Surface Tension Measurements of Mixtures at Elevated Pressures. R. E. Padilla, M. D. A Lightfoot +, S. A. Dancyzk +

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1 ILASS-Americas 29th Annual Conference on Liquid Atomization and Spray Systems, Atlanta, GA, May 2017 Surface Tension Measurements of Mixtures at Elevated Pressures R. E. Padilla, M. D. A Lightfoot +, S. A. Dancyzk + University of California, Los Angeles Department of Mechanical and Aerospace Engineering Los Angeles, CA USA + Air Force Research Laboratory, Edwards Air Force Base Edwards, CA, USA Abstract An experimental study has been conducted to determine the effects of high pressures on the surface tension of H 2 O-N 2 and MeOH-CO 2. The motivation for this work is operations at high pressure and temperature, such as diesel and rocket engines. At high pressures and temperatures the system moves towards its thermodynamic critical point. The interfacial behavior as liquid moves towards this critical condition is not well understood. To examine the interface behavior, an experiment was developed to measure surface tension at different pressures. The experimental setup consists of a pool of either water and methanol placed inside a pressure vessel whic was pressurized with N 2 or CO 2, respectively. Capillary waves are created on the liquid surface using a metal rod that is attached to a speaker and excited via a function generator. Diffused light illuminates the liquid and waves are captured with a digital camera. Waves are observed in MeOH-CO 2 below 5 MPa and as the critical pressure was approached the solubility of CO 2 into methanol increased and contributed to lowering the amplitude of the waves. Surface tension decreased significantly in MeOH-CO 2 compared to H 2 O-N 2 due to the increased solubility and the widening of the interface region due to nearing the critical point of MeOH-CO 2. Experimental challenges in making surface tension measurements in these conditions are also discussed. Corresponding Author: repadill@g.ucla.edu

2 Introduction Understanding high-pressure, transient temperature processes involving atomization and mixing is of critical importance to the prediction of rocket, turbine and diesel engine performance. In a typical engine, relatively cold fuel enters the hot combustion chamber at high pressures. Mass and heat transfer occur between the combustion chamber environment (a highly localized mixture of oxygen and combustion products) and the fuel. Therefore, a fuel may be in a subcritical state with a finite surface tension prior to entering the engine but its surface tension will likely change dramatically, and may even go to zero if there are local areas where supercritical conditions are reached. In the past, these changes have largely been neglected, due to necessary simplifications for modeling, due to time-scale arguments or due to an imperfect understanding (or quantification) of the critical properties. This has led to a major difference in modeling approaches between the rocket and diesel communities rocket designers frequently neglect surface tension at all points, [1] while diesel designers often assume that surface tension is important throughout the spray [2, 3]. However, there is recent experimental evidence [4] that suggests a measurable change in both surface tension and its importance occurs at some engine conditions. Accounting for the change in surface tension and its relative importance compared to other forces may, then, be critical to accurate prediction of engine mixing and, therefore, overall performance. To date, however, little quantitative data for surface tension at conditions of interest to engines is available. Determining the properties, including surface tension, of fluids requires a knowledge of the local pressure, temperature and mole fraction of all species [5, 6]. In single component systems, this simplifies to a pressure and temperature dependence only, and many models exist to accurately predict properties including surface tension [7]. While a relatively mature process exists for predicting the surface tension of mixtures, it relies on empirical data (which is often not available at engine conditions), contains assumptions that are violated at high pressures, and fails to accurately predict systems with polar molecules such as water [5, 6, 8]. Recently, though, Dahms et al. [9] have developed a model to predict at which pressure and mixture conditions the surface tension will become negligible. While this model is an important step towards improving predictive capabilities, a lack of quantitative surface tension data at conditions of relevance persists. The work reported here is a first step towards measuring surface tension at pressures, temperatures and in mixtures of interest to engines. A multitude of methods exist for measuring surface tension, including several for which commercial instruments are available such as the Du Nouy ring method [10], the Wilhelmy plate method [11] and the pendant drop method [12]. As with all measurement techniques, various approaches have their strengths and weaknesses. Because the current goal is the measurement of surface tension at high pressures and temperatures, possibly in a dynamic environment, as the surface tension tends to zero, a method which is non-intrusive and enables low values of the surface tension to be measured is needed. This study has selected a method based on measuring the wavelength of excited capillary waves. The dispersion equation for capillary waves is well established, and may be derived in a variety of ways including from the Lagrange equation of motion, the Euler-Bernoulli equation or from energy conservation arguments. σ = ω2 ρ k 3 (1) where k=2π/λ is the wavenumber with λ defined as the wavelength, ω = 2πf is the angular frequency (f is the excited frequency), and ρ is density of the fluid. The given form of the equation neglects gravity and viscosity terms, but these terms can be easily added when important. The technique of using capillary waves to measure surface tension is not unique to this work: prior studies have used a variety of methods for measuring wavelength including scattering light [13], acoustic methods [14], capillary rise method [15], and laser interferometry [16]. This paper reports the initial steps in a wider study working to quantify surface tension and viscosity at high pressure and temperatures and within mixtures of interest to hydrocarbon engines. Here the changes in surface tension with pressure and composition are the focus; in particular, a discussion of the changes that occur as the critical point is approached are included. Experimental Description The experimental configuration schematic appears in Fig.1. The figure shows the high pressure chamber that contains quartz windows for optical access on two sides. A cylindrical container with the liquid fuel of interest is placed inside the chamber. For this study water and methanol (containing 0.006% water) were, independently, studied. The interior dimensions of the cylindrical container are 40 mm with a liquid depth of 25.4 mm. Capillary 2

