Review of Refractive Index-Matching Techniques of Polymethyl Methacrylate in Flow Field Visualization Experiments

Fan, Dajun; Li, Rongjie; He, Minghan; Li, Xianwen; Li, Jinyang; Wen, Jun; Hu, Yongping; Li, Yanan; Li, Yue; Gu, Long; Li, Zhifeng

doi:https://doi.org/10.1155/2023/3413380

International Journal of Energy Research

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Abstract Introduction Analysis Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Review Article | Open Access

Volume 2023 | Article ID 3413380 | https://doi.org/10.1155/2023/3413380

Review of Refractive Index-Matching Techniques of Polymethyl Methacrylate in Flow Field Visualization Experiments

Dajun Fan,^1,2,3Rongjie Li,^1,2Minghan He,^1,2Xianwen Li,^1,2Jinyang Li,^1,2Jun Wen,^1,2,3Yongping Hu,^1,3Yanan Li,¹Yue Li,¹Long Gu,^1,2,4and Zhifeng Li⁵

Academic Editor: Mahmoud Ahmed

Received28 Sept 2022

Revised26 Nov 2022

Accepted10 Dec 2022

Published06 Feb 2023

Abstract

The development of modern computational fluid dynamics (CFD) technology provides many preliminary references for experimental design. In addition, the CFD calculation results verified by experiments can display enormous microdata in areas that are difficult to measure through experiments, as an extension. This can make measurements more reasonable and effective, shorten measurement times, and save manpower and capital significantly. Therefore, it is vital to verify the accuracy of CFD calculation results, especially in cases of complex structures and multiphase flows. The results of model tests can be utilized in a prototype experiment by properly designing a test section and selecting a working fluid if the Reynolds similarity criterion is met. Optical measurement technology is a noninvasive measurement method, and the impact on the flow field can be almost negligible. It is advised to use transparent materials and prepare a refractive index-matching (RIM) fluid to obtain a good optical path. Polymethyl methacrylate (PMMA) is widely used in flow field visualization experiments because of its good light transmission and mechanical strength. This review is aimed at introducing the current status of different flow field measurement techniques; moreover, it is intended to help the readers to become more familiar with the principles of RIM, the characteristics, applications, and usage suggestions of various RIM fluid schemes of PMMA, providing references for researchers in the design, preparation, and conducting stages of flow field visualization measurement experiments. This review is divided into five sections. In the introduction section, Chapter 1, relevant research developments and related results of flow field measurements are presented, followed by the innovations and benefits of this paper. In Chapter 2, the flow field visualization measurements are presented and a derivation is shown. In Chapter 3, some RIM fluid schemes of PMMA and their applications are given, which are very valuable for peers. In Chapter 4, the measurement and analysis of some physical properties are described. In the RIM process, it is necessary to focus on the RI, density, dynamic viscosity, compatibility, stability, safety, and cost of RIM fluids. These factors greatly impact the accuracy of experimental results, experimental progress, and safety of the experimenters. Based on the analysis and our practical experience, some suggestions are given for preparing and using RIM fluids. In the conclusion section, Chapter 5, the results and practical implications of this paper are summarized.

1. Introduction

Numerical simulations and experimental measurements are two of the most critical methods for studying fluid dynamics. Three-dimensional computational fluid dynamics (CFD) techniques can provide researchers with accurate theoretical predictions, and the simulation results verified by experimental data can provide more detailed flow field information. High-quality experimental results can be used to examine the applicability of the software, improve existing theories, or even propose new ones. Flow field visualization experiments mainly study the pressure distribution and velocity distribution of working fluids in channels, which play a vital role in biological, medical, chemical, mechanical, and nuclear fields. The data obtained from flow field visualization experiments based on the similarity principle and dimensional analysis can be applied to prototype experiments with harsh conditions, opaque flow, or high cost [1], which can significantly reduce the experimental difficulty, save the experimental cost, and improve the measurement accuracy.

Various measurement methods have been developed successively to study the flow characteristics of the working fluids in the channels. According to whether the measuring device is in contact with the flow field, the measurement methods can be divided into invasive and noninvasive. The invasive measurement method requires direct contact between the measuring devices (such as pitot tubes and porous probes) and the flow field to be measured, and these devices can interfere with the flow field formation and affect the measurement accuracy. In addition, most of these methods can only measure at a single point, making it difficult to obtain detailed and accurate flow field information. In contrast, the noninvasive measurement method does not need to embed measuring devices in the flow field (or only need to scatter a small number of tracer particles). Thus, the impact on the flow can be almost negligible. Such methods mainly include (1) particle- and magnetic field-based tomography techniques, such as positron emission tomography [2], nuclear magnetic resonance imaging (NMRI) [3], gamma-ray attenuation [4], and X-ray tomography [5]; (2) techniques based on the Doppler principle, such as laser Doppler anemometry (LDA) [6] and ultrasonic Doppler velocimetry (UDV) [7]; and (3) visual image-processing techniques based on optical measurement methods, such as particle image velocimetry (PIV) [8], particle-tracking velocimetry (PTV) [8], and planar laser-induced fluorescence (PLIF) [9]. Among them, tomography techniques can obtain global flow field information, but the measuring devices are very expensive, and the spatial and temporal resolution of the measurement is poor [10–12]; Doppler principle-based velocimetry can only perform single-point measurements or statistic average velocity; optical measurement techniques are simple to operate and moderate in cost and provide three-dimensional, transient, and high-resolution experimental data.

