrothermal waves (HTWs) on two droplets with similar diameters (R1g 5 2.81 mm and Rμg 5 2.77 mm) that are evaporating on equally heated substrates (TS 5 35 C) under two levels of gravity. In both cases, the droplets of ethanol are hemispherical, and the initial contact angles (θi) are less than 40 . Utilizing the work of Garnier et al. (2006), the two cases can be compared using
Gravity 389 (A)
(B) 5 mm
5 mm
HTWs Apex HTWs
Triple line
FIGURE 25.3 Infrared visualization of ethanol droplets under normal gravity (A) and reduced gravity (B) (normal gravity (TS 5 35 C; P 5 1013: 25 mbar; R1g 5 2.81 mm), and reduced gravity (TS 5 35 C; P 5 835 mbar; Rμg 5 2.77 mm)).
characteristic dimensionless numbers. The Rayleigh number, representing the buoyancy forces, is compared to the Marangoni number, representing the thermocapillary forces. In both cases shown, buoyancy forces are quite small, allowing the thermo-capillarity effect to dominate. In this configuration, the instabilities that develop are of type hydrothermal waves 2 (HTW2). The use of a microgravity environment induces a 113-fold decrease in the static Bond number and a 74-fold decrease in the dynamic Bond number. Under normal gravity, the thermo-convective effects are dominated by the thermo-capillary ones but are not negligible (Bd1g 5 Ra 5 Ma 0.08), whereas under microgravity, only the thermocapillary effects exist (Bdµg 5 0.001). Under normal gravity, a temperature gradient develops during the evaporation from the apex of the droplet and the contact line, resulting in a gradient of surface tension. This gradient then generates the thermo-capillary instabilities. These HTWs propagate radially around the apex, where most of the evaporation occurs. The HTWs are spaced by an almost constant angle along the axial symmetry of the triple line. Two different spatial dynamics were observed. The HTWs were found to run orthoradially around the edge of the droplet, either from a source point where they are established to a well where they collapse or all in the same direction but with no preferred direction (clockwise or counterclockwise), depending on the temperature of the substrate and the height of the droplet (Sobac and Brutin, 2011). Under microgravity, the temperature gradient is not as well defined as it is under normal gravity, but the apex maintains a temperature below the temperature of the triple line. In this configuration, HTWs have the same trend, but their movements are not as systematic as they are under normal gravity. The instabilities develop during the transitional phase. During the quasi-stationary regime, the HTWs propagate from a
390 Droplet Wetting and Evaporation source point to a well. These instabilities also propagate on the edge of the droplet, but the angle of propagation is not as constant as it is under normal gravity. This change in propagation could be caused by the vibrations of the aircraft, which cause significant fluctuations in the level of microgravity. Despite this lack of stability, the evolution of the number of HTWs is similar under both gravitational conditions.
25.2.2 DROP TOWER Several drop towers exist over the world (including Germany, Australia, Japan, and Spain). The one used here is in Brisbane, Australia, at the Queensland University of Technology (QUT). The QUT drop tower facility enables testing for 2 s in reduced gravity. The experimental rack is contained inside a drag shield, and both are raised to the top of the tower and suspended by a single thin metal wire. The facility incorporates a simple wire cutting release mechanism to initiate the drop of the experimental rack independently from the drag shield at the same instance. The drag shield and experiment are caught by an airbag mechanism, where release vents allow for high-pressure air release during impact in order to reduce peak deceleration levels. A network of bungee cords and ropes are used to provide horizontal stability to the drag shield during deceleration. The experimental rack experiences typical levels of reduced gravity around 1025g. Diana et al. (2012) observed that the droplet shape is adequately described by the YoungLaplace equation in using the drop tower facility, whereby a variation occurred in the diameter and height upon the surface energy to obtain the lowest free energy shape (sphere-like). The dimensional variations showed that an increase in the Bond number correlated well with the change in the wetted diameter and the height of the droplet (Figure 25.4). The triple-line perimeters of the drops were observed to be lower in reduced gravity than in normal gravity, and differences in contact angle were observed between these two different gravity environments and do not seem well described by theory. The YoungLaplace equation, therefore, can be used to determine the contact angle in reduced gravity
FIGURE 25.4 Digital image of sessile drops of water in normal gravity exhibiting various diameters (different Bond numbers). (A) corresponds to a Bond number of less than 1 (diameter less than capillary length), (B) corresponds to a Bond number of about 1 that is equal to the capillary length), and (C) corresponds to a Bond number greater than 1 (diameter greater than the capillary length). Images from Diana et al. (2012).
Gravity 391 for small droplets, but it was not optimal for describing the contact angle for larger drops (above the drops’ associated capillary length). Because hysteresis is the result of the drop pinning due to roughness, one could consider whether the hysteresis is affected by the microgravity conditions. The way in which the roughness affects the contact angle also could be gravitydependent. In fact, weightlessness could promote the droplet liftoff (Wenzel versus CassieBaxter behavior) in the case where one assumes some air pockets are trapped at the rough solidliquid surface.
