Near-critical fluid boiling: Overheating and wetting films

Eur. Phys. J. E 26, 345–353 (2008) DOI 10.1140/epje/i2007-10333-x THE EUROPEAN PHYSICAL JOURNAL E Near-critical fluid boiling: Overheating and wetting films J. Hegseth1,a , A. Oprisan2 , Y. Garrabos3 , C. Lecoutre-Chabot3 , V.S. Nikolayev4 , and D. Beysens4 1 Department of Physics, University of New Orleans, New Orleans, LA 70148, USA 2 Physics & Astronomy, College of Charleston, Charleston, SC 29424, USA 3 ESEME, Institut de Chimie de la Matière Condensée de Bordeaux, CNRS, Université de Bordeaux I, Avenue du Dr. Schweitzer, F-33608 Pessac Cedex, France 4 Laboratoire de Physique et Mécanique des Milieux Hétérogènes, École Supérieure de Physique et de Chimie Industrielles de la ville de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France Received 3 September 2007 and Received in final form 16 January 2008 Published online: 26 June 2008 – c EDP Sciences / Società Italiana di Fisica / Springer-Verlag 2008 Abstract. The heating of coexisting gas and liquid phases of pure fluid through its critical point makes the fluid extremely compressible, expandable, slows the diffusive transport, and decreases the contact angle to zero (perfect wetting by the liquid phase). We have performed experiments on near-critical fluids in a variable volume cell in the weightlessness of an orbiting space vehicle, to suppress buoyancy-driven flows and gravitational constraints on the liquid-gas interface. The high compressibility, high thermal expansion, and low thermal diffusivity lead to a pronounced adiabatic heating called the piston effect. We have directly visualized the near-critical fluid’s boundary layer response to a volume quench when the external temperature is held constant. We have found that when the system’s temperature T is increased at a constant rate past the critical temperature Tc , the interior of the fluid gains a higher temperature than the hot wall (overheating). This extends previous results in temperature quenching experiments in a similarly prepared system when the gas is clearly isolated from the wall. Large elliptical wetting film distortions are also seen during these ramps. By ray tracing through the elliptically shaped wetting film, we find very thick wetting film on the walls. This wetting film is at least one order of magnitude thicker than films that form in the Earth’s gravity. The thick wetting film isolates the gas bubble from the wall allowing gas overheating to occur due to the difference in the piston effect response between gas and liquid. Remarkably, this overheating continues and actually increases when the fluid is ramped into the single-phase supercritical phase. PACS. 05.70.Np Interface and surface thermodynamics – 44.35.+c Heat flow in multiphase systems – 68.03.-g Gas-liquid and vacuum-liquid interfaces 1 Introduction time) of a near-critical fluid keeps the heat near the wall to form a long-lasting hot boundary layer (HBL). The 1.1 Critical fluids high thermal expansion makes this HBL into a “piston” that compresses the bulk. The high compressibility of the Near the liquid-gas critical point, material and thermal bulk implies an almost instantaneous increase in the tem- properties, which play an important role in the boiling perature of the bulk. In a two-phase system a surprising process such as surface tension, liquid-gas density differ- response called overheating has been observed [3]. A gas ence, and thermal diffusivity, vary considerably with tem- bubble isolated from the heating wall by liquid responds to perature [1]. These properties vary according to the well- a temperature quench with the gas temperature becom- known universal power laws that either converge or di- ing larger than the liquid temperature and the heating verge as the critical temperature Tc is approached (e.g., surface temperature. This is a transient effect that soon the surface tension goes to zero while the compressibil- equilibrates so as to not violate the second law. ity and thermal expansion diverge). These properties lead to perfect wetting by the liquid phase (zero contact an- gle) near Tc [2]. When heat is applied to a wall of a con- 1.2 Previous results stant volume system, the low diffusivity (long relaxation We previously observed a boiling process where heat was a applied to a fluid near the critical point, pushing the Current address: Department of Radiation Oncology, Uni- versity of Louisville, 529 S. Jackson Street, Louisville, KY system slightly out of equilibrium [4]. The perfectly wet- 40202, USA; e-mail: jjhegseth@yahoo.com ted walls dried from evaporation resulting in spreading 346 The European Physical Journal E liquid-gas-solid contact lines. The same physics that made Table 1. The CO2 cell’s critical densities δρ/ρc is given in perfect wetting at equilibrium resulted in a well-defined this table for experiments 1-4. Also listed is the temperature boundary condition of zero contact angle in the case where difference δTmax for different off-critical densities δρ/ρc as de- a contact line appears. These spreading contact lines were scribed the text. We can see that the higher-density runs had associated with the wall drying that is observed prior to higher-overheating effects as measured by δTmax . The thermis- the near-critical boiling crisis [5] and produce very thick tors inside the cell were not recording in experiment 3. wetting layers in front of the receding lines. A