17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Refractive Index and Solubility Control of Para-cymene Solutions

Philippe M. Bardet1,*, Christopher D. Fu1, Carl E. Sickel1, Noah A. Weichselbaum1

1: Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC,

United States * correspondent author: bardet@gwu.edu

Abstract Refractive index matched facilities are of primary importance for non-intrusive optical measurement techniques. Optical distortions at the interface of non-index matched media can be detrimental to the accuracy of these measurements, particularly at curved surfaces. A binary mixture of para-cymene and cinnamaldehyde provides a viable option for index matching with acrylic that is a useful material for fluid test sections. Experimental data on this mixture and constituents are presented, including the temperature dependencies and effect on solubility control, that are both important parameters for fluids experiments utilizing techniques such as particle image velocimetry and planar laser induced fluorescence. 1. Introduction Due to its low kinematic viscosity (ν = 0.846×10−6 m2/s), high-refractive index (n ~ 1.49), good chemical compatibility, and low toxicity at 293 K, para-cymene, or p-cymene (1-methyl-4-isopropylbenzene), has been employed by several groups as a working fluid in index matched facilities, Haam et al (2000); Hassan and Dominguez-Ontiveros (2008); Huang et al (2008); Amini and Hassan (2012). Near room temperature its refractive index can be matched to several materials including one readily available and affordable solid: acrylic. In some applications it is also primordial to dissolve fluorescent dye in the solution to identify the solid phase with planar laser induced fluorescence; however p-cymene has a low solubility for most fluorescent dyes resulting in a weak fluorescence signal. In experiments where a careful index matching is required, the experimentalist has two options: controlling the environment temperature and/or adding solvent to the working fluid. Solvents can also be beneficial to increase concentration of dissolved dye and, hence, intensity of fluorescence. Here we report data on refractive index and solubility control of para-cymene by employing binary mixtures. 2 Para-cymene refractive index control The temperature dependence of fluids is determined in this investigation with use of a Thermo Scientific Abbe-3L refractometer with white light. This refractomer has an accuracy of ± 0.0001 for refractive index with a range of nD = 1.3000 -- 1.7100. The temperature of the measurement cell is controlled by circulating fluid with a bench-top chiller, which has a temperature stability of ± 0.1 K with a range of -5 to 50°C. Three measurements of refractive index are taken at each temperature to increase accuracy; for each temperature, outliers are discarded and the resulting average value is reported. . 2.1 Acrylic refractive index Refractive index of poly(methyl methacrylate) (PMMA), or acrylic, has been characterized by several groups and its property varies slightly with polymer composition. As a reference the data Geidur et al (1989) are reported; they measured four types of common clear polymers. They also found that the spectral dependence of temperature coefficient was weak for light between 400 and 700 nm; hence the spectral and temperature dependence can be decoupled. Temperature dependence of PMMA is reproduced below:

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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𝑛 𝑇 = 𝑛! + 𝛽(𝑇 − 𝑇!) (1) with nD = 1.4912 at To = 293 K and λ = 589 nm, and β = dn / dT is the temperature coefficient of the refractive index, which is independent of wavelength. For acrylic β = - 1.22×10−4 K−1 for 288 K < T < Tv. Above the vitrification temperature, Tv, the material transitions from a vitreous state, where segments of the polymer chain are “held frozen”, to a state where the polymer segments have enough thermal energy to overcome intermolecular interaction and start vibrating and rotating. For PMMA, Tv = 330 K and β = - 2.02×10−4 K−1 for Tv < T < 373 K. It should be noted that published values of nD varies between 1.490 and 1.494. Kasarova et al (2007) gives the spectral dependence of PMMA at To = 293 K:

𝑛! =  2.399964   −  8.308636×10!!𝜆!  −  1.919569  ×10!!𝜆!! +  8.720608  ×10!!𝜆!!− 1.666411×10!!𝜆!! +  1.169519  ×10!!𝜆!!

where λ is the light wavelength in micrometer. For index matched facilities, cast acrylic should be chosen over extruded components. In extruded materials, the solid has residual stress that locally affects the refractive index preventing tight and uniform matching of the indexes. 2.2 Temperature dependence of para-cymene The temperature dependence of liquids can be modeled with equation (1). The terms nD and β for the different fluid combinations tested here are reported in Table 1. Para-cymene tested here is a 99% purity sample from Sigma-Aldrich. At 293 and 298 K the refractive index measured in this study are 1.4910 and 1.4888 respectively. These values are noticeably lower than reported in Amini and Hassan (2012) (1.4944 at 293 K and 1.4924 at 298 K), but are in better agreement with values of Comelli et al (2002) and references therein (range of 1.4865 – 1.4885 at 298 K). Table 1: measured values of refractive index between 288 and 313 K. Mixtures are volumetric fractions. To = 293 K. Fluid mixture nD β (K-1) Para-cymene (p-c) 1.49079 - 4.58 × 10-4 Cinnamic aldehyde (c-a) 1.62063 - 4.63 × 10-4 99% p-c – 1% c-a 1.49222 - 4.48 × 10-4 98% p-c – 2% c-a 1.49311 - 4.55 × 10-4 2.3 Binary mixture index matching Binary mixtures are commonly used to match refractive indexes of materials as well as other thermophysical properties, such as density and viscosity. For example, Nguyen et al (2004) used mixtures to develop an index matched surrogate for blood. Comelli et al (2002) characterized the dissolution of n-hexane in p-cymene to control refractive index, density, and viscosity of the mixture. Because n-hexane has a lower refractive index than p-cymene, the resulting solution had a lower index and could be matched to Pyrex (n ~ 1.475) with 10% n-hexane at 298 K. To match acrylic near room temperature, the refractive index of p-cymene must be increased with a solvent. Depending on the nature of the liquids, the refractive index of binary mixtures is given by either the Lorentz-Lorentz, Wiener, Heller, Gladstone-Dale, Edwards, or Arago-Biot equations. The Arago-Biot equation reproduces experimental results within less than 1% and is a good model for the concentrations of interest here. Hence analytically, the refractive index of the mixture can be approximated as:

𝑛!"# =   𝑛!𝜙!!