The resolution of PIV can reach the magnitude of camera pixels (about 10 μm) [13]. In recent years, optical measurement techniques have received more attention and applications and have become one of the most important means to measure the velocity distribution inside the flow field.

Flow field visualization refers to the visualization of the flow field by various techniques, and the three commonly used methods [14] are (1) adding tracers to the fluid to characterize the velocity distribution of the fluid by the motion of tracers, such as scattering tracer particles or dyes into the liquid and injecting smoke, water vapor, and chemical components into the gas; (2) adding tracers to the boundary of the fluid, such as dropping oil droplets or liquid films on the fluid surface; and (3) using the difference in density or material structure between fluid and solid boundaries to distinguish fluid from boundaries, such as using X-ray, ultraviolet light, charged particle radiation, and nuclear magnetic resonance.

A clear and correct optical path is crucial for flow field visualization experiments. The two most important factors affecting the optical path are (1) the light transmittance of the model materials, a low light transmittance material will reduce the clarity of images, affecting the image quality and the range of measurement areas, so it is necessary to choose materials with high transmittance. (2) Refractive index-matching (RIM) result of the model material and the working fluid, the difference in refractive index (RI) between the two can lead to problems such as alteration of the optical path, illumination of irrelevant flow regions, or formation of hot spots due to total reflection, and wrong experimental results are obtained [15, 16]. Therefore, the RIM technique is needed to adjust the refractive indices of the working fluid and the model material to achieve optical measurements in complex models, porous media, fluidized beds, highly concentrated particle suspensions, and density-stratified flows.

RIM techniques could date back to the 1950s and be used to study fluidized beds with high concentrations of non-agglomerated particle suspensions [17]. In recent decades, researchers have proposed various RIM fluid schemes for research in the fields of biology, medicine, chemistry, mechanics, engineering, and nuclear energy. (1)In the field of biology and medicine, Hopkins et al. [18] studied the flow characteristics inside the nasal cavity using a transparent model and observed the vortex flow inside it by PIV. Kim and Chung [19] reconstructed the airflow inside normal and pathological nasal cavity models by PIV. Budwig et al. [20] studied steady flow inside an abdominal aortic aneurysm and found that a circulating vortex structure surrounded the laminar flow, and the magnitude of wall shear stress within the circulating region was about 1/10 of that at the entrance to the angioma. Gijsen et al. [21] studied the flow in a carotid bifurcation and found that the stability of the shear layer within the carotid artery was highly susceptible to pathological stenosis of the carotid artery. Curran and Black [22] studied the shear stress and mixing processes within an annular-flow bioreactor and found that the relative magnitude of shear stress decreased with vessel size, and the number of cells remained in suspension in the vortex of Taylor flow was more than that in Couette flow(2)In the field of chemistry, Kohnen and Bohnet [23] studied the flow of solid-liquid suspensions in agitated vessels using LDA and found that CFD calculation results agreed well with the experimental data. Lyon and Leal [24, 25] compared the particle velocity and concentration data of the fully developed region obtained from LDA measurements with different theoretical models (e.g., Leighton and Acrivos model, Phillips model, and Mills and Snabre model), and found that the Mills and Snabre models were in the best agreement. Averbakh et al. [26] used LDA to obtain the velocity distribution of the suspension in a rectangular duct and the velocity fluctuations due to particles and detected the net drift of particles. Shauly et al. [27] found that the predictions of the Leighton and Acrivos model and the Phillips model were in good agreement with the axial and transverse velocities in a rectangular tube measured by LDA and observed particle migration. Chaudhuri et al. [28] focused on single-particle trajectories in colloidal suspensions and found that the self-part of the von Hove distribution function describing the spatial and temporal distribution of suspension dynamics was not Gaussian distribution. Kegel and Blaaderen [29] obtained evidence for dynamic heterogeneity in viscous liquids by analyzing particle trajectories in colloids. Dibble et al. [30] found that the heterogeneity of the particle cluster structure in colloids increases with short-range attractive interactions. Kaufman and Weitz [31] confirmed the existence of reentrant glass transition points by experimental images and found qualitative differences in the attraction and repulsion dynamics between glasses. Gao and Kilfoil [32] examined the self-parts and distinct parts of the von Hove function by observing the particle motion in suspension through confocal fluorescence microscopy and found that two populations with significantly different migration velocities appeared in the self-part and pronounced dynamic heterogeneity existed near the gel transition in the distinct part(3)In the field of mechanics and engineering, Uzol et al. [33] studied the flow in the near-blade region inside a turbopump with a rotor, stator, and vanes by PIV and measured the instantaneous and phase-averaged velocity distribution as well as the kinetic energy distribution of the turbulent flow. Liu et al. [34] studied the flow of coolant inside an internal combustion engine by LDV and found that the velocity near the cylinder head was higher than that near the gas face. Tindal et al. [35] investigated the steady flow inside an engine intake and cylinder by LDA and found that four flow patterns existed within the axially symmetrical intake and discussed the effects of valve opening and intake shape on the downstream flow development of the valve. Bovendeerd et al. [36] measured the axial velocity and secondary flow inside the steady-state inlet of an elbow by LDA. Parker and Merati [37] measured the axial-radial velocity vector of Taylor-Couette turbulence in an annulus using LDA and observed the vortex structure at high Taylor numbers(4)In the field of nuclear energy, Hassan and Dominguez-Ontiveros [38] used PIV to measure the velocity distribution within a pebble bed modular reactor, improving researchers’ understanding of the microscopic flow inside it. Dominguez-Ontiveros et al. [39] studied the flow characteristics within a rod bundle of pressurized water reactors, obtaining experimental data under different test cases (e.g., experimental manipulation dimension, measurement area, test setup, and boundary conditions). Zhang et al. [40] studied the flow characteristics inside a 7-pin wire-wrapped fuel bundle of a fast reactor using PIV and found that wire-wrapper spacers enhance the crossflow. Delgado et al. [41] studied the flow inside a helical coil steam generator using PIV and found that the flow characteristics were only related to the relative position of the flow in the rod bundle, independent of the ratio of tube spacing and tube diameter

