Measuring the Refractive Index, Density, Viscosity, pH, and Surface

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Measuring the Refractive Index, Density, Viscosity, pH, and Surface Tension of Potassium Thiocyanate (KSCN) Solutions for Refractive Index Matching in Flow Experiments Yogesh K. Agrawal,†,§ Reza Sabbagh,†,§ Sean Sanders,‡ and David S. Nobes*,† †

Optical Diagnostics Group, Department of Mechanical Engineering, University of Alberta, Edmonton, Canada Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada

‡

ABSTRACT: Refractive index matching (RIM) methods are widely used in combination with optical flow measurement techniques such as particle image velocimetry and laser Doppler velocimetry to investigate fluid flows. In applying RIM, matching the refractive indices of the fluid and solid eliminates the problem of refraction/reflection at the solid−liquid interface. An experimental analysis of the effects of salt mass fraction and temperature on the refractive index of potassium thiocyanate (KSCN) solutions is conducted to quantify its performance as a RIM solution that is used in flow experiments. This enables the researchers to control the refractive index of the test medium under different test conditions by manipulating the KSCN mass fraction in the solution. Empirical correlations are developed by fitting the refractive index results, which highlight a nonlinear dependency on mass fraction and a linear dependency on temperature. The refractive index of the KSCN solution is found to be much less sensitive to changes in salt mass fraction and temperature compared to sodium iodide (NaI) solutions, a salt solution more commonly used for RIM studies. For a demonstration case, the refractive index of a KSCN solution was adjusted to align with borosilicate glass, a common transparent material used in two-phase experiments. The refractive index of the solid is a function of the quality and mass fraction of the ingredients used in the batch manufacturing operation and the process itself. For the batch of borosilicate beads used, a 0.624 (kg/kg) KSCN solution provided a perfect index matching rendering the glass beads transparent. Using this approach, the refractive index of a solid with a small and complex shape could be measured. In flow experiments, in addition to the refractive index, other fluid properties are influential and might need to be matched with the application. A discussion is also provided on the density, viscosity, surface tension, and pH of KSCN solutions to enable fluid dynamic scaling of experimental flow conditions through a set of correlations, developed to predict the properties of different KSCN solutions. and fluid properties to match nondimensional groups for scaling the flow, such as the Reynolds number, and include density, viscosity, pH, and surface tension. In addition, the usability, flammability, toxicity, reactivity, and cost must be considered.4,5 Aqueous sodium iodide (also called sodium iodine or anayodine with a molecular formula of NaI)6 is commonly used as index matched fluids for RIM applications. For example, Chen and Kadambi7 used a refractive index matched suspension of silica gel particles and a 50% (by mass) NaI solution to measure mean and fluctuating velocities of both continuous and dispersed phases in slurry pipe flows. Detailed studies describing the use of NaI as an index matching fluid are also available in the literature.3,8,9 Another solution that is used for RIM is the colorless and clear aqueous potassium thiocyanate (also called potassium rhodenate or rhodanide10) with a molecular formula of KSCN

1. INTRODUCTION Nonintrusive optical techniques such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) are often used in experimental multiphase flow studies.1,2 In these optical methods, light refracts through and reflects at each solid−liquid interface along the beam path of the illumination system, typically a laser. Differing refractive indices between the transparent solid and liquid phases therefore introduce difficulties in optical access, including insufficient illumination and image distortion.1 One method to eliminate such difficulties is to match the refractive indices of the liquid and solid phases. Budwig1 and Wiederseiner2 provided comprehensive reviews of the refractive index matching (RIM) technique. The RIM method has been used extensively in flow visualization studies, including the investigation of fluidized beds, porous media, particulate suspensions, and complex geometries.2,3 Organic and inorganic solutions such as zinc iodide (ZnI2), sodium iodide (NaI), alcohols, and mineral oils are widely used as the RIM fluid to achieve optical accessibility.4 These fluids are selected for individual applications based on system-specific requirements © XXXX American Chemical Society

Received: October 14, 2017 Accepted: April 23, 2018

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DOI: 10.1021/acs.jced.7b00904 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

For the same experimental conditions, the kinematic viscosity of ν = 2.02 × 10−6 m2 s−1 was reported by Gijsen et al.28 A more complete study investigating the effect of KSCN mass fraqction on density and viscosity was provided by Mitchell et al.25 Mass fractions were varied over a range of w = 0− 0.70 kg/kg at a constant temperature of 298 K. No information was found in the literature for the surface tension of aqueous KSCN or the effect of KSCN mass fraction on pH. For aqueous KSCN, the pH range has been reported to be 6−11 at 298 K.29 The lack of a detailed study in the literature of the important physical properties of KSCN solutions and an incomplete review of the potential benefits over NaI solutions provide the motivation for the present study. The first objective of the present study is to provide refractive index measurements of an aqueous KSCN solution as a function of salt mass fraction and solution temperature. The second aim is to compare the mass fraction sensitivity of KSCN and NaI solutions for a broad mass fraction range. Additionally, the most important physical properties, i.e., density, viscosity, surface tension, and pH, are provided to allow flow scaling of an experimental system using dimensionless numbers. The RIM method with KSCN is also implemented using borosilicate beads as the dispersed phase in experiments to assess optical properties.