spectacular Experiment δρ/ρc (%) δTmax (mK) spreading event occurs near the critical temperature Tc [5], 1 0.00 85.3 where the gas bubble changes shape to cover almost half the cell wall. Both the gas spreading and the contact line 2 1.87 96.3 motion occur when the bubble is free to move inside the 3 4.90 unknown cell and is initially in contact with a highly conductive cop- 4 −3.50 63.1 per side-wall. This behavior has been identified with the boiling crisis near the critical point, i.e., a reaction of the fluid to the heating surface where the heating surface be- with fluid very close to the liquid-gas critical density and comes covered with gas [5]. Similar behavior also occurs in heated. These thin cells produce a considerable constraint the boiling crisis in terrestrial gravity. In practical applica- on the bubble and allow the entire bubble to be observed tions, the boiling crisis most often results in a catastrophic as heat is applied. No spreading is observed just below failure of the heat transfer device. A mechanism for this Tc in this cell that occurs when a piston and temperature spreading is clearly revealed near the critical point: the va- sensors are present inside of the cell to prevent the bub- por recoil from the evaporating fluid pushes the fluid near ble from moving and touching the side-wall [4]. We report the liquid-gas-solid contact line. Such an effect occurs both and document very thick wetting films —at least one order in near-critical fluids and in high heat flux technology. of magnitude thicker than films that form in the Earth’s The behavior of the gas bubbles was quite different gravity— in weightlessness. The thick wetting film isolates when they were constrained to maintain their position the gas bubble from the wall allowing gas overheating to throughout the temperature ramp [4]. In this case the occur due to the difference in the piston effect response be- particular phase distribution appears stationary near Tc tween gas and liquid. We also observe overheating when and all dynamical activity stops in what was called a me- the fluid is heated into the single-phase supercritical fluid. chanical slowing down. Above Tc the liquid-gas interfaces As reported below, large deformations in the very thick become large density gradients that slowly disappear. liquid films and significant gas overheating (where the gas Gas overheating was previously reported in a weight- is hotter than the heating wall) is seen when the temper- less two-phase mixture where a temperature quench is ature is ramped. In addition to observing a continuous applied to a gas bubble that is isolated from the solid sur- overheating effect during a ramp in the two-phase state, face of the cell [3]. This effect, where the gas temperature similar to the overheating reported in [3], we also report is actually larger than the heating wall of the container, overheating in a single-phase supercritical fluid. has been qualitatively explained as an adiabatic heat transfer process caused by the diverging compressibility and thermal expansion coefficient particular to near- 2 Apparatus critical fluids [6]. If the fluid also has a very small thermal diffusivity, as in this case, the thermal energy conducted 2.1 Experimental cell from the heating wall remains near the wall for a long time and this higher-temperature fluid greatly expands. The experimental cell and its associated instrument were The bulk of a highly compressible pure fluid may have placed in the weightlessness of an orbiting spacecraft [8]. its internal energy increased through compression. In This instrument is specially designed to obtain high- a liquid-gas mixture, the compression by the boundary precision temperature control (stability of ≈ 10 μK over layer may heat the gas more than the liquid, leading to 50 hours, repeatability of ≈ 40 μK over 7 days). To place a quite large temperature difference [7]. This mechan- the samples near the critical point, constant-mass cells are ical short-circuit of the usual heat conduction is very prepared with a high-precision density, to 0.02%, by ob- efficient in near-critical fluids. If the gas in a two-phase serving the volume fraction change of the cell as a function near-critical fluid is isolated from the heating wall, as in of temperature on the ground [9]. reference [3], the expansion near the walls occurs in the These experiments were performed using a variable liquid and the gas can overheat the walls because of the volume cell (see Tab. 1) filled with CO2 and containing different thermal response in the gas and the liquid (the 3 thermistors. Experiment 1 was performed first at the gas and liquid have a different [ dP critical density with experiments 2-4 following. Between dT ]ρ coefficient). each experiment a piston in the variable-volume cell was changed and the response recorded. The boiling experi- 1.3 New results ments done in this cell yielded quite different results from the boiling results previously reported. A thin layer of CO2 In the following we report on the behavior of a single gas of width D was sandwiched between two sapphire win- bubble inside a thin constant mass cell. The cells are filled dows and surrounded by a copper housing in the optical J. Hegseth et al.: Near-critical fluid boiling: Overheating and wetting films 347 CuBeCo CuBeCo window b Th2 liquid D L window Th3 Th1 Parallel light Fig. 2. a) A schematic representation of the