25.3 Increased gravity conditions Increased gravity conditions are investigated using centrifuge. Experimental results on the dynamics of sessile water drops are presented by Kabov and Zaitsev (2013) and Kabov et al. (2014). They performed experiments under normal gravity (1g), microgravity (μg), and hypergravity (up to 20g). The microgravity experiments were conducted during the parabolic flights of the European Space Agency (ESA). The hypergravity experiments were carried out on the ESA large diameter centrifuge. The objective was to study the effect of the gravity on (i) the shape of a static sessile drop and (ii) the dynamic advancing contact angle in a growing sessile drop (Figure 25.5). Different smooth and rough surfaces were used, with different contact angles and different contact angle hysteresis. Water was used for the working liquid. The main variable parameters were gravity (μg20g); drop volume (1 µL5 mL); liquid flow rate (0.0616 mL min21); and contact angle (30 130 ). The drop shape was visualized from the top with the help of the Phase Schlieren System and from the side with the help of the shadow technique with resolution of 6 µm pix21. The spreading of a sessile liquid drop under the influence of gravity was observed experimentally on surfaces with relatively low contact angle hysteresis (,15 ) (A) 1 mm
1g
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FIGURE 25.5 Parabolic flight experiments, static drop gravity effect on drop shape. (A) 0.146 mL water drop on Teflon surface (contact angle hysteresis is 12.6 ). (B) 0.313 mL water drop on polyvinylacetate (contact angle hysteresis is 34.5 ). From Kabov et al. (2014).
392 Droplet Wetting and Evaporation 120 1.8g Advancing contact angle (°)
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FIGURE 25.6 Parabolic flights experiments, dynamic drop. Dynamic advancing contact angle versus time in growing water drop on copper surface under different gravity levels. Flow rate is 1 mL min21. Shown are 16 µL drops. From Kabov et al. (2014).
(Figure 25.6). In this case good agreement is obtained between the experiment data and modeling (Picknett and Bexon, 1977) with assumption of constant contact angle. For surfaces with relatively high contact angle hysteresis (.30 ), the contact line is pinned while the contact angle adjusts for different gravity levels (Figure 25.6). The dynamic advancing contact angle was found to increase with the gravity.
References Bartashevich, M.V., Kuznetsov, V.V., Kabov, O.A., 2010. Gravity effect on the axisymmetric drop spreading. Microgravity Sci. Technol. 22 (1), 107114. Brutin, D., Zhu, Z.Q., Rahli, O., Xie, J.-C., Liu, Q.-S., Tadrist, L., 2009. Sessile drop in microgravity: creation, contact angle and interface. Microgravity Sci. Technol. 21 (Suppl. 1), 6776. Brutin, D., Zhu, Z.Q., Rahli, O., Xie, J.-C., Liu, Q.-S., Tadrist, L., 2010. Evaporation of ethanol drops on a heated substrate under microgravity conditions. Microgravity Sci. Technol. 22, 387395. Carle F., 2014. Flow Motion in Sessile Droplets: Evaporation and Nanoparticles Assembly (Ph.D. thesis). Aix-Marseille University. Carle, F., Sobac, B., Brutin, D., 2012. Hydrothermal waves on ethanol droplets evaporating under terrestrial and reduced gravity levels. J. Fluid Mech. 712, 614623. David, S., Sefiane, K., Tadrist, L., 2007. Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids and Surfaces A 298, 108114.
Gravity 393 Diana, A., Castillo, M., Brutin, D., Steinberg, T., 2012. Sessile drop wettability in normal and reduced gravity. Microgravity Sci. Technol. 24, 195202. Garnier, N., Chiffaudel, A., Daviaud, F., 2006. Hydrothermal waves in a disk of fluid. In: Mutabazi, I., Wesfreid, J.E., Guyon, E. (Eds.), Dynamics of spatio-temporal cellular structures: Henri Be´nard centenary review, vol. 207. Springer, pp. 147161. Kabov, O.A., Zaitsev, D.V., 2013. The effect of wetting hysteresis on drop spreading under gravity. Doklady Phys. 58 (7), 292295. Kabov, O., Zaitsev, D., Gatapova, E., Semenov, A., Bykovskaya, E., Karnauhova, E., et al. (2014). Drop spreading and evaporation on a heated substrate under variable gravity conditions. In: Proceedings of the 15th International Heat Transfer Conference, IHTC-15, August 1015, 2014, Kyoto, Japan. Paper # IHTC15-9504. McGuckin, C.P., Forraz, N., Baradez, M.-O., Navran, S., Zhao, J., Urban, R., Tilton, R., Denner, L., 2005. Production of stem cells with embryonic characteristics from human umbilical cord blood. Cell Prolif. 38 (4), 245255. Picknett, R.G., Bexon, R., 1977. The evaporation of sessile or pendant drops in still air. Journal Colloid Interface Science 61, 336350. Sobac, B., Brutin, D., 2011. Triple-line behavior and wettability controlled by nano-coated substrates: Influence on sessile drop evaporation. Langmuir 27, 1499915007.