(or CKNS or KCNS) according to the Hill system of writing empirical chemical formulas.11 Common physical constants and a general description such as appearance, solubility and change in state,12 electrical conductivity,13 vapor pressure,14 compressibility,15 and Raman spectra16 of aqueous KSCN can be found in the literature. A number of researchers studied the properties of KSCN solutions combined with other chemicals.17−20 Surface tension and liquid and vapor density of the sulfur dioxide solutions of KSCN have also been investigated.19,21 Presently, however, no comprehensive study of the properties of KSCN solutions related to multiphase flow experiments can be found in the literature, despite the fact that KSCN solutions have been used as index matching fluids in a number of applications. For instance, Harris et al.22 used an aqueous KSCN solution inside a packed bed of glass Ballotini to obtain 3D optical images from confocal laser scanning microscopy. Aguilar-Corona et al.23 investigated particle collision phenomena in a solid−liquid fluidized bed where Pyrex beads were fluidized using a w = 0.64 kg/kg aqueous KSCN solution. The mass fraction (w) is defined as the ratio of the mass of salt to the total mass of the aqueous solution. In another study, Jean-Franc et al.24 used 0.64 kg/kg aqueous KSCN solution for index matching to measure the velocity field of a pulsed flow in a glass column using PIV. Interestingly, Aguilar-Corona et al.23 and Jean-Franc et al.24 used the same mass fraction of KSCN at a fixed temperature of 293 K but reported refractive index values for their KSCN solutions that varied by a value of 0.0016. Even this small difference can result in imperfect index matching and impaired optical access. Although the reasons why aqueous KSCN solutions were used in the aforementioned studies were not explicitly given, it is notable that NaI salt is more expensive and relatively more toxic than KSCN salt.22 Additionally, KSCN solutions remain colorless/transparent in contrast to NaI solutions that become yellowish with exposure to oxygen.3 The latter can reduce the intensity contrast between the tracer and image background in flow measurements using PIV. When KSCN is used for refractive index matching for flow experiments, knowledge of its properties such as density, viscosity, surface tension, and pH becomes important. It is not just the refractive index of the KSCN solution that should be matched with that of the particles; other physical properties must be accurately known so that scaling laws can be met when the aqueous KSCN solution is used as a surrogate for the actual fluid of interest. For instance, it has been shown that the KSCN density and viscosity increase with the salt mass fraction in the aqueous solution.25 Therefore, these parameters should be taken into account when the Reynolds number of the aqueous KSCN is to be matched with a specific flow Reynolds number. In addition, in microscale flow investigations, the properties of surface tension and pH can profoundly influence the flow phenomenon because of capillary forces and surface charges, respectively. The literature provides some insight into some physical properties of aqueous KSCN solutions but typically over relatively narrow ranges or for fairly specific conditions. Najjari et al.26 reported the kinematic viscosity and density of a w = 0.6815 kg/kg KSCN solution at 298 K to be ν = (2.02 ± 0.06) × 10−6 m2 s−1 and ρ = 1429 ± 10 kg m−3. Gijsen et al.27 used KSCN solution as a blood analogue fluid and found that at 309 K a w = 0.71 kg/kg solution of KSCN in water had a dynamic viscosity of μ = 2.9 × 10−3 Pa·s and ρ = 1410 kg m−3. This gives a calculated kinematic viscosity of ν = 2.056 × 10−6 m2 s−1.

2. EXPERIMENTAL METHODS 2.1. Refractive Index of Solutions. The refractive index of a salt solution is a function of three main parameters: the salt mass fraction, solution temperature, and wavelength of the passing light.8 In the present study, the effects of mass fraction and temperature are investigated. Variation of refractive index with wavelength (also called the dispersion effect) is not considered in this study because the effect is small over the visible light spectrum.1 As part of the test program, both KSCN and NaI solutions were prepared by dissolving the desired mass of the salt in a known mass of freshly demineralized water that was collected from a water purification system (Elix Advantage, Millipore SAS). Details on the source and specifications of the salts are provided in Table 1 and Table 2. The mass of the components Table 1. KSCN Salt Specifications KSCN assay impurities color pH melting point anion traces cation traces

≥99.0% iodine consuming substances, passes test ≤0.005% insol. water colorless to white 5.3−8.7 (298 K, 5%) 446 K chloride (Cl−): ≤0.005% sulfate (SO42−): ≤0.005% Fe: ≤2 ppm NH4+: ≤0.003% Na: ≤0.005% heavy metals (as Pb): ≤5 ppm

Table 2. NaI Salt Specifications NaI vapor density assay form particle size melting point B

>1 (vs air) 99.999% trace metals basis beads −10 mesh 934 K DOI: 10.1021/acs.jced.7b00904 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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was measured using an analytical balance (Mettler Toledo AB analytical balance, model AB104-S) having 0.1 mg precision. During the KSCN solution preparation, the solution temperature decreased due to the endothermic nature of the dissolving salt reaction. A hot plate was used to heat the solution and maintain it at room temperature (296 K). In contrast, the temperature of a NaI solution increases in temperature when dissolving the salt into solution; i.e., it involves an exothermic reaction. The NaI solution required natural cooling to maintain the solution at room temperature (296 K). For both salts, their solubility (S) is a function of the temperature of the bulk solution. The effect observed for KSCN in the present study is compared with results available in the literature6,10 in Figure 1. While KSCN has a reported linear relationship

The refractive index of each salt solution was measured at a wavelength of 589.3 nm (sodium D line) using a commercial refractometer (Abbe-3L, Bausch and Lomb) having an accuracy of nD = ±0.00025. The refractive index of each KSCN solution was measured over a temperature range of 293−313 K. The refractive index of each NaI solution was measured at two temperatures: 296 and 298 K. This refractometer has an internal flow loop that allows connection to an external liquid source for temperature control. The temperature was controlled using a programmable temperature controller (Polystat, Cole-Parmer) at ±0.025 K to provide a range of controlled temperatures for the study. The data for refractive index measurement at different temperatures can be found in Tables 3−8. Table 3. Aqueous NaI Refractive Index nD at Different Mass Fractions w, Temperatures T, and Pressures Pa T = 296 K, P = 101.3 kPa

T = 298 K, P = 101.3 kPa

w

nD

w

nD

0.332 0.359 0.374 0.390 0.408 0.427 0.449 0.460 0.472 0.485 0.498 0.513 0.528 0.544 0.560 0.579 0.598