Review articles [42, 43] on the introduction of RIM techniques of different solid materials have been published for a long period of time, many new RIM fluid schemes and applications developed in recent years have not been included, or the analysis of PMMA is not very detailed. In this article, we expound on the principles of RIM techniques, summarize the schemes, applications, properties, and usage suggestions of RIM fluids of PMMA in detail, and prospect the new RIM fluid schemes, which can provide some reference for researchers in the design, preparation, and conduct stages of flow field visualization experiments.

2. Flow Field Visualization Measurement Technology

When light from a medium obliquely into another medium with a different RI, its propagation direction usually changes, which is called the phenomenon of refraction of light. As shown in Figure 1, the intersection between the two media is a surface, the incidence angle and speed of the incident light in medium 1 is and ; the refraction angle and speed of the refracted light in medium 2 is and .

According to Huygens principle [44] and relevant geometry knowledge, we obtained and ; and . Therefore,

Define RI as the ratio of the propagation speed of light in a vacuum to that in a medium, from which it follows that

In Equation (2), and represent the refractive indices of medium 1 and medium 2, respectively.

The materials of experimental sections and working fluids have a great influence on the measurement accuracy. The five most important factors affecting the imaging quality of a flow field visualization experiment are (1) the transmittance of model materials and working fluids; (2) RIM result of working fluids and model materials; (3) compatibility between working fluids and model material; (4) stability of working fluids (color and composition); and (5) reduction or elimination of stray light. In order to allow the laser to reach the entire plane and the reflected light from the tracer particles to enter the camera, the experimental section needs to be made of materials with high transmittance, good mechanical strength, and easy purchasing and processing. Commonly used model materials are fluorinated ethylene propylene (FEP), polyvinyl acetate (PVAc), polystyrene (PS), and polymethyl methacrylate (PMMA). Among them, FEP has poor transmittance and causes substantial decay of the laser flux [45, 46]; PVAc has a low softening point (38°C) and is unsuitable for medium- and high-temperature tests; PS has poor toughness and is difficult to machine. PMMA, with its good transmittance and easy processing, is the most used model material in flow field visualization experiments. At 28°C, the density of PMMA is 1.175 g/cm³ and the RI is 1.491 when irradiated by light with a wavelength of 589.3 nm.

The optical velocimetry technique obtains the flow field information by the strong interaction between the incident light (usually laser) and the heterogeneous phase in a fluid. For transparent liquids whose motion cannot be observed directly, tracer particles need to be scattered into the fluids, and the tracer particles are displayed by illumination or fluorescence, and then the optical images are recorded employing cameras or videos, and the velocity distribution of the working fluid is obtained by corresponding algorithm process.

Based on the Doppler principle, velocimetry methods such as LDA, phase Doppler anemometer (PDA), tunable diode laser absorption spectroscopy (TDLAS), and UDV have been developed. Among them, the TDLAS is only applicable to gas flow field measurement, and its application range is narrow; the UDV method can be used for velocimetry of opaque fluids, but like LDA or PDA methods, only single point or average velocity measurement can be performed.

PIV is a transient, multipoint, noninvasive method of flow field velocimetry developed in the late 1970s. The PIV technique surpasses the limitations of single-point velocimetry techniques (e.g., LDA and PTV) by recording velocity distribution information at a large number of spatial points at the same transient and providing rich spatial data on the structure of the flow field as well as flow characteristics. In addition, the pressure distribution can be extracted from the velocity distribution data measured by PIV through theoretical calculations [47]. Flow field visualization experiments focus on the velocity distribution of the working fluid in the flow channel. The optical measurement technique is basically noninterfering to the flow field, with high-measurement accuracy and a wide range of applications.