3 waves as shown in Fig.2 are generated by a pointed metal rod immersed in the liquid and mounted on the speaker. The speaker is driven with a function generator set to a single frequency. The function generator provides a sine waveform excitation. The system is placed on a vibration free table to minimize extraneous excitation from the environment. The optical system was composed of a Lumix camera equipped with a long-distance microscopic lens (Infinity- K2 CF1 objective) and a halogen quartz lamp as the light source. A diffused backillumination sphere was used to produce light distribution on the liquid surface. The camera had a resolution of pixels. The camera was set to an ISO of 200 and an exposure time between seconds. Fig.2 shows a typical image used for the analysis of surface tension with an inset of the area inside the depth of focus of the lens; this inset area was the only one on which analysis was conducted. The exact area varies depending on the system s composition (due to the impact the composition has on the amplitude and wavelength produced), light source arrangement, camera inclination, and the lens focus. experiments. Density values used reflect the changes in temperature. The pressure was determined using a pressure transducer, Stellar Technology, psi with an uncertainty of 0.1% of full scaled. The function generator has an uncertainty of 2%. The main uncertainty in these experiments was the measurement of the wavelength discussed later. The experimental results presented in the next section feature visualizations of waves for water-n2 and methanolco2 up to injection pressures of 5 MPa (48.3 bar). Table 1 lists the experimental conditions. Figure 2. Example of an image and the selected region of interest used for measuring the surface tension. A close up view is seen in Fig.4. The camera s RAW format images were converted to TIFF images using the DCRAW software. A custom written Matlab script was used to process the data. Images were captured at an angle, necessitating the use of a projective transform. The cameras inclination, coupled with the microscope lens small depth of field leads to a limited area available for the analysis. The projective transform was verified through the use of a calibration image. This image was also used to calculate the spatial resolution: the typical spatial resolution of the images is 0.03 mm/pixels. Once the projective transform was applied and the in-focus area identified, waves were identified by examining the pixel intensity. More details on the extraction of wavelength from the image data is provided in the Results section of this paper. Figure 1. Experimental schematic showing the high pressure chamber and instrumentation, hand regulators and hand valves. PH stands for the speaker holder, PT is pressure transducer, TC is the thermocouple and PG is a dial pressure gauge. Table 1. Experimental operating conditions. Pressures were measured as gauge; typical atmosphere pressure at Edwards AFB is between 0.09 and MPa. The basic approach to the high pressure experiments is to set the liquid inside the chamber and gradually increase the gas pressure (with N2 or CO2 ) while monitoring pressure and temperature. The chamber is initially purged with N2 /CO2 prior to every experiment. The temperature in the cell is measured by a type K thermocouple (operating range: C, ± 2.2 C). The ambient temperature inside the chamber was not controlled, and varied from approximately 298 to 303 K over the course of these Case Water-N2 Methanol-CO2 3 f (Hz) P(MPa) T (K)