optical system and Fig. 1. Shown is a cross-section of the cylindrical sample cell. the cell. The convergent lens, L, that has a focal point F and The fluid volume is contained between two sapphire windows a center C, projects the out-of-focus grid image on the CCD and a CuBeCo alloy ring. The cell consists of a 12 mm diameter plane Π. b) The corresponding image recorded by the CCD cylinder made of CuBeCo containing a 2.204 mm thin layer of that shows the grid shadows that allow the density changes CO2 sandwiched between two sapphire windows (9 mm thick). and film distortions to be visualized. The grid line shadow is The dimensions (L, D) of the cell are indicated. The semicir- distorted indicating the existence of a curved gas-liquid inter- cular liquid-gas meniscus between the two parallel windows is face. The position of the three thermistors, Th1, Th2, and Th3 shown. This interface appears dark in the images because the is shown in b). Th3 is in the gas while the Th1 and Th2 are in liquid-gas meniscus refracts the normally incident parallel light the liquid. away from the cell axis. edge distance of approximately 1 mm is not visible in our images, i.e., the light at the edge of the cell is blocked by cell shown in Figure 1. Two cylindrical sapphire windows the glue that was used in manufacturing the cell. We find 12 mm in diameter and 9.0 mm long are pressed into a cop- the cell center and cell edge using a 10 mm diameter ref- per block with a corresponding cylindrical hole and glued erence etching on the sapphire window that is concentric to the copper at the sides of the sapphire. This method with the cell. avoids the unknown volume associated with o-rings, etc., Similar ground-based experiments were done before allowing the above high-precision density measurements these experiments, yielding completely different results [9]. to be verified. Table 1 summarizes the key features of the In this case, the interface is horizontal except very near a cell. In these boiling experiments a two-phase liquid-gas wall. When a cell window is also horizontal and the bot- mixture consisting of a single bubble was heated into a tom is heated, drops form at the wetted top of the cell in supercritical fluid as it passed the critical temperature. what appears to be a Rayleigh-Taylor instability. These Figure 2b shows the cell that contains three thermistors drops initially form and grow at the top of the cell and (Th1, Th2, Th3) used to measure the local temperature fall continuously on to the interface. of the fluid. The position of the three thermistors is also shown in Figure 2b. Typically the thermistor Th3 is in the gas while the thermistors Th1 and Th2 are in the 2.2 Temperature ramps and visualization liquid. These small thermistors have a response time of approximately 10 ms. The dark square region to the left Temperature data in each phase was obtained as the cell is the piston that apparently pushes the bubble interface was heated from two-phase fluid to supercritical fluid. deforming its shape. This sealed piston can slide in and These heating runs were then repeated in the same sam- out of the cell volume to change the fluid’s average den- ple at different off-critical densities, both above and be- sity. These objects constrain the gas bubble in this cell low the critical density. During these experiments an au- from moving and prevented it from touching the copper tomatic Tc search was performed. Quenches of 100 mK, side-wall as the cell was heated. 50 mK, 25 mK, and 15 mK were performed to bring the The cell had a thickness, D = 2.204 mm, or the aspect system close to Tc . Quenches of 1 mK were then performed ratio Γ = 5.445 (Γ = L/D, see Fig. 1). In our system, past the point of phase separation. The critical point was the liquid wets the solid, so that the initial state (be- crossed on the very last quench so that the critical tem- fore heating) is a flat gas bubble constrained by the two perature is 45.5543 ◦ C ± 0.5 mK. windows, the cell edge, and the objects inside the cell. This cell was heated linearly in time to a tempera- Because the contact angle is zero near the critical point, ture greater than the critical temperature Tc , as shown the liquid-gas meniscus between the two parallel windows in Figure 3a, while the liquid-gas interface was visualized forms a semicircular interface in the plane perpendicular through light transmission normal to the windows. The to the windows, as shown schematically in Figure 1. The curve marked Tw in Figure 3 shows the temperature profile interface appears dark in the image because the liquid-gas that was imposed on the system during these experiments meniscus refracts the normally incident light away from as measured by a thermistor placed in the copper wall sur- the cell axis. In normally incident light, the dark region rounding the cell. This thermistor has a response time of measures the radius of the semicircular meniscus. A radial approximately 2 seconds. The temperature ramps for all 348 The European Physical Journal E 32500 The density changes in this highly compressible fluid a were visualized by using a defocused grid (or grid-shadow) 32000 Temperature (mK) Time vs Tw technique [8]. As discussed in reference [4], this technique 31500 4d Time vs Th1 allows thickness changes in the liquid wetting film to be Time vs Th2 visualized. Figures 2b, 4a, e and i, and Figures 5b-d show Time vs Th3 examples of film thickness changes. Figures 4d, h, and l 31000 4c show examples of density changes in supercritical fluid 30500 Tc (opalescence in image) that are indicated using this technique. Figure 2 shows 4b how the defocused grid is projected on to the plane of the 30000 CCD [10]. More details can be found in reference [4]. 