Benefiting from the advanced development in software (computation models and processing algorithms) and hardware (computers, lasers, and photographic equipment), PIV has developed rapidly and is used in a wide variety of measurement environments. The stereoscopic PIV [48], which emerged in the 1990s, can measure a third velocity component perpendicular to the laser plane and two orthogonal velocity components parallel to the laser plane of the particle. Currently, PIV can reach a resolution of the order of a camera pixel (about 10 μm) [13] and has become a very crucial technology for measuring velocity distributions of working fluids, which is widely used in research fields such as power engineering, multiphase flows, biological flows, and microstructural flows.

In the case of well RIM, the key to PIV measurement lies in the alignment and shading of a laser beam. There are two ways to eliminate stray light: (1) escape and (2) be absorbed. Among them, the escaping laser accounted for the main part. Through investigation and practice, it can effectively absorb stray light by using light absorption cloth and Stuart Semple black paint. Wrap the light absorption cloth on the fixed support of the experimental section and apply paint at the place where it is inconvenient to wrap. Figure 2 shows the effect of using a laser level to illuminate aluminum alloy, paint, and light absorption cloth, respectively. It can be seen that the effect of the photographic light-absorbing cloth is better.

3. RIM Fluid Schemes of PMMA

In flow field visualization experiments, the RI mismatch between the model material and the working fluid can lead to refraction and reflection of light at the intersection of the two, resulting in problems such as dead zones in the optical path, generation of image ghosting, formation of hot spots and reduction of the signal-to-noise ratio of the velocity distributions. Therefore, choosing an existing RIM fluid or formulating a new one according to the experimental characteristics is necessary. It is generally expected to use an RIM fluid with simple and stable physical properties, good compatibility with the materials, good RIM result with the model materials, high color and composition stability, and little harm to the human body. There are two ways to formulate new RIM fluid solutions for PMMA: (1) choosing one or more substances with a similar RI to PMMA; (2) mixing different substances with high- and low-refractive indices in different proportions. Fan et al. [49] prepared a new RIM fluid scheme: a mixture of tetralin- (72.2 vol%) ethyl alcohol (27.8 vol%) at 25°C. Figure 3 shows the photographs of a PMMA rod in water and the 72.2 vol% RIM fluid. The left rod is “bent” caused by the RI difference between the PMMA and water, and the right rod is invisible in the mixture.

Table 1 summarizes the RIM fluid schemes of PMMA and their applications over the years, where wt% represents the mass fraction and vol% represents the volume fraction. It can be seen that sodium iodide solution and p-Cymene are the two most used RIM fluids of PMMA.

4. Physical Properties Measurement and Analysis

In the RIM process, it is necessary to focus on the RI, density, dynamic viscosity, compatibility, stability, safety, and cost of RIM fluids. These factors have a great impact on the accuracy of experimental results, experimental progress, and safety of the experimenters.

4.1. Refractive Index

The RI of a mixed solution obtained by mixing two or more substances in different proportions can be predicted in advance by solving empirical equations. The existing empirical equations for the RI of mixed solutions are as follows:

Arago-Biot equation [152]:

Dale-Gladstone equation [153, 154]:

Lorentz-Lorenz equation [155]:

Wiener equation [156]:

Heller equation [157]:

Lichtenecker equation [157–159]:

Newton equation [160]: where is the RI, is the volume fraction (%), is the mass fraction (%), (kg/m³) is the density, the subscripts 1 and 2 represent two pure liquids, and 12 represents the mixture of these two liquids.

The RI varies by the wavelength of the incident light, and Narrow et al. [161] proposed a relation for the RI of sodium iodide solution where is the RI of sodium iodide solution, (°C) is the temperature of the solution, (%) is the mass fraction of sodium iodide solution, and (nm) is the wavelength of the corresponding light.

The Cauchy equation [162, 163] can be used to calculate the RI of a model material when it is irradiated by incident light of different wavelengths where , , etc. are the dispersion coefficients and (μm) is the wavelength of light. Kasarova et al. [162] obtained the dispersion coefficients used to calculate the RI of PMMA.

The preparing efficiency of RIM fluids can be improved by predicting the ratio of the mixed solution by the above formulas and combining it with RI measuring instruments (e.g., Abbe refractometer). If the RI at a specific wavelength is to be measured, a narrow bandpass filter of a specific wavelength can be placed at the inlet of the refractometer to filter the incident light at other wavelengths. Fan et al. [110] used a monocular Abbe refractometer to measure the RI of a mixture of two substances, tetralin and absolute alcohol, and found that the calculation results of the Newton equation were closest to the experimental measurement results.

4.2. Density

As the diameter of the tracer particle increases, its ability to scatter light becomes stronger, but its following behavior to surroundings becomes worse [164]. Therefore, on the premise of clear imaging, tracer particles with a density similar to that of the working fluid should be selected. When the tracer particle is continuously accelerated in working fluids, the density difference between the working fluids and the tracer particles will cause a velocity lag effect [165]. The velocity lag equation is given by where (m/s) represents the velocity lag of the tracer particle, (m) is the diameter of the tracer particle, and (kg/m³) is the density of the tracer particle and the working fluid, respectively, (Pa·s) represents the dynamic viscosity of the working fluid, and (m/s²) is the acceleration of the working fluid. From Equation (13), it can be seen that the velocity lag effect is negligible when the densities of both the tracer particles and the working fluid are equal.