1.39390 1.40055 1.40450 1.40905 1.41365 1.41930 1.42600 1.42950 1.43335 1.43760 1.44210 1.44705 1.45230 1.45810 1.46480 1.47200 1.47970

0.498 0.512 0.518 0.524 0.530 0.536 0.543 0.549 0.556 0.563 0.570 0.577 0.585

1.44280 1.44745 1.44985 1.45195 1.45405 1.45645 1.45915 1.46150 1.46395 1.46660 1.46940 1.47210 1.47440

Figure 1. Effect of temperature T on the solubility S of KSCN and NaI in water in weight fraction. Dot (●), present; circles (○), KSCN;10 diamonds (◊), NaI;6 lines show the curves fitted to the data for KSCN (S = 0.00223T + 0.018), RMSE = 0.0048, R2 = 0.997 and for NaI solubility (S = −2.82 × 10−7T3 + 2.67 × 10−5T2 − 0.0826T + 8.95), RMSE = 0.0027, R2 = 0.998.

Standard uncertainties are u(w) = 0.0001, u(T) = 0.1 K, u(P) = 0.5 kPa, and u(nD) = 0.00025.

with temperature, NaI has a clear nonlinear relationship. The relation between the temperature and solubility for KSCN can be expressed using a linear fit as S = 0.00223T + 0.018. In this study, the solubility limit was measured at 296 K only. The saturation point of KSCN at 296 K was determined by finding the maximum mass of salts that could be dissolved while avoiding the formation of any salt crystals. The solubility of KSCN in water was found to be w = 0.705 (uncertainty is 0.0001) at 296 K and 101.3 kPa, which is the average pressure for the measuring time period (uncertainties are u(T) = 0.1 K, u(P) = 0.5 kPa) which compares well with reported results reported in the literature10 with 0.0041 deviation from the linear fit, root-meansquared error (RMSE) of 0.0048 (an indication of the difference between the predicted values by the fit and the data which shows how close the data are to the fit and has the units of the data), and goodness of the fit (R2) of 0.996, as shown in Figure 1. The KSCN solutions were prepared with mass fractions varying between the saturation point, w = 0.705 and a low mass fraction point of w = 0.20. To vary the mass fraction of the salt solution, a 5 mL syringe was used to add a measured amount of demineralized water and then the solution was stirred until well mixed. A similar methodology was used in the preparation of the NaI solutions. It has been reported that the maximum solubility of NaI at 298 K is w = 0.648.30,31

2.2. Refractive Index of a Solid−Liquid Mixture. Refractometer experiments provided quantitative analysis of the refractive index of KSCN. However, additional tests involving refractive index matching in a solid−liquid mixture were undertaken to better understand RIM implementation for optical analysis. Borosilicate beads can be used as a dispersed phase in solid−liquid flows and were used here as a test case for index matching. To match the refractive index of these beads, a transparent rectangular beaker that was 6.5 cm in depth was approximately half-filled with a packed bed containing monosized 3 mm (diameter) beads. The beaker was then filled with KSCN solution of a desired mass fraction at room temperature (296 K). A photograph of the experimental setup is shown in Figure 2. A target, positioned behind the beaker (at its midplane) was used as an image reference. The target had equally spaced white dots of equal diameter on a black background. A 2048 × 2048 pixel camera (TM-4200GE, JAI Inc.) was used to collect images of the target, KSCN solution, and borosilicate beads at varying KSCN mass fractions. The distortion of the dots on the target as a result of changing the refractive index of the solutions was assessed by comparing the portion of the target image observed through the beaker and KSCN solution with that observed through the packed bed of borosilicate beads.

a

C



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Table 4. Aqueous KSCN Refractive Index nD at Different Mass Fractions w, Temperatures T, and Pressures Pa T = 293 K, P = 101.3 kPa

a

w

nD

w

nD

w

nD

w

nD

0.705 0.697 0.689 0.681 0.674 0.667 0.659 0.652 0.646 0.639 0.632

1.49315 1.49135 1.48910 1.48750 1.48485 1.48275 1.48090 1.47800 1.47710 1.47505 1.47330

0.626 0.620 0.613 0.607 0.601 0.595 0.590 0.584 0.579 0.565 0.553

1.47155 1.46940 1.46810 1.46720 1.46515 1.46350 1.46215 1.46045 1.45915 1.45545 1.45210

0.540 0.529 0.518 0.507 0.497 0.487 0.477 0.468 0.451 0.435 0.420

1.44930 1.44650 1.44370 1.44100 1.43825 1.43580 1.43375 1.43175 1.42755 1.42345 1.41995

0.406 0.381 0.359 0.321 0.291 0.265 0.244 0.218 0.00

1.41705 1.41155 1.40610 1.39825 1.39085 1.38565 1.38075 1.37540 1.33330


Table 5. Aqueous KSCN Refractive Index nD at Different Mass Fractions w, temperatures T, and pressures Pa T = 298 K, P = 101.3 kPa

a

w

nD

w

nD

w

nD

w

nD

0.705 0.697 0.689 0.681 0.674 0.667 0.659 0.652 0.646 0.639 0.632

1.49220 1.49070 1.48850 1.48685 1.48460 1.48260 1.48050 1.47805 1.47675 1.47470 1.47285

0.626 0.620 0.613 0.607 0.601 0.595 0.590 0.584 0.579 0.565 0.553

1.47145 1.46930 1.46775 1.46635 1.46505 1.46305 1.46140 1.46015 1.45870 1.45505 1.45205

0.540 0.529 0.518 0.507 0.497 0.487 0.477 0.468 0.451 0.435 0.420

1.44905 1.44635 1.44300 1.44045 1.43755 1.43520 1.43300 1.43085 1.42705 1.42300 1.41945