29500 3600 3800 4000 4200 4400 3 Results Time (seconds) 3.1 First temperature ramp 140 The images in Figure 5b-d show the features occurring 120 b Time at Tc during the initial heating ramp of experiment 1. The ini- 100 Tw - Th3 (mK) tial response of the bubble, at all δρ, to the temperature 80 increase occurs at the edge of the bubble where the grid 60 lines become distorted and lines appear in the transmitted light image. These distortions appear to start at the edge 40 of the bubble and may propagate into the bubble. These 20 structures are very similar to the shape and behavior of 0 the spreading contact lines reported in [4] and briefly dis- cussed in the Introduction. They are caused by a change -20 in the thickness of the wetting film, i.e., a wetting film 3400 3600 3800 4000 4200 4400 4600 that is inclined relative to the window refracts the par- Time (seconds) allel light input to the cell so that the grid shadows are displaced in the imaging plane of the camera. The ini- Fig. 3. All of the experiments reported here were heated lin- tial changes are quite complex but evolve into two circles early in time to a temperature greater than the critical tem- shown in Figures 4a, e, i (see arrow) and 5c, d (see arrow). perature Tc . These temperature profiles consisted of two ramps These two circular film distortions appear on each side of (8.7 mK/s and 7.4 mK/s, respectively) separated by a 40 min the cell. They later evolve into a single circle although constant temperature plateau. a) Shows the later tempera- they still exist on each of the sapphire windows but are ture ramp performed in experiment 1. The curve marked Tw aligned so they appear as one circle. The appearance of in a) was measured by a thermistor placed in the copper wall these circles occurs at the end of the initial ramp. During surrounding the cell and shows the temperature profile that the constant-temperature plateau these two circles slowly was imposed on the system. Also shown are the times and temperatures corresponding to Figures 4b-d. A temperature disappear. The piston position changes the phase distribu- difference between Th3, Th2, Th1, and Tw is observed and tion for the different runs at different δρ, i.e., at minimum this difference is shown in more detail in b). Th3 is seen to be δρ the piston is almost out of the cell and at maximum δρ consistently higher in temperature than the wall temperature the piston pushes the gas bubble far into the cell. Similar and this overheating also continues into the supercritical fluid behavior is still seen, however, in identical temperature state as shown in b). ramps (to within ±1 mK) at different δρ. The circles form later at lower δρ during the ramp and the circles relax more slowly at the plateau at lower δρ. of the experiments are very similar. Identical commands were given to our automated instrument (ALICE 2) for 3.2 Second temperature ramp experiments 1-4. The imposed ramps that resulted were identical to within 1 mK, as checked by comparing corre- When the second ramp commences, a very similar behav- sponding temperature data. Two temperature ramps were ior is also seen at each δρ. An example of the features sequentially performed in each experimental run. The first that occurred in the final ramp at various off-critical den- temperature ramp brought the system from ambient tem- sities, δρ = ρ − ρc , where ρc is the critical density, is perature to a given initial temperature to maintain con- shown in Figure 4 (Figs. 4a-d at δρ = 0.0% with the time sistent initial conditions in each run. The cell was then of Figs. 4b-d shown in Fig. 3a, Figs. 4e-h at δρ = 4.9%, maintained at the initial temperature for 40 minutes be- and Figs. 4i-l at δρ = −3.5%). A spreading contact line fore the second ramp started. In the second ramp readings appears at the edge of the bubble in a very similar man- from the three internal thermistor were recorded as the ner to the previous ramp. After about a minute of ramp- temperature of the cell was increased through Tc . ing, however, small gas bubbles begin to nucleate at the J. Hegseth et al.: Near-critical fluid boiling: Overheating and wetting films 349 a b c d e f g h i j k l Fig. 4. Shown are some of the events that occurred during the final ramps in experiments 1, 3, and 4. The dark square region to the left is the sliding piston that varies the fluid’s average density and also pushes the bubble interface. Each row shows features that occurred in different runs where each run was done at a different off-critical density, δρ = ρ − ρc , where ρc is the critical density. The first row of images, Figures 4a-d, from experiment 1, was taken at δρ = 0.0%, see also Figure 3a. The second row of images, Figures 4e-h, was taken in experiment 3 at δρ = 4.9%, and the last row, Figures 4i-l, was taken during experiment 4 at δρ = −3.5%. Corresponding times and events between runs are shown in the columns. The first column, Figures 4a, e, and i, shows the circular distortions that appear on each side of the cell and align so they appear as one circle (see also Figs. 5c-e). The appearance of these circles