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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where ϕi is the volumetric fraction of fluid i in the mixture, and ni the refractive index of the pure liquid. Cinnamic aldehyde, or cinnamaldehyde, is an unsaturated organic liquid that is conjugated, has relatively low toxicity, and has a high refractive index n ~ 1.62 at 293 K and 589 nm. Nguyen et al (2004) suggested it as a candidate for index matched hydraulic experiment, but did not further characterize it due to its high-cost. Cinnamaldehyde is a basically a phenyl group with an unsaturated aldehyde attached to it. It is fairly low in polarity, as only the aldehyde group is capable of hydrogen bonding. This low polarity and structural similarity allow for the intermolecular forces between cinnamaldehyde molecules to not be significantly higher than the intermolecular forces between cinnamaldehyde and para-cymene molecules, allowing for miscibility. While low in toxicity, cinnamaldehyde does increase the overall toxicity of the solution used for index matching as some people can have an allergic reaction to it, and it can target mucous membranes and lungs on inhalation. A respirator and gloves should be used at all times when handling cinnamaldehyde, especially when mixed with p-cymene. Another drawback is cinnamaldehyde reacts slowly with acrylic. When a piece of acrylic was left in pure cinnamaldehyde for three days, the mass of the acrylic piece decreased from 3.163 g to 3.153 g. When using cinnamaldehyde with acrylic, procedures should be taken to minimize time of contact as much as possible. Fortunately, since cinnamaldehyde has a high refractive index, it represents only a small percent of the total solution volume. For the index matched solution, compatibility tests were performed and the weight of the acrylic sample stayed unchanged after prolonged exposure and grazing was not visible on the surface. Temperature dependence of solutions of p-cymene and cinnamaldehyde (1 and 2% per volume) are displayed on figure 1. P-cymene is nearly matched to PMMA at 18.8°C or slightly below room temperature, which requires active cooling of flow loops where pumps and head losses are sources of heat. For comparison, Teng (2003) found best results at 15°C. With 1% cinnamaldehyde, fluid and PMMA are index matched at 23.1°C; with a solution of 2% cinnamaldehyde, the matching is accomplished at 25.8°C. This temperature, slightly higher than room temperature, simplifies operation and temperature control of large flow loop with powerful pumps.

Fig 1. Temperature dependence of pure and binary mixture of p-cymene used to matched refractive index of

acrylic.

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Higher concentration of cinnamaldehyde is necessary to match the refractive index of N-BK7 glass at room temperature. 3 Fluorescent dye solubility P-cymene is a simple hydrocarbon (a toluene with an isopropyl in the para position) and has low affinity with fluorescent dyes, e.g. Fluorescein, Rhodamine . Because the rhodamine molecules are not very polar, they are able to dissolve at low concentrations in para-cymene. In fact, Rhodamine 6G was the only dye tried that did so. The addition of cinnamaldehyde is able to increase the solubility of Rhodamine 6G in para-cymene thanks to the unsaturated aldehyde chain in cinnamaldehyde. The oxygen in the aldehyde group is capable of forming hydrogen bonds with the dye molecules, allowing for the affinity between solvent and solute to increase. In pure cinnamaldehyde we measured a saturation concentration of 2 mg of R6G per milliliter. After a 2 weeks period the R6G was still in solution. When cinnamaldehyde saturated in R6G was put in solution with p-cymene in the concentrations mentioned above, a little bit of aggregation was noticeable, but the solution stayed strongly pink and no separation of the solution occurred. This leads to significantly more intense PLIF signals, as presented in the next section. 4 Sample PLIF Results Fig. 2 illustrates the importance of closely matching the liquid and solid refractive indexes in complex and regular geometries. In a 6×6 array of acrylic rods, close matching of the refractive indexes is primordial to minimize optical aberration that limit resolution in identifying the rods location in the laser sheet plane with PLIF, fig. 2 (a). In particular on the rod at upper left, i.e. the first column of rods imaged by the camera, the bright region around the first rod is due to light scattered at the interface between the liquid and the solid is an artifact of slight mismatch between the materials, fig. 2 (b). While this was taken advantage by other groups (Huang et al (2008)), it must be avoided here as it decreases the resolution in finding the rod location, and limit the accuracy of velocity measurements near the wall. In this periodic geometry, for the last column of rods imaged by the PLIF camera, each rod in front of the camera introduces distortion that appears on the following column. This is particularly noticeable on the rod at the lower right corner of the PLIF frame, fig. 2 (c). These distortions disappear once a para-cymene and 1% cinnamaldehyde mixture is used. Furthermore, because a higher concentration of Rhodamine 6G can be dissolved in the solution, the signal to noise ratio is significantly increased, fig. 2 (d). This leads to increase resolution in identifying the rod location.

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Fig. 2 Index matching control in PLIF data. Camera is imaging the PLIF signal from the left hand side

5 Conclusions The refractive indexes of p-cymene - solvent binary mixtures have been characterized to closely match the mixture to either acrylic. This provides an alternative to controlling the working fluid temperature and does not necessitate operating below room temperature, which would be expensive in large facilities. Fine control of temperature is still necessary, but is now slightly above room temperature. The solvent has the added benefit of increasing the amount of fluorescent dye that can be dissolved in the solution and hence in PLIF images the fluorescence signal is stronger. These combined effects enable to resolve structure location with high spatial resolution, which would not have been possible otherwise.

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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