Since most of the solid substances used in RIM fluid schemes obtained by solid-liquid mixing are electrolytes, this section only presents the density calculations of electrolyte solutions. Since the 18th century, researchers have investigated the volume and density of solid-liquid mixed solutions. In 1770, Watson [166] experimentally measured the volume change of a solution when adding salt to the water. In 1887, Arrhenius [167] proposed the theory of dissociating an electrolyte into ions when it dissolves. There are several empirical relations for calculating the density change of electrolyte solutions, such as the Tammann-Tait-Gibson model and the Pitzer equation [168–171]. In addition, the density-concentration relationship of solid-liquid mixed solutions can also be determined by simple measurement experiments.

The empirical relations for the density calculation of RIM fluids mixed with multiple pure liquids are the Corresponding State Liquid Density (COSTALD) relation developed by Hankinson and Thomson and Thomson et al. [172, 173], which is applicable to a variety of nonpolar and weak-polar pure and mixed solutions; the earlier Chueh-Prausnitz relation [174] and the Li relation [175] are less accurate compared to the COSTALD equation.

The COSTALD equation is where (cm³/mol) means the molar volume of the mixed solution, is the characteristic molar volume and takes the value of the critical molar volume of the mixed solution, i.e., which can be calculated by Equation (18); and are the corresponding state function and corresponding state deviation function of the mixed solution, is the acentric factor of the mixed solution, is the mole fraction of the pure liquid , is the Soave-Redlich-Kwong acentric factor of the pure liquid , and is the relative temperature, which is the ratio of the temperature of the mixed solution to its critical temperature . Constants such as can be obtained by checking the literature of Hankinson and Thomson [172]. It is important to note that the application range of Equation (15) is ; and the application range of Equation (16) is . where is the characteristic molar volume of the pure liquid , which can be taken as the critical molar volume of the pure liquid . The recommended values of and for various pure liquids can also be found in the literature [172].

After the molar volume of the mixed solution was obtained, the average molar mass of the mixed solution (g/mol) can be obtained by Equation (19), and then the density of the mixed solution (kg/m³⁾ is obtained.

According to Eslami and Azin [176], the average absolute deviation of the COSTALD equation for the densities of mixed solutions of an organic compound and mixed solutions of organic compound and water at room temperature and pressure compared with the experimental values is around 0.57%-3.46%. The COSTALD equation can be used to determine the approximate mixed solution proportions first and then rely on the densitometer to gradually fine-tune until a suitable ratio is obtained. where the subscript denotes the value calculated from the COSTALD relation and denotes the experimental value; denotes the number of experimental data points.

4.3. Dynamic Viscosity

Viscosity is a physical parameter that measures a fluid’s resistance to flow. As seen from Equation (22), it is difficult to carry out experiments at high-Reynolds numbers if the viscosity of the working fluid is too high. where (m) is the characteristic length, (m/s) is the characteristic velocity of the working fluid, (kg/m³) is the density of the working fluid, and (Pa·s) is the dynamic viscosity of the working fluid.

The dynamic viscosity of a mixed solution can be calculated using empirical relations, such as the Grunberg-Nissan equation [177] and the Teja-Rice equation [178, 179]. The Grunberg-Nissan equation is applicable to a wide range of mixed solutions but is less applicable to aqueous solutions and has the following equation: where (mPa·s) denotes the dynamic viscosity of the mixed solution, is the mole fraction of the pure liquid , and is a function of the properties of each pure liquid and temperature (in some cases independent of temperature) and is 0.

In the calculation, the pure liquid which meets the following conditions is given priority as a pure liquid and the other pure liquid as a pure liquid : (a) when it is alcohol; (b) when it is an acid; (c) when it contains the most carbon atoms; (d) when it contains the most hydrogen atoms; and (e) when it contains the most methyl groups (-CH₃). If two pure liquids meet the condition at the same time, the condition with the higher ranking takes precedence; if no pure liquid meets the condition or two pure liquids meet the same condition, then is 0.

The Teja-Rice equation [180] is an empirical equation proposed by Teja and Rice in 1980 for calculating the dynamic viscosity of mixed solutions, which is comparable in accuracy to the Grunberg-Nissan equation for calculating the dynamic viscosity of nonpolar-nonpolar as well as nonpolar-polar systems; for polar-polar systems as well as aqueous solutions, it is more accurate and can compensate for the insufficient accuracy of the Grunberg-Nissan equation when calculating aqueous solution’s viscosity. The form of the Teja-Rice equation is as follows: where the superscripts and refer to the two pure liquid components of the mixed solution; the subscript refers to the mixed solution, (mPa·s) refers to the dynamic viscosity of the liquid, is the acentric factor, and is defined as follows: where (cm3/mol), (K), and (g/mol) are the critical molar volume, critical temperature, and molar mass of the pure liquid, respectively. As for the acentric factor , critical molar volume , critical temperature , and molar mass of the mixed solution , Teja and Rice recommended the following equations: where refers to the mole fraction of the pure liquid ; interaction parameters are to be obtained from experimental data.