occurs at the end of the initial ramp. During the constant-temperature plateau these two circles slowly disappear. The second column, Figures 4b, f and j, shows a cluster of bubbles has formed at the edge of the cell. One of these bubbles has coalesced with the large bubble producing a plumb that travels toward the center of the large bubble. The third column, Figures 4c, g and k, shows a considerably distorted grid shadow image with a critical opalescence at the side-wall in the region just where the bubbles were nucleating. The dynamical activity suddenly stops at about the same time as this layer forms. The particular phase distribution that existed just before the critical temperature was passed appears to be frozen in place. The images in the last column, Figures 4d-h-l, are above the critical temperature Tc and the grid shadows in these images show significant density changes. The liquid-gas interface is replaced with a large density gradient above Tc but still refracts the light in an almost identical way. Slower mass fluxes continue, however, and the system evolves to a uniform super-critical fluid not long after Figures 4d-h-l. a b c d e f Fig. 5. Images of the variable-volume sample cell in experiment 1 during the initial temperature ramp. Figure d) shows the two aligned circular film distortions. Figures d)-f) show the relaxation of these circles at constant temperature during 10 minutes. 350 The European Physical Journal E wall and the circle simultaneously disappears. A cluster and f (see arrows). The grid shadow displacements at the of bubbles has formed at the edge of the cell as can be side-wall in Figure 6b are in the opposite sense to the seen in Figures 4b, f and j (see arrow). One of these gas displacements at the wall in Figure 6f. In Figure 6b the bubbles has coalesced with the large bubble producing a gas is heated by compression while the wall remained at a plumb that travels toward the center of the large bubble. constant temperature so that a cold boundary layer (CBL) The shadow-graph image of the plumb can be seen in the forms near the wall. In the latter case the gas expands and images of the second column of Figure 4 (see arrow in cools so a hot boundary layer (HBL) forms near the side- Fig. 4b). The gas released from this coalescence has pro- wall. This illustrates the adiabatic heat transfer process duced a strong shadow-graph image because the bubbles that typically occurs in highly compressible near-critical contain gas of different density. The critical/coexistence fluids (coined the “piston-effect”) [11]. This is somewhat temperature (these two temperatures are within 50 μK for different from previous observations, however, because the all of the densities discussed here) is easily seen at the bulk fluid is directly heated or cooled by the mechanical wall, however, because a region of bright light, probably compression or expansion from an actual piston, whereas from critical opalescence, appears at the side-wall in the in the usual piston effect a HBL forms from external heat- region just where the bubbles were nucleating, as shown in ing that compresses the bulk. Figures 6b and f were taken Figs. 4c-g-k (see arrow in Fig. 4k). This opalescence region 30 seconds after the first image (Figs. 6a and e). Figure 6g follows the side-wall. Figures 4c-g-k also show a consider- (see arrow), taken at the end of the piston displacements, ably distorted grid shadow image. Although the velocity shows that the grid shadows at the cell edge have reversed of the coalescing bubbles and plumbs slows considerably their curvature, implying that the boundary layers that as the temperature increases, the dynamical activity sud- were cold are now hot and vice versa. No significant den- denly stops at about the same time as the opalescence sity changes occur in the cell 10 minutes after the piston layer forms. The particular phase distribution that existed displacement, as shown in Figures 6d and 6h (see arrow). just before the critical temperature was passed appears to be frozen in place. This process was called mechanical slowing down in reference [4], see also the discussion in 3.4 Single-phase overheating the Introduction. Figures 4d-h-l are clearly above the crit- ical temperature Tc and the grid shadows in these images Figure 3a shows a temperature difference between the show significant density changes. A large density gradi- thermistors Th3, Th2, Th1, and Tw on the final temper- ent separates low-density gas-like fluid from high-density ature ramp for experiment 1. This difference is shown in liquid-like fluid. This large density gradient appears dark more detail in Figure 3b. Because all four thermistors have in Figures 4d-h-l (see arrow in Fig. 4h) because of signifi- the same temperature before and after the ramp, this dif- cant light refraction. Slower mass fluxes continue, however, ference is not an instrumental artifact. The walls of the and the system evolves to a uniform super-critical fluid not cell are in thermal contact with the fluid. The side-wall long after Figures 4d-h-l. The bubble clusters that form of the cylindrical cell is made of copper and the windows in Figures 4b-f-j does not appear at δρ = 4.9 because the are made from sapphire. The copper side-wall of the cell large bubble is pushed near the wall and it occupies that conducts heat at a faster rate and is in direct thermal space. Coalescence events occur all along