4 Results The function generator was adjusted to create low frequency, f, waves of Hz and 100 Hz in H 2 O-N 2 and MeOH-CO 2 mixtures, respectively. Typical images for H 2 O-N 2 are shown in Fig.3 and images for MeOH-CO 2 are given in Fig.4. A liquid with a lower viscosity here methanol, (0.594 mpa-s in a CO 2 vs the water viscosity of mpa-s) required a lower frequency and a higher camera angle to observe the waves. The images are used to calculate the surface tension by obtaining the wavelength via a Matlab routine, combining the measurement with the known excited frequency and density and applying Eq.1. To obtain the wavelength a line profile of the pixel intensities is defined from the center of the container along a radius where waves are clearly visible to the eye. Figures 5 and 6 show example line profiles. The location of the peaks in these profiles correspond to wave crests, so the difference in distance between peaks is the wavelength. To make comparisons easier a radial peak at a specific location was chosen to normalize the intensities. Images are analyzed at different regions on the liquids surfaces depending on the visibility of the waves. Higher amplitudes and an increased number of waves are observed in H 2 O-N 2, (seen in Fig.3) compared to MeOH-CO 2 (seen in Fig.4). The H 2 O-N 2 studies were aimed at investigating the impact of pressure on the surface tension while the MeOH-CO 2 mixture was selected to examine the impact to surface tension as the critical point is approached. Methanol is not of particular interest to most engines, but the critical point of MeOH and CO 2 is within the pressure range available to the current experiment at room temperatures. The pressure range for these experiments were from 0 to 4.8 MPa gauge in all mixtures. Using CO 2 posed some experimental challenges because the resolution became degraded as the pressure and, consequently, the density increased. The difference in intensity between wave crests and ridges became lessened as well. Additionally, as seen in the region marked on Fig.4, the waves became obscured by a cloud-like structure, likely composed of methanol vapor, that was generated on the surface. The carbon dioxide dissolves into the methanol and the vapor pressure of the methanol increases as the chamber pressure increases [17]. These phenomena can cause experimental difficulties by two means. First, they may change the liquid level more rapidly than evaporation at similar temperatures and, second, modified the density of both liquid and gas phases which alters the optical properties of the system. The density of both the liquid and gas near the surface must also be taken into account when computing surface tension [17]. Measurements with water-n 2 do not have the same high pressure complexities since the critical point of the water-n 2 mixture is far beyond the current experimental conditions, and the dissolution of nitrogen-water is very low at the conditions investigated [18]. The critical properties for pure substances and mixtures (at temperatures near room temperature) are listed in Table 2. Figure 3. Typical image used for the analysis and measurements of wavenumber for water-n 2 waves. Waves are generated at Hz for 0 MPa gauge (top image) and 4.8 MPa gauge (bottom image). Images are taken at exposure times of 1.3 s. Higher amplitude waves are seen for measurements using H 2 O-N 2 as seen in Fig.5 in comparison to MeOH-CO 2 waves, Fig.6. Figures 6 further show that at 5 MPa the waves are at a lower amplitude for MeOH-CO 2 than for H 2 O-N 2. Some of this difference is a result of approaching the critical point where the surface tension is trending to zero. Beyond 5 MPa, measurements are not possible for MeOH-CO 2 ; it is unclear at this time if this cut-off is due to obscuration resulting from large density gradients or a result of interface disappearance changes and the low value of surface tension. Videos taken at pressures beyond the 5 MPa (while waiting for equilibrium to be reached) confirm that the inability to make measurements was not due to the mechanical settings or malfunctioning of the driver due to elevated densities. It is well known in the literature that the equilibrium surface tension of a pure fluid decreases and tends to zero as the critical point is approached [6]. In mixtures, surface tension is not a function of the liquid alone, it also depends on the surrounding gas. At low pressures the effect of the gas on the sur- 4