0.406 0.381 0.359 0.321 0.291 0.265 0.244 0.218 0.00

1.41615 1.41050 1.40540 1.39675 1.39060 1.38520 1.38020 1.37475 1.33260


Table 6. Aqueous KSCN Refractive Index nD at Different Mass Fractions w, temperatures T, and Pressures Pa T = 303 K, P = 101.3 kPa

a

w

nD

w

nD

w

nD

w

nD

0.705 0.697 0.689 0.681 0.674 0.667 0.659 0.652 0.646 0.639 0.632

1.49135 1.48960 1.48760 1.48595 1.48350 1.48130 1.47950 1.47730 1.47570 1.47385 1.47210

0.626 0.620 0.613 0.607 0.601 0.595 0.590 0.584 0.579 0.565 0.553

1.46985 1.46820 1.46630 1.46500 1.46330 1.46155 1.45990 1.45840 1.45690 1.45340 1.44990

0.540 0.529 0.518 0.507 0.497 0.487 0.477 0.468 0.451 0.435 0.420

1.44675 1.44455 1.44095 1.43855 1.43665 1.43440 1.43190 1.42950 1.42585 1.42200 1.41830

0.406 0.381 0.359 0.321 0.291 0.265 0.244 0.218 0.00

1.41470 1.40970 1.40460 1.39600 1.38960 1.38440 1.37960 1.37415 1.33210


Mitchell et al.25 The density (ρ) and surface tension (σ) of the solutions were measured at a room temperature of 295 K using a force tensiometer (K100, Kruss, Germany). The measuring ranges of the tensiometer are 1−2200 kg m−3 with a resolution of 1 kg m−3 for liquid density and 1−2000 mN m−1 for liquid− air surface tension measurement. The Wilhelmy plate method34 was used to measure the surface tension. The tensiometer measures density using a density kit, and the measurement is based on the buoyancy principle. This kit includes a standard weight and a hook that holds the weight. To measure pH values of KSCN solutions, a commercial pH meter (AR50, Fisher Scientific/Accumet Research) with a relative accuracy of ±0.002 using a Ag/AgCl combination electrode35 was used.

2.3. Viscosity, Density, Surface Tension, and pH. Other important properties of KSCN solutions including viscosity, density, and surface tension were also measured in this study. Viscosity (μ) was measured using a concentric cylindrical32 rheometer (Rotational Rheometer: RheolabQC, Anton Paar USA Inc.33) with a double gap cylinder measuring system (DG42) and calibrated using a liquid with a known viscosity (D10 viscosity reference standards, Paragon Scientific Ltd.). The rheometer was controlled using the commercial software (Rheoplus/32 V3.62, Anton Paar USA Inc.), and the measurements were performed by setting the shear rate range. The temperature was kept at 298 ± 0.1 K during the viscosity measurements so that the results would be comparable with those of D



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a

w

nD

w

nD

w

nD

w

nD

0.705 0.697 0.689 0.681 0.674 0.667 0.659 0.652 0.646 0.639 0.632

1.49005 1.48840 1.48650 1.48455 1.48215 1.48045 1.47840 1.47610 1.47355 1.47195 1.46980

0.626 0.620 0.613 0.607 0.601 0.595 0.590 0.584 0.579 0.565 0.553

1.46845 1.46645 1.46415 1.46265 1.46085 1.45950 1.45790 1.45590 1.45455 1.45115 1.44730

0.540 0.529 0.518 0.507 0.497 0.487 0.477 0.468 0.451 0.435 0.420

1.44510 1.44230 1.43930 1.43715 1.43470 1.43245 1.43035 1.42810 1.42410 1.41990 1.41675

0.406 0.381 0.359 0.321 0.291 0.265 0.244 0.218 0.00

1.41390 1.40790 1.40330 1.39490 1.38835 1.38300 1.37855 1.37310 1.33165



a

w

nD

w

nD

w

nD

w

nD

0.705 0.697 0.689 0.681 0.674 0.667 0.659 0.652 0.646 0.639 0.632

1.48924 1.48710 1.48550 1.48300 1.48105 1.47875 1.47655 1.47450 1.47240 1.47040 1.46890

0.626 0.620 0.613 0.607 0.601 0.595 0.590 0.584 0.579 0.565 0.553

1.46715 1.46495 1.46305 1.46200 1.45960 1.45870 1.45645 1.45540 1.45360 1.45065 1.44725

0.540 0.529 0.518 0.507 0.497 0.487 0.477 0.468 0.451 0.435 0.420

1.44415 1.44175 1.43850 1.43620 1.43375 1.43150 1.42940 1.42720 1.42290 1.41875 1.41585

0.406 0.381 0.359 0.321 0.291 0.265 0.244 0.218 0.00

1.41305 1.40725 1.40235 1.39375 1.38760 1.38205 1.37790 1.37280 1.33085


Table 9. Density ρ, Viscosity μ, pH, and Surface Tension σ of Aqueous KSCN at Temperature T (298 K for Density and 295 K for Viscosity, pH, and Surface Tension) and Pressure P = 101.3 kPa and at Different Mass Fractions wa w

ρ (kg m−3)

μ (mPa·s)

pH

σ (mN m−1)

U(σ) (mN m−1)

0.00 0.03 0.05 0.07 0.10 0.20 0.30 0.40 0.50 0.60 0.65 0.68

999 1013 1022 1031 1047 1100 1157 1218 1283 1353 1392 1414

0.975 0.834 0.845 0.825 0.843 0.881 0.916 1.101 1.321 1.979 2.588 3.125

6.698 6.574 6.600 6.775 6.692 6.741 6.908 7.388 7.501 8.216 8.820 8.849

72.282 67.247 61.979 58.585 57.199 57.786 rejected 55.455 56.475 62.930 73.264 74.619

0.4 1.1 5.4 12.9 12.9 4.6 NA 5.8 5.4 3.9 1.2 1.2

a

Standard uncertainties are u(w) = 0.0001, u(T) = 0.1 K, u(P) = 0.5 kPa, u(ρ) = 3 kg m−3, and u(pH) = 0.002, and expanded uncertainties are U(μ) = 0.07 mPa·s and U(σ) as given in the table at 0.95 level of confidence.