the region of the contact with the large copper heat reservoir of the Peltier bubble that is close to the wall indicating that the large heat pumps used for the temperature regulation system. bubble is not in contact with the wall. The same mechan- Although the long cylindrical sapphire windows (9 mm in ical slowing down and opalescence is also observed. This length) make a relatively large area of thermal contact mechanical slowing down and frozen phase distribution is with the copper reservoir, a thin layer of glue is used to caused by the decrease of surface tension as the critical connect the windows to the copper reservoir and dimin- point is approached [4]. ishes the rate of heat transfer to the windows. The sap- phire also has a smaller thermal conductivity than copper and we therefore should expect the center of the thin layer 3.3 Piston effect visualization of fluid between the windows to have a delayed response to a temperature change as compared to the response of Between experimental runs the density of the fluid was the side-wall. If the measured temperature difference were changed by moving the piston inside the cell. Figure 6 caused by conductive heat transport in the cell, then we shows two sequences of images during a volume decrease would expect that the thermistors Th1 and Th2 which are (density increase) and a volume increase (density de- closer to the side-wall would have a greater temperature crease), respectively. Figures 6a-d show a volume decrease during the ramp. Figure 2 shows, however, that thermis- of −1.87% (density increase of +1.87%) and Figures 6e-h tor Th3 is at the center of the cell. Clearly the gas in the show the largest volume increase between experiments 3 center of the cell has a consistently higher temperature and 4 that produces a density changed from δρ = +4.9% than the fluid as measured by Th1 and Th2. More remark- to δρ = −3.5%. The straight grid lines in Figures 6a and e able yet is that the temperature measured by the ther- show that there are insignificant density gradients before mistor Th3 is consistently higher in temperature than the the piston is moved. During the piston motion the density wall temperature. Overheating was previously observed in gradients appear around the piston and at the side-wall, two-phase near-critical fluids using a temperature quench as shown by the grid shadow displacements of Figures 6b protocol [3] as briefly discussed in the Introduction. This J. Hegseth et al.: Near-critical fluid boiling: Overheating and wetting films 351 a b c d e f g h Fig. 6. Shown are two sequences of images during a volume decrease (density increase between experiments 1 and 2) and a volume increase (density decrease between experiments 3 and 4), respectively, in single-phase supercritical CO2 . Figures 6a-d show a volume decrease of −1.87% (density increase of +1.87%) and Figures 6e-h show the largest volume increase that produces a density changed from δρ = +4.9 to δρ = −3.5. The uniform fluid in Figures 6a and e before the piston is moved changes as seen by the density gradients that appear around the piston and at the side-wall as shown by the grid shadow displacements of Figures 6b and f. The grid shadow displacements at the side-wall in Figure 6b are in the opposite sense to the displacements at the wall in Figure 6f. In the first case the gas is heated by compression while the wall remained at a constant temperature so that a cold boundary layer (CBL) forms near the wall. In the latter case the gas expands and cools so a hot boundary layer (HBL) forms near the side-wall illustrating the adiabatic heat transfer process (the “piston-effect”). Figures 6b and f were taken 30 seconds after the first image (Figs. 6a and e). Figures 6c and g, taken at the end of the piston displacements, show that the grid shadows at the cell edge have reversed their sense of curvature. No significant density changes occur in the cell 10 minutes after the piston displacement, as shown in Figures 6d and h. gas overheating also continues into the single-phase (su- the circles. The reasons were as follows: no convection was percritical) fluid state and actually increases (see Fig. 3b). observed, the interface is essentially at saturation so that The response of the three thermistors was very similar in any gradients are strongly damped by evaporation and the other runs at different δρ. This response included the condensation, and if there were convection it would also overheating, δT = Th3−Tw , shown in Figure 3b, that was dampen any δT along the liquid-gas interface [15]. Such also seen in other experiments. Th3 exhibited a maximum a flow could modify the shape of the wetted surface and value when the fluid was supercritical, as can be seen in create large sustained circles and contact lines. The same Figure 3b. When the ramp was stopped the spread in δT reasons for an isothermal bubble interface, however, also decreased and Th3 and Tw also had a maximum before re- apply to the wetting layer. The proximity of the wetting turning to a slightly lower steady temperature. This time layer to the heating wall could possibly drive such a gra- is marked by the arrow in Figure 3b. The fact that Th3, dient. Again, we have not seen any evidence of the steady Tw , and δT all simultaneously showed steady values makes convection that is required to create and maintain these this a convenient time to compare the three data sets. circles in our experiments. As discussed above, we have oc- δTmax , the overheating at the maximum of Th3 and Tw casionally seen transient plumbs from bubble coalescence. (not the maximum of the difference), is shown in Table 1. The fact that there is no convection shows that the inter- From this table we conclude that δTmax increases with δρ. face is isothermal. In previous experiments the gas is in contact with the side-wall. References [13, 4] and [5] show that an isother- 4 Discussion and analysis mal interface could only deform the bubble shape through an external force. In reference [5] this external force was 4.1 Convection, vapor recoil, and the isothermal identified as the vapor recoil force, where the bubble is gas-liquid interface deformed through the process of evaporation, i.e., by the normal stress exerted on the interface by the recoil from If a temperature change, δT , appeared along the liquid- departing vapor [16, 17]. In reference [4] spreading contact gas interface, it would create a surface tension gradient lines were documented and explained using vapor recoil. δσ = (dσ/dT )δT that would drive a thermal-capillary or The circles seen in experiments 1-4 appear after the a Marangoni flow in the bulk of both fluids [12–14]. The spreading contact lines. Gas overheating was recorded at possible effects of surface tension gradients were consid- the end of the first ramp, correlated with the appearance ered in reference [5]. It was shown that such effects would of the circles. Unfortunately the internal thermistors were be unlikely to cause large-scale interface deformations, like not engaged when the contact lines were active at the 352 The European Physical Journal E for a given index of refraction (corresponding to a given temperature). The axis b is the maximum thickness of the b wetting film. The curved interface has two effects on the a grid image: it displaces the center of each line of the grid and it changes the linewidth. These two quantities were measured and compared with the results of a ray-tracing a algorithm. This algorithm projects 103 –106 equally spaced rays through the optical system and the elliptic interface to compute these quantities. Figure 7a corresponding to Figure 5d shows that b can be very large and the elliptical distortions are a significant feature of the film and the overall bubble shape (b ≈ L/3). Figure 7b corresponding to Figure 5f shows that the film thickness decreased and the distortion relaxed consider- ably after 10 minutes at the same temperature. Using the b same procedure for Figure 5f, we find that the maximum film thickness was between 240 μm and 320 μm, where we Fig. 7. Schematic diagram of the shape of the gas-liquid in- used the entire bubble for the major axis. Because the terface with an elliptical distortion in the interface. The liquid, bubble size does not change, within the resolution of our gas, copper, and sapphire are the same as shown in Figure 1. The value of the major axis a is fixed and the maximum thick- video system, we conclude that the liquid film thickness is ness b of the ellipse is calculated. The estimated values of b for much larger than would be found on Earth, by one to two Figure 5d is 800 μm–990 μm and is illustrated in a). The esti- orders of magnitude. This very large liquid film thickness mated values of b for Figure 5f is 280 μm–320 μm and is illus- isolated the gas bubble from the sapphire wall and allows trated in b). the overheating mechanism discussed below. beginning of the first ramp. Based on previous results, 4.3 Adiabatic overheating however, reported in [4], we would expect the overheating to be suppressed when the contact lines are present as this Overheating that was similar to that presented in Fig- would imply a dried wall exposed to the gas. The circular ures 3a, b and Table 1 was previously observed during distortions occur when the gas is hotter than the liquid temperature quench experiments [3]. The maximum over- —during overheating— and would seem to exclude va- shoots seen in reference [3] were approximately twice as por recoil as a driving mechanism. The vapor recoil force, large as those measured during the temperature ramps in however, pushes on the liquid interface in the same sense this experiment. Reference [3] measured a transient over- whether there is evaporation or condensation at the in- shoot during temperature quenches and provided an ex- terface. The circles are probably also caused by the vapor planation of the gas overheating as discussed in the Intro- recoil force. A more thorough quantitative examination duction. In particular it is necessary to prevent a cooler should help to clarify the cause of this result. wall from being in contact with the gas. Such thermal contact would result in a CBL in the gas so that the gas 4.2 Elliptical film shapes and the film thickness would decompress (cf. Fig. 6). The isolation is needed to estimate prevent the gas from decompressing and cooling. In this case it appears that the majority of the gas bubble is in The circles on each window aligned to appear as a sin- contact with the wetted sapphire window. The overheating gle circle at the end of the first ramp when the heating can be explained using the above theory if the previously ended. In reference [5] we found a very thick rim of fluid discussed large wetting film also isolates the gas bubble in front of a receding contact line. This suggests that the from the wall. This implies that most of the expansion at wetting films in weightlessness may be quite thick, espe- the boundary layer from the hot sapphire wall occurs in cially since they are not limited by gravitational effects [2]. the liquid film. All the evidence observed in these exper- We have used ray tracing to analyze several images to es- iments suggests that the wetting film can isolate the gas. timate the thickness of these distortions and the thickness We have argued previously that the interface is isother- of the wetting film. Figures 5d and f show two circles that mal, primarily from latent-heat exchanges that keep the align and appear to distort the shadows of the wires in interface at the saturation temperature. This would im- the grid. To find the thickness of these wetting films, we ply condensation of the hot gas at the interface accom- assume an identical elliptical shape for the CO2 liquid- panied by a decompressing boundary layer in the gas [7]. gas interface as shown in Figure 7. The eccentricity of the This is evidently not as large or as fast an effect as the assumed elliptic interface is constrained so that the ma- liquid compression from the boundary layer at the heating jor axis of the ellipse is fixed and equals the diameter of wall. The largest overheating in this experiment is seen, the circular distortion as measured in the recorded im- however, above the critical temperature, highlighting the ages. Different degrees of distortion of the grid shadows density dependence of the thermo-physical properties. A are found by changing the axis b of the elliptic surface relatively thick high-density liquid-like layer exists at the J. Hegseth et al.: Near-critical fluid boiling: Overheating and wetting films 353 sapphire windows that isolates the low-density gas-like References fluid and prevents decompression of the low-density fluid to lower temperature as can be seen in Figures 4d, h, l. 1. M.R. Moldover, J.V. Sengers, R.W. Gammon, R.J. Hoken, The absence of the latent heat or interfacial boundary Rev. Mod. Phys. 51, 79 (1979). condition apparently increases the thermal isolation of the 2. P.G. de Gennes, Rev. Mod. Phys. 57, 827 (1985). low-density (gas-like) fluid from the high-density (liquid- 3. R. Wunenburger, Y. Garrabos, C. Lecoutre-Chabot, like) fluid near the sapphire windows. A more thorough D. Beysens, J. Hegseth, Phys. Rev. Lett. 84, 4100 (2000). quantitative examination should help to clarify the cause 4. J. Hegseth, A. Oprisan, Y. Garrabos, V.S. Nikolayev, of this result. C. Lecoutre-Chabot, D. Beysens, Phys. Rev. E 72, 031602 (2005). 5. Y. Garrabos, C. Lecoutre-Chabot, J. Hegseth, V.S. Niko- 5 Conclusion layev, D. Beysens, Phys. Rev. E 64, 051602 (2001). 6. Y. Garrabos, M. Bonetti, D. Beysens, F. Perrot, We have reported and interpreted a variety of phenom- T. Fröhlich, P. Carlès, B. Zappoli, Phys. Rev. E 57, 5665 ena observed as a two-phase fluid temperature is ramped (1998). past its critical temperature (near-critical boiling) in a 7. J. Straub, L. Eicher, A. Haupt, Phys. Rev. E 51, 5556 weightless environment. Significant gas phase overheating (1995). that increases with average density was observed in a con- 8. C. Morteau, M. Salzman, Y. Garrabos, D. Beysens, in strained CO2 bubble. Large distortions in the wetting film Proceedings of the 2nd European Symposium on Fluids in between the bubble and the sapphire wall were visualized Space, edited by A. Viviani (Congressi srl, Rome, 1997) using a grid shadow technique. Using an elliptical model p. 327. to represent several large distortions, we used ray tracing 9. J.P. Delville, C. Salzman, Y. Garrabos, D. Beysens, in Proceedings of the 2nd European Symposium on Fluids in to calculate grid shadow displacement. This showed that Space, edited by A. Viviani (Congressi srl, Rome, 1997) the wetting film is at least one order of magnitude larger p. 312. than wetting films on Earth. These thick wetting films 10. V. Gurfein, D. Beysens, Y. Garrabos, B. Le Neindre, Opt. isolate the gas from the walls allowing the overheating re- Commun. 85, 147 (1991). sults to be explained by an adiabatic mechanism (piston 11. B. Zappoli, D. Baylly, Y. Garrabos, B. Le Neidre, P. Gue- effect). This adiabatic mechanism was also demonstrated noun, D. Beysens, Phys. Rev. A 41, 2264 (1990). in supercritical fluid using a mechanical piston that cre- 12. S.H. Davis, Annu. Rev. Fluid Mech. 19, 403 (1987). ated density gradients at the cell’s side-wall when it was 13. J. Hegseth, Y. Garrabos, V.S. Nikolayev, C. Lecoutre- displaced. We have also observed single-phase overheating Chabot, R. Wunenburger, D. Beysens, Int. J. Thermophys. when the temperature was ramped past Tc . In this case, a 23, 89 (2002). denser liquid-like fluid surrounds a less dense gas-like fluid 14. J.R.A. Pearson, J. Fluid Mech. 4, 489 (1958). and overheating actually increases. 15. J. Hegseth, N. Rashidnia, A. Chai, Phys. Rev. E 54, 1640 (1996). We gratefully acknowledge the support of CNES and NASA 16. H.J. Palmer, J. Fluid Mech. 75, 487 (1976). through NASA-OBPS grants NAG3-1915 and NAG3-2447. We 17. J. Straub, in Proceedings of the IX European Symposium thank all of the Alice II team, especially J.F. Zwilling, and on Gravity-Dependent Phenomena in Physical Sciences, all individuals involved in the Mir missions for their technical edited by L. Rathe, H. Walter, B. Feuerbacher (Springer, support. Berlin, 1995) p. 351.