5 MPa 3.8 MPa 4.8 MPa Maximum Peak Intensity Radial Distance from the Center (mm) Figure 4. Typical images used for the analysis and measurements of wavenumber for MeOH-CO 2. Waves are generated at 100 Hz at 0 MPa gauge (top image) and 4.8 MPa gauge (bottom image). Images are taken at exposure times of 1.3 s. Maximum Peak Intensity MPa 3.5 MPa 4.8 MPa Radial Distance from the Center (mm) Figure 5. Intensity profiles of waves generated for Water-N 2 at Hz for pressures of 0.7, 3.5, 4.8 MPa gauge taken from images with an exposure time of 1.3 seconds. face is small as long as the density difference between the gas and liquid is large (as is the case for both mixtures under examination here), but at increasing pressures the gas has an increasing effect on Figure 6. Intensity profiles of waves generated for MeOH-CO 2 at 100 Hz for pressures of 0.7, 3.5,4.8 MPa gauge taken from images with an exposure time of 1.3 seconds. the surface properties due to the density ratio decreasing as well as the diffusion of the gas changing the composition of the surface (which, additionally alters the critical point and nearness to the statechange conditions). Theoretical work from Dahms et al. [9] used through theory to quantify how the interface between the liquid and vapor broadens at high-pressure and high temperature conditions, reducing surface tension. This broadening increases the nearer the system is to the critical point and is viewed as the reason for the changes in the surface tension value. Pressures, and densities, have an additional impact in the current experiment because the density that appears in the capillary dispersion equation must be an overall system density; again, near atmospheric conditions the gas-phase contribution can be neglected for the systems under study, but at elevated pressures the gas density becomes appreciable. Indeed, the surface tension of both mixtures showed a decay with pressures as expected. However, the decrease for the methanol-carbon dioxide system was much more rapid than the water-nitrogen system, see Fig. 7. The increase in solubility of CO 2 in methanol is an additional factor influencing the decrease of surface tension with pressure in that system versus the H 2 O-N 2 system. Chang et al.[17] made measurements, showing the increase in density and solubility in MeOH-CO 2. As shown in the list of critical properties in Table 2, the H 2 O-N 2 critical point is well beyond the experimental conditions. Consequently, the changes in surface tension with pressure are not 5

6 the result of nearing the critical point. Additionally, the amount of nitrogen dissolved on the surface of the liquid is considered negligible at the pressure and temperature conditions of these experiments, so this system does not have the complexities of changes in surface composition [19]. In the MeOH-carbon dioxide system composition change and interface diffusion due to approaching the critical point are both present simultaneously making it impossible to propose what the individual contributions of each are. However, the results in Fig. 7 clearly show that the combined contributions have a marked impact on the lessening of surface tension at elevated pressures. High densities gradients and diffusion near the critical point (i.e., measured at 4.8 MPa) influenced the visibility of capillary waves. Videos of the phenomena near the critical point were taken to ensure the difficulty in identifying waves was not a result of the wave-driving set-up H 2 O-N 2 CH 3 OH-CO 2 5 MPa. As expected, the surface tension decreased with pressure for both mixtures. The methanol-carbon dioxide mixture showed a more rapid decrease with pressure due to the increased solubility of carbon dioxide (versus nitrogen in water) and the nearing of the critical point, where the interface becomes more diffuse. These effects also created a lower amplitude wave on the MeOH-CO 2 mixtures compared to the H 2 O-N 2 mixtures. The pressure sensitivity of H 2 O-N 2 was not drastically influenced by either mass transport of the gas into the liquid nor interface diffusion at the conditions tested, so that this mixture can be used as a baseline for comparison. Acknowledgement The authors wish to thank Professor Ann Karagozian, Dr. Alexander Schumaker, and Dr. Chiping Li for their continued support and discussion throughout this experimental investigation. This work was supported by Air Force Office of Scientific Research and Engineering Research and Consulting, Inc. and staff. 0.8 Normalized Surface Tension Reduced Pressure Figure 7. Normalized surface tension for MeOH-CO 2 and H 2 O-N 2 versus reduced pressure, P/P critical. Conclusion A sinusoidally oscillating speaker with an attached metal rod was used to create surface capillary waves on a liquid contained within a high pressure chamber. A digital camera was used to capture the capillary waves on the surface MeOH-CO 2 and H 2 O- N 2 mixtures. Wavelengths were determined from these images and calculations of surface tension from these wavelengths were used to examine the impact of pressure and behavior as the conditions neared the critical point. Experimental measurements were made to up to pressures of 4.8 MPa, and videos of the mixing process were captured for MeOH-CO 2 at 6

7 Table 2. Critical conditions of interest to the study are given. References for CO 2, CH 3 OH, and water- CH 3 OH are from [17], water-n 2 [19], for N 2 [20]. P c and T c are defined as the critical pressure and critical temperature. The mole fraction is defined as X. Case CO 2 CH 3 OH N 2 CH 3 OH-CO 2 H 2 O H 2 O-N 2 P c (MPa) >10 T c (K) X <10 4 7

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