Figure 2. Photograph of the experimental setup used for RIM tests.

The pH meter was calibrated using two pH buffers at a pH of 4 and 7 (Buffer-Pac Color-Coded Solutions, Fisher Scientific). The measured data for aqueous KSCN properties are provided in Table 9.

and 298 K for a broad range of salt mass fractions. The comparison here is to give assurance in the present experimental methodology, and hence, 296 and 298 K were chosen for a comparison as the data cover a wide range of NaI solution mass fractions. The results show that the refractive index of NaI increases with mass fraction, as illustrated in Figure 3. These measured refractive index values at different mass fractions were

3. RESULTS AND DISCUSSION 3.1. Refractive Index of NaI. In the present study, the refractive index of the NaI solutions was measured at T = 296 E



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Figure 3. Comparison of the refractive index nD of NaI solutions at different mass fractions w, measured during the present study and empirical relationships published previously. Circles (○), present, 296 K; squares (□), present, 298 K; solid line, Bai and Katz,3 298 K, maximum deviation is 0.081%; dashed line, Narrow et al.,8 298 K, maximum deviation is 0.049%.

compared with results available in the literature,3,8 which are also plotted in Figure 3 for comparison. Bai and Katz3 made refractive index measurements with a digital refractometer for NaI solutions at T = 296, 303, 308, and 313 K at a wavelength λ = 589 nm. The effect of NaI mass fraction on refractive index was expressed using the following correlation:3 n DNaI = 0.2425w 2 + 0.09511w + 1.335

(1)

This highlights that there is a quadratic dependency of refractive index on mass fraction. Narrow et al.8 measured the refractive index of NaI solutions for the mass fraction range w = 0.55−0.585 at T = 293−308 K and at interrogation wavelengths of λ = 589.3 and 632.8 nm. An empirical model based on their measurements and the Cauchy dispersion relation,36 with addition of the results of Kadambi et al.,37 gives (T is in K) n DNaI = 1.252 − 2.91 × 10−4w−1T + 0.365w − 0.0795w−1 + 5542λ−2

(2)

It is evident in Figure 3 that the present NaI refractive index results match with past models with a maximum deviation of 0.049 and 0.081% with Narrow et al.8 and Bai and Katz3 correlations, respectively. Note also the good agreement between the Narrow et al.8 and Bai and Katz3 correlations. The experimental results of Figure 3 also reinforce the conclusion that the refractive index of a NaI solution does not change significantly over the 2 K temperature range in which the NaI measurements of the present study were made. 3.2. Refractive Index of Aqueous KSCN Solutions. Refractive index measurements were made for KSCN solutions over the mass fraction range 0.20 ≤ w ≤ 0.705 at temperatures of T = 293, 298, 303, 308, and 313 K. The wide range of refractive index data for different mass fractions and temperatures is shown in Figure 4a for the full range and Figure 4b for the region with high KSCN mass fraction. This experimental data were fitted with a polynomial equation that is linear in T and

Figure 4. Measurements showing the effects of salt mass fraction w and solution temperature T on the refractive index nD of KSCN solutions. Dots (●), 293 K; circles (○), 298 K; triangles (△), 303 K; diamonds (◊), 308 K; squares (□), 313 K; the overall fit of the empirical model, eq 3, is also shown, for T = 298 K (solid line) and 313 K (dashed line). (a) Full range and (b) the high mass fraction region. The maximum standard deviations in measurements are 0.0006 at 313 K, 0.0008 at 308 K, 0.0009 at 303 K, 0.0004 at 298 K, and 0.001 at 293 K.

quadratic in w with R2 = 0.997 and a maximum deviation of 0.12% such that n DKSCN = 0.0774w 2 − 0.00015T (w + 1) + 0.216w + 1.379

(3)

It is interesting to note in Figure 4b that, for a 293 K rise in solution temperature (i.e., from 293 to 313 K), the refractive F



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[dnDKSCN/dT], was found to be ∼0.0002 K−1 for all mass fractions. This highlights that there is only a very small change in refractive index even with relatively large temperature changes. A relatively similar robustness to temperature change was observed for NaI solutions.3 In many larger-scale flow visualization studies, this robustness is important, as the process temperature may be controlled to, for example, ±1 K.38 3.3. Comparison of Sensitivity to Mass Fraction Variation. While both KSCN and NaI solutions are not particularly sensitive to temperature variation, there is a significant difference between the two refractive index matching fluids in terms of the mass fraction effect. Mass fraction sensitivity can be estimated for the entire mass fraction range by calculating the change in refractive index with a change in salt mass fraction, [dnD/dw], of NaI and KSCN at T = 296 K using eq 1 and eq 3, respectively, to give

index decreases by only nD = 0.004 (on average) for each KSCN mass fraction tested, indicating that the temperature sensitivity is low. The empirical correlation, eq 3, for predicting the refractive index of KSCN is cross-validated with independent measurements. The new data sets were obtained at T = 295.5 and 293.6 K and are shown in Figure 5. It can be seen that the correlation

dn DNaI dw

= 0.485w + 0.095

dn DKSCN dw

= 0.155w + 0.2604

(4)

(5)

From eq 4 and eq 5, it is obtained that the derivative coefficient for NaI is 3.13 times greater than that calculated for KSCN, indicating that index matching with KSCN will be easier to establish and maintain during an experiment. Mass fraction sensitivity of both salt solutions is further compared by considering a commonly used solid transparent material, borosilicate glass. For this purpose, a mass fraction range of w = 0.54−0.66 kg/kg was selected for both fluids, since the corresponding range of refractive indices overlaps the refractive index of a commercial laboratory grade borosilicate glass slide, which has a documented value of nD = 1.473.39 The intersection point between the refractive index of solid and liquid for both solutions is shown in Figure 7 for the mass fraction range 0.54 ≤ w ≤ 0.66.

Figure 5. Cross-validation of the new correlation (eq 3) for refractive index nD of KSCN solution as a function of solution temperature T and salt mass fraction w. Circles (○), present, 295.5 K; squares (□), present, 293.6 K; dashed line, eq 3 for 295.5 K; solid line (red), eq 3 for 293.6 K. The maximum deviation between data and eq 3 is 0.26% for 295.5 K and 0.10% for 293.6 K.

accurately predicts the refractive index of aqueous KSCN solutions over a wide range of salt mass fractions with a maximum deviation equal to 0.26%. Figure 6 demonstrates the effect of temperature on the refractive index of KSCN solutions for salt mass fractions of

Figure 6. Refractive index nD of KSCN solution as a function of solution temperature T and salt mass fraction w; circles (○), 0.4; triangles (△), 0.5; diamonds (◊), 0.6; squares (□), 0.7. Figure 7. Comparison of refractive index nD, change for NaI and KSCN in the mass fraction w, region that provides refractive indices similar to the value reported for borosilicate glass beads; T = 298 K. Squares (□), nDNaI; circles (○), nDKSCN; dashed line, linear fit, eq 6; solid line, linear fit, eq 7; dotted line, nDBorosilicate.

w = 0.40, 0.50, 0.60, and 0.70. The figure shows that there is a slight trend, regardless of KSCN mass fraction, of the refractive index to decrease with increasing solution temperature for the temperature range tested here. For example, for w = 0.50, the indices are nD = 1.4410, 1.4405, 1.4385, 1.4372, and 1.4362 at temperatures of 293, 298, 303, 308, and 313 K, respectively. The derivative of refractive index nD with respect to temperature T,

Focusing on the high mass fraction range of w = 0.54−0.66, the refractive indices of both solutions appear linearly G



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correlated with mass fraction. For the sensitivity comparison at higher mass fractions, experimental data for both solutions were fitted using linear regression to provide the following: n DNaI = 0.3982w + 1.243 →

dn DNaI

n DKSCN = 0.2605w + 1.308 →

dw

= 0.3982

(6)

dnDKSCN = 0.2605 dw

(7)

Equations 6 and 7 show that the derivatives of refractive index nD with respect to mass fraction w (dnD/dw) for NaI and KSCN are 0.3982 and 0.2605, respectively. This result highlights that the sensitivity of the NaI refractive index to mass fraction changes is 1.53 times greater than that of KSCN in the refractive index region surrounding the stated value for borosilicate. Utilizing the refractive index of a KSCN solution with its substantially lower sensitivity to mass fraction changes than a NaI solution is likely to have important practical applications, particularly for larger-scale experiments or flow facilities where it may be difficult to meet an exact mass fraction target, or possibly to avoid significant evaporation during a test. 3.4. Other Physical Properties of Aqueous KSCN Solutions. A generalized approach was undertaken here to map out and define the effects of KSCN mass fraction on the important flow parameters of viscosity, density, pH, surface tension, and, for consistency, refractive index. For each parameter, the measured results are expressed in terms of the weight mass fraction of KSCN, w, by fitting an exponential function f(w) such that f (w) = a1 exp(a 2w) + a3 exp(a4w)

Figure 8. Effect of KSCN mass fraction w on solution density ρ. Dots (●), present at 295 K; triangles (◁), Mitchell et al.25 at 298 K; square (□), Gijsen et al.27 at 309 K; diamond (◊), Najjari et al.26 at 298 K; line, eq 8. The maximum standard deviation in density measurement is 0.577. For the curve fitting, RMSE = 2.86 and R2 = 0.999.

(8)

where a1−a4 are constants and their values for each parameter are given in Table 10 and f(w) can be any of the parameters Table 10. Values for the Coefficients of eq 8 for Viscosity μ, Density ρ, pH, Surface Tension σ, and Refractive Index nD of Aqueous KSCN as a Function of Mass Fraction f(w) f(w)

a1

a2

a3

a4

μ (mPa·s) ρ (kg m−3) pH σ (mN m−1) nD

0.8612 995 5.85 51.68 1.274

−0.1210 0.5135 −0.4938 −3.26 0.0799

8.039 × 10−3 0 0.9154 18.08 0.0581

8.33 0 2.421 1.962 1.295

Figure 9. Effect of KSCN mass fraction w on solution dynamic viscosity μ. Dots (●), present at 295 K; triangles (◁), Mitchell et al.25 at 298 K; square (□), Gijsen et al.27 at 309 K; diamond (◊), Najjari et al.26 at 298 K; line, eq 8. The maximum standard deviation in dynamic viscosity measurement is 1.6 × 10−5. For the curve fitting, RMSE = 0.049 and R2 = 0.997.

represented in Table 10. For each of these, the regression equation is selected such that the goodness of fit is preferably R2 > 0.97 for the range w = 0−0.70. Root-mean-squared error (RMSE) that is a scale dependent indication of the difference between predicted values by the regression model and the data is also given for each fit. 3.4.1. Viscosity and Density. To understand the trend effects of varying mass fraction on results for μ and ρ, the experimental data and the fitted curves described in eq 8 are plotted in Figure 8 for density and in Figure 9 for dynamic viscosity. Comparing the correlations developed here for predicting the density and viscosity of the KSCN solutions with the available data in the literature shows that the correlations predict the parameters well and can be used as a predictive tool in flow experiments. In the mass fraction range generally of interest for RIM experiments, the dynamic viscosity increases sharply with increasing KSCN mass fraction. It is important to note that, for

a Reynolds number calculation, for example, it will be ∼0.50 of the value obtained if the properties of water are used compared to a KSCN solution where w = 0.60 KSCN. 3.4.2. pH. For aqueous KSCN solutions, pH was measured and it was found to be in the range from 6.5 to 9, which matches the range provided by the supplier.29 The effect of mass fraction on solution pH was measured, and the results are plotted in Figure 10. The results show that aqueous KSCN solutions become more basic with increasing KSCN mass fraction. The pH values of KSCN solutions can be expressed by eq 8, with R2 = 0.98 and the constants given in Table 10. 3.4.3. Surface Tension. The surface tension (σ) of the KSCN solutions becomes important when investigating flows where capillary action is present or surface tension forces are dominant. As highlighted in the Introduction, KSCN is used for H



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3.5. Results on Index Matching for Solid−Liquid Interfaces. While the value of the refractive index of solid particles is sometimes available in the literature, the refractive index of a set of test particles may vary from what is found for the base material used to make the particles. This can be due to the manufacturing process or the quality and mass fraction of the ingredients used that causes a small change in the refractive index of single particles or to the homogeneity of the particle mixture. Such changes can affect the performance of the RIM method. To investigate the performance of the KSCN solution for matching the refractive index of borosilicate beads, images of a target were collected to investigate image clarity. These images are shown in Figure 12 for different KSCN solutions containing

Figure 10. Effect of KSCN mass fraction w on the pH of the aqueous solutions. Dots (●), present; line, eq 8. The maximum standard deviation in pH measurement is 0.015. For the curve fitting, RMSE = 0.117 and R2 = 0.986.

flow experiments in porous media where the pore sizes are small enough that the surface forces may become dominant. The surface tension of KSCN solutions at different mass fractions was measured using a force tensiometer, and the results are shown in Figure 11. The surface tension measurement is a

Figure 12. Images of the target in packed bed beads for KSCN mass fraction w and refractive indices n: (a) w = 0.608, nD = 1.4672; (b) w = 0.624, nD = 1.4714; (c) w = 0.643, nD = 1.4765; (d) w = 0.682, nD = 1.4872.

w = 0.608, 0.624, 0.643, and 0.682, respectively, which provided refractive index values of nD = 1.4672, 1.4714, 1.4765, and 1.4872, respectively. The camera is viewing the target through a transparent square beaker of packed beads, as shown in Figure 2. In Figure 12, target dots are distorted for w = 0.608, as shown in Figure 12a, because the solution and beads have different refractive indices. As the KSCN mass fraction is increased, the solution refractive index approaches that of the beads. This leads to the appearance of an undistorted image of the target dots. At w = 0.624, undistorted views of the target dots were obtained, as shown in Figure 12b. This is the point of perfect index matching comparing the other images, and its mass fraction is also close to the mass fraction obtained for a perfect index matching, as shown in Figure 7. The perfect match on Figure 7 is for a sheet made from borosilicate material and may be slightly different for beads (spherical particles) with a size distribution. The 2 K change in temperature between this test and the values shown in Figure 7 results in a 0.02% change in the refractive index and is considered negligible. When mass fraction is further increased, a mismatch in refractive indices of the phases occurs. Figure 12c shows distorted dots for mass

Figure 11. Effect of KSCN mass fraction w on the surface tension σ of the aqueous solutions. Dots (●), present; line, eq 8. For the curve fitting, RMSE = 3.04 and R2 = 0.876.

sensitive procedure. For that reason, large variations were observed in the results, which led to the large uncertainty bars in the plot of the data in Figure 11. Surface tension measurement is highly sensitive to the test conditions particularly for solutions where equilibrium state is an important factor. Therefore, the measurement is limited to the equipment conditions and deviations such as the local evaporation effect at low mass fraction are inevitable. As is seen from this figure, surface tension decreases first by adding KSCN to water and then it increases with increasing mass fraction. A fit to the data is represented by eq 8 with a goodness of fit of R2 = 0.87 with the values of the best-fit coefficients found in Table 10. I



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Author Contributions

fraction w = 0.643. As the KSCN mass fraction is increased to w = 0.682, the target dots are completely obscured, as shown in Figure 12d, because the light is dispersed and scattered due to the presence of the borosilicate beads and the mismatch in refractive index. Given the complex shape and potential variation in different batches of commercially manufactured beads, this approach can be used to measure the refractive index of the solid phase prior to conducting any large-scale RIM experiment.

§

Y.K.A. and R.S. contributed equally to this work.

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(1) Budwig, R. Refractive Index Matching Methods for Liquid Flow Investigations. Exp. Fluids 1994, 17, 350−355. (2) Wiederseiner, S.; Andreini, N.; Epely-Chauvin, G.; Ancey, C. Refractive-Index and Density Matching in Concentrated Particle Suspensions: A Review. Exp. Fluids 2011, 50, 1183−1206. (3) Bai, K.; Katz, J. On the Refractive Index of Sodium Iodide Solutions for Index Matching in PIV. Exp. Fluids 2014, 55, 1−6. (4) Hassan, Y. A.; Dominguez-Ontiveros, E. E. Flow Visualization in a Pebble Bed Reactor Experiment Using PIV and Refractive Index Matching Techniques. Nucl. Eng. Des. 2008, 238, 3080−3085. (5) Nguyen, T. T.; Biadillah, Y.; Mongrain, R.; Brunette, J.; Tardif, J.C.; Bertrand, O. F. A Method for Matching the Refractive Index and Kinematic Viscosity of a Blood Analog for Flow Visualization in Hydraulic Cardiovascular Models. J. Biomech. Eng. 2004, 126, 529. (6) Chemical-Book. Sodium Iodide. https://www.chemicalbook. com/ChemicalProductProperty_EN_CB6170714.htm (accessed Dec 20, 2017). (7) Chen, R. C.; Kadambi, J. R. Discrimination between Solid and Liquid Velocities in Slurry Flow Using Laser Doppler Velocimeter. Powder Technol. 1995, 85, 127−134. (8) Narrow, T. L.; Yoda, M.; Abdel-Khalik, S. I. A Simple Model for the Refractive Index of Sodium Iodide Aqueous Solutions. Exp. Fluids 2000, 28, 282−283. (9) Jellison, G. E.; Boatner, L. A.; Ramey, J. O.; Kolopus, J. A.; Ramey, L. A.; Singh, D. J. Refractive Index of Sodium Iodide. J. Appl. Phys. 2012, 111, 043521. (10) Chemical-Book. Potassium thiocyanate. https://www. chemicalbook.com/ChemicalProductProperty_EN_CB8853514.htm (accessed Dec 20, 2017). (11) Hill, E. A. On a System of Indexing Chemical Literature; Adopted by the Classification Division of the U. S. Patent Office. J. Am. Chem. Soc. 1900, 22, 478−494. (12) Tyner, T.; Francis, J. Potassium Thiocyanate. ACS Reagent Chemicals; American Chemical Society: Washington, DC, 2017. (13) Lomelin, J. M.; Neubert, T. J. Electrical Conductivity of Potassium Thiocyanate. J. Phys. Chem. 1963, 67, 1115−1118. (14) Pearce, J. N.; Hopson, H. The Vapor Pressures of Aqueous Solutions of Sodium Nitrate and Potassium Thiocyanate. J. Phys. Chem. 1937, 41, 535−538. (15) Hoeiland, H.; Kvammen, O. J. Partial Molal Volumes, Expansibilities, and Compressibilities of Aqueous KSCN Solutions from 15 to 35 °C. J. Chem. Eng. Data 1983, 28, 179−181. (16) Chien, J. Raman Spectra of Aqueous Sotutions of Potassium Thiocyanate. J. Am. Chem. Soc. 1947, 69, 20−22. (17) Wadi, R. K.; Goyal, R. K. Densities, Viscosities, and Application of Transition-State Theory for Water + Potassium Thiocyanate + Amino Acid Solutions at 288.15−308.15 K. J. Chem. Eng. Data 1992, 37, 377−386. (18) Kraemer, E. O. The State of Dispersion of Gelatin in Concentrated Potassiumthiocyanate Solutions. J. Phys. Chem. 1941, 45, 660−670. (19) Eversole, W. G.; Wagner, G. H.; Bailey, G. C. Surface Tension, Liquid Density, and Vapor Density of Sulfur Dioxide Solutions of Potassium Thiocyanate at 10°, 15°, 20°, and 25°C. J. Phys. Chem. 1941, 45, 1388−1397. (20) Kalita, G.; Rohman, N.; Mahiuddin, S. Viscosity and Molar Volume of Potassium Thiocyanate + Sodium Thiocyanate + Acetamide Melt Systems. J. Chem. Eng. Data 1998, 43, 148−151. (21) Eversole, W. G.; Hart, T. F.; Wagner, G. H. Surface Tension and Activity of Sulfur Dioxide Solutions of Potassium Thiocyanate. J. Phys. Chem. 1943, 47, 703−709. (22) Harris, R. J.; Sederman, A. J.; Mantle, M. D.; Crawshaw, J.; Johns, M. L. A Comparison of Experimental and Simulated Propagators in Porous Media Using Confocal Laser Scanning Microscopy, Lattice Boltzmann Hydrodynamic Simulations and

4. CONCLUSION The results presented here indicate that KSCN solutions can be used to match a broad range of refractive indices, from nD = 1.3308 to 1.4931, primarily by varying the salt mass fraction and, to a much lesser extent, solution temperature. An empirical model has been developed which can be used to predict the refractive index of a KSCN solution over a wide range of mass fractions and temperatures. The variation of refractive index with salt mass fraction, dnD/ dw, is found to be about 3 times smaller for KSCN than that observed for another commonly used index matching fluid, aqueous NaI solution. Additionally, images of a target set behind a container approximately half-filled with borosilicate beads and KSCN solution show that the beads are essentially invisible at w = 0.624 with a refractive index of 1.4714. At this KSCN mass fraction, there is a significant change in the density and viscosity of the solution, which must be accounted for in any nondimensional scaling calculations of the type often required for cold-flow modeling experiments. Physical and chemical properties of KSCN including density, viscosity, surface tension, and pH were obtained and modeled. In conclusion, KSCN solutions are recommended as a more stable index matched fluid for refractive index matching experiments than other more commonly used fluids, such as aqueous NaI solutions. KSCN can be a better choice for flow experiments, as its aqueous solutions are less toxic than NaI solutions and its refractive index is less sensitive to mass fraction and temperature changes. This is an advantage in flow experiments when refractive indices are matched and particularly when small temperature changes from the flow itself or from external sources are inevitable.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Reza Sabbagh: 0000-0001-6446-6676 Funding

This research was conducted through the support of the NSERC Industrial Research Chair in Pipeline Transport Processes (held by R. S. Sanders). The contributions of Canada’s Natural Sciences and Engineering Research Council (NSERC) and the Industrial Sponsors (Canadian Natural Resources Limited, CNOOC-Nexen Inc., Saskatchewan Research Council’s Pipe Flow Technology Centre, Shell Canada Energy, Suncor Energy, Syncrude Canada Ltd., Total E&P Canada Ltd., Teck Resources Ltd., and Paterson & Cooke Consulting Engineering Ltd.) are recognized with gratitude. The authors also gratefully acknowledge additional financial support from the Alberta Ingenuity Fund and the Canadian Foundation for Innovation (CFI). Notes

The authors declare no competing financial interest. J



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Measuring the Refractive Index, Density, Viscosity, pH, and Surface

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