Equation (23) is calculated the dynamic viscosity of the mixed solution at temperature , whereas and are the dynamic viscosities at temperature and at temperature , respectively. According to Equation (32), when the mixed solution consists of two pure liquids, Equation (27) can also be simplified to the following form (subscripts 1 and 2 replace superscripts R1 and R2):

4.4. Compatibility

The life of a visual test section includes two aspects: (1) transmittance and (2) integrity. Transmittance will affect laser penetration and camera imaging; integrity will affect the formation of a flow field. The main factors affecting the transmittance of the experimental section are as follows: (a) the transmittance of model material; (b) the transmittance of the working fluid; and (c) the extent to which rust particles, tracer particles, or fluorescent particles are attached to the surface of the test section. The two main factors affecting the integrity of a test section are (a) crack or fracture occurs when the test section is scoured by the working fluid and (b) crack or fracture occurs when the test section is corroded by the working fluid. The compatibility between PMMA and RIM fluids affects the integrity of a test section significantly, and it is mainly considered from the following two aspects: (1) compatibility with PMMA and (2) compatibility with loop pipes and sealing rings. Loop pipes mainly include main pipes, injection and discharge system hoses, and transparent round pipes of the liquid level gauge and pressure pipes. Sealing rings mainly have flange sealing gaskets, mechanical sealing rings of pumps, internal sealing rings of quick connectors, and exhaust valves and measuring instruments. (1)Using organic compounds such as p-Cymene, absolute ethanol, tetralin, dimethyl sulfoxide, Triton X-100, and cinnamaldehyde [34, 103, 125, 181] as RIM fluids, the PMMA was susceptible to swelling and cracking upon contact. Figures 4(a) and 4(b) show the comparison of the butadiene rubber-sealing ring and silicone sealing ring with their control group after 24 hours of immersion in p-Cymene, both of which showed swelling and an increase in outer diameter and wire diameter after immersion; Figure 4(c) shows the plastic adapter splitting into multiple fragments after exposure to absolute ethanol and p-Cymene

(a)

(b)

(c)

We can qualitatively explain the phenomenon from the perspective of the rule of the like dissolves each other; if a solute and a solvent have similar structures or polarities, they are easily miscible. At the same time, the solubility parameter can be used to quantitatively judge the resistance of organic materials to organic compounds; the solubility parameter is the square root of the cohesive energy density of materials and was derived by Hildebrand and Scott based on thermodynamic theory [182]. In general, the closer the solubility parameters of two substances are, the easier they are to dissolve in each other. Table 2 lists the solubility parameters of common materials used in experimental loops and common liquids in RIM fluids [183]. As shown in Table 2, the range of solubility parameters of PMMA intersects with those of ethanol, diethyl phthalate, and tetralin; thus, PMMA is easily corroded after contact with the aforementioned organic compounds. (2)The use of electrolyte solutions such as sodium iodide solution and ammonium thiocyanate solution as RIM fluid can largely avoid the corrosion of organic materials by organic compounds (ammonium thiocyanate solution is still corrosive to silica [65]), but they have a strong erosive effect on metals such as iron and stainless steel, which can cause rusting of metal parts, and only a few stainless steels or aluminum alloys can resist their corrosion [65, 129, 184]. In addition, zinc chloride solutions can corrode aluminum and are incompatible with PMMA and many fluorescent dyes [148, 185].

The following measures can be taken to reduce corrosion: (1) use the same metal to avoid the formation of a primary battery when metals with different activities are in contact with electrolyte solution at the same time; (2) do not use the above-mentioned organic compounds or reduce the contact time with them; (3) select inorganic materials or corrosion-resistant organic materials, such as polytetrafluoroethylene, polypropylene, and polyproplyene-homo; (4) add linings made of corrosion-resistant materials in metal pipes; and (5) sinter corrosion-resistant coatings in metal pipes, for example, ethylene tetrafluoroethylene coating. In negative pressure areas (for example, in the pump inlet pipe), it is recommended to sinter the coating instead of adding the lining, because the coating has stronger pressure resistance.

p-Cymene has a corrosion effect on PMMA, and the corrosion process is a slow-thinning process if there is no stress. According to the rule of the like dissolve each other, there are three kinds of corrosion when p-Cymene flows through the channel of the PMMA test section: (1) the corrosion of p-Cymene to glue; (2) the corrosion of the glue to the test section; and (3) the corrosion of p-Cymene to PMMA. We can take the following measures to enhance the corrosion resistance of PMMA: (1) coating on the surface of PMMA, such as the silicon-based coating on the surface of PMMA to enhance its resistance to Triton X-100 [112]. (2) Relief stress of PMMA, such as by natural aging or using an oven or water bath [34, 137]. As shown in Figure 5, the left side shows a newly wrapped rod made of PMMA, the wire-wrap spacer broke and fell off after just being immersed in p-Cymene for 5 minutes; the right side shows a stress-relieved model, which did not break after being immersed in p-Cymene for 168 hours. Natural aging is a uniform and safe release, but it takes a long time and has low efficiency. When using an oven to speed up relieve the stress of PMMA models, if the internal stress is released not uniformly or affected by external forces, it is easy to cause the model deformation. The thermal-deformed PMMA rod can be reshaped by putting it into a straight round tube. (3) Operating in a relatively stable environment to reduce the influence of temperature change on stress change of PMMA.

4.5. Stability

The instability of RIM fluids has an enormous impact on the clarity of optical imaging and the working fluids’ physical properties. The instability of RIM fluids is divided into two types: instability of the proportion and instability of the composition, according to whether there will be material changes. (1)The instability of the proportion refers to the change in the mass (volume) fraction of single or multiple substances caused by volatilization, separating out, and moisture absorption. Since volatility is positively correlated with temperature, it is recommended to install temperature-regulating equipment on the experimental loop or control the temperature of the entire laboratory and operate in medium and low temperature conditions. At the same time, do a good job of experimental loop-sealing treatment to reduce the volatilization and moisture absorption of substances. In addition, attention should be paid to the influence of operation temperature changes on the solubility of solid substances to ensure that the RIM fluid is always in an unsaturated state(2)The instability of the composition refers to the change in the composition of single or multiple substances caused by reactions such as combination, decomposition, or oxidation-reduction, which usually leads to precipitation and discoloration. These reactions are related to the resistance of substances to the factors such as temperature, light, and oxidation. Sodium iodide powder is highly hygroscopic, and Figure 6 shows the discoloration process of sodium iodide solution when exposed to light and oxygen, with the newly prepared solution on the left and from left to right, the solution at each interval of one day. Without any treatment, the sodium iodide solution is dark brown after three days, and the change process of the precipitation of iodine triple ions is

When using sodium iodide solution as an RIM fluid, the following three problems need to be solved: (a) the sodium iodide solution discoloration due to iodine precipitation. A small number of reductants (e.g., 0.1~1 wt% sodium thiosulfate) can be added to the sodium iodide solution to inhibit the oxidation process [67, 161], and it can be used in the environment of shading, airtight, or filled with inert gas.

As shown in Figure 7, on the left is a newly prepared sodium iodide solution exposed to light and air for a short time and slightly discolored; in the middle is a sodium iodide solution placed in a shading, oxygen-free environment for two weeks, and slightly yellowed; on the right is a sodium iodide solution exposed to sunlight for two weeks with the addition of an appropriate amount of sodium thiosulfate and no discoloration. An exciting situation was found in the stability test: by readding sodium thiosulfate particles to the discolored sodium iodide solution, the sodium iodide solution’s light transmittance can be largely restored (not 100%). In addition, sodium salicylate solution and zinc iodide solution are also prone to discoloration [65, 144]; potassium thiocyanate reacts with iron and turns red [135]. TBE is easily decomposed when exposed to ultraviolet light or iron, and Tinuvin can be added to inhibit this process [119–122].

(b) Sodium iodide solution rusts metals such as cast iron, stainless steel, and copper. Corrosion results of sodium iodide solution on 304 stainless steel and 316 L stainless steel within two weeks are shown in Figure 8, and 304 stainless steel is severely corroded compared to 316 L stainless steel. Figure 9 shows the corrosion result of sodium iodide solution on a copper exhaust valve, and then replace it with a plastic one. The corrosion of sodium iodide solution on cast iron and stainless steel can be divided into the following three categories. (i)The water and oxygen in the sodium iodide solution contact with iron, and oxygen absorption corrosion occurs (ii)The formation of a primary battery composed of iron and other elements due to the conductivity of sodium iodide solution is higher than that of water. This reaction of iron and carbon is the same as Equation (35), and it is not easy to carry out due to the existence of passivating film on the surface of stainless steel. However, as an active anion, iodine ions can replace oxygen atoms in the passivating film, resulting in local damage [281]. The stainless steel substrate is exposed after the passivation film is dissolved. The activated stainless steel and the passivation film in the passivation state form an active-passive primary battery, causing local pitting corrosion(iii)The aqueous iodine vapor has strong reducibility and corrosiveness. Reacting with the passivating film on the surface of stainless steel can seriously damage the passivating film and cause corrosion of stainless steel [186]. The iodide element formed by the oxidation of iodide ions will immediately combine with sodium iodide to form iodine trinegative ions

Through investigation and practice, corrosion-resistant materials (such as aluminum, aluminum alloy, or Teflon) or Teflon lining and spraying Teflon are selected for physical isolation; a small amount of deoxidant can be added to the circuit to consume the oxygen content in the loop.

After the sodium iodide solution rusts the metal parts, the solution can be purified by the method of hydrostatic sedimentation or suction filtration (such as using a nuclear pore membrane or filter membrane). Both ways can filter the turbid sodium iodide solution to obtain a liquid with light transmittance close to the color of the newly prepared solution. The hydrostatic sedimentation method has a low cost, a large amount of single filtration, but a long period cycle, so it is better to prepare several plastic frames for multistage filtration; the filtration method is fast, the amount of filtration is small, but the filter membrane needs to be constantly replaced. Figure 10 shows the purification effect of sodium iodide solution by hydrostatic sedimentation method and suction filtration method.

(a)

(b)

(3)Precipitation of sodium iodide solution at low and evaporation at high temperatures. The solubility of sodium iodide particles in deionized water decreases with the temperature decreases, and a sudden drop in temperature easily leads to the precipitation and crystallization of sodium iodide. It is necessary to determine the minimum operating temperature of the loop and control the temperature and humidity of the laboratory during the experiment; the circuit shall be strictly sealed to reduce the influence of moisture absorption and volatilization on the concentration (physical property) of sodium iodide solution and slow dissolution or dissolution failure of sodium iodide particles after precipitation on the flow field formation due to the hygroscopic and volatile process

4.6. Safety Characteristics

RIM fluids involve many chemical substances with varying properties. When choosing an RIM fluid scheme, we should fully understand the nature of the chemical substances involved. The safety of RIM fluids consists of the following three main aspects:

4.6.1. Health Safety

Some chemical substances are irritating or toxic, such as ammonium thiocyanate, which can be poisoned after ingestion and cause irritation reactions in the skin [129], and TBE, which is highly toxic and can be irritating to the eyes. When the RIM fluid contains irritating or poisonous chemicals, experimenters should be thoroughly familiar with their information, correctly wear protective appliances, and learn about emergency treatments such as substance leakage and personnel poisoning. At the same time, appropriate emergency treatment drugs should be equipped in the laboratory for proper laboratory safety management.

4.6.2. Environmental Safety

In addition to threatening the health of experimenters, toxic chemicals also pollute the environment and threaten biodiversity. For example, TBE, tetralin, turpentine, and Triton X-100 can have long-term toxicity to aquatic organisms [135]; dibutyl phthalate is highly toxic to hydrobionts and may damage the fertility of animals [137]; ammonium thiocyanate can cause water pollution, etc. The waste solutions of these toxic substances should be treated harmlessly and then discharged after meeting the discharge standards or transported to specialized departments for treatment.

4.6.3. Fire Safety

Flammable and explosive substances, such as absolute ethanol, p-Cymene, tetralin, and cyclohexyl bromide, have low-flash points and strong volatility, which are susceptible to fire and explosion accidents. Laboratories using and storing the substances mentioned above should install illuminating equipment and measuring instruments with explosion-proof functions, be equipped with fire-fighting facilities and fire-fighting equipment, and regularly conduct fire drills for experimenters. Meanwhile, the laboratory should maintain a safe distance from the office and residential premises, strengthen ventilation, and strictly prohibit fireworks.

4.7. Experimental Cost

The procurement costs of different RIM fluids are listed in Table 1, which can be used as a reference for experimenters. In addition, the additional costs of using an RIM fluid should be considered, which mainly include (1) selecting or replacing a piece of suitable power equipment and experimental measurement equipment, such as using pumps with stainless steel bases to drive the flow of sodium iodide solution and using fluororubber mechanical sealing rings to resist the corrosion of p-Cymene; (2) purchasing waste gas and waste liquid treatment equipment for adsorbing and treating harmful or volatile substances; (3) purchasing protective appliances for experimenters, such as respirators and gloves, to reduce inhalation or contact with irritating and toxic substances; (4) procurement of first-aid kits and first-aid drugs; (5) procurement of fire-fighting equipment for emergency treatment of fires and explosions caused by flammable and explosive substances; (6) installation of illuminating equipment and measuring instruments with explosion-proof functions; and (7) personnel training costs, which mainly include fire safety training and emergency handing of gas poisoning and other emergencies.

4.8. Usage Suggestions

Based on the above analysis and our practical experience, some recommendations are given regarding the preparation and use of RIM fluids. (1)Regardless of which RIM fluid is chosen, the experimenter should carefully look up the information before close contact with the sample, sufficiently understand the nature of the RIM fluid, especially its hazardous characteristics and safety information, regulate the operation, and do a good job of personal protection(2)For RIM fluids containing organic compounds, the solubility parameters of the substance and the PMMA test section, loop pipes, and loop-sealing materials should be queried. If the two parameters are similar, these materials are likely to be corroded by the RIM fluid; for RIM fluids containing electrolyte solutions, attention should be paid to their erosion of metal parts. The following measures can be taken to reduce the corrosion of the RIM fluid on the test section and loop materials. (a) Reduce the contact time between the working fluid and the PMMA test section, empty the RIM fluid in the test section or even the entire loop when not measuring data, and reject the loop when measuring data; (b) coating the surface of the PMMA; and (c) replacing all the sealing rings in the loop with corrosion-resistant materials(3)For RIM fluids containing volatile substances, the loop should be well-sealed to reduce the impact of volatilization on the transmittance, mass (volume) fraction of the RIM fluids, and experimenter’s health and operate under conditions of medium or low temperatures(4)For RIM fluids containing poorly stable substances, the loop should be well-sealed, shaded, temperature-controlled, and avoid contact with substances prone to react. An appropriate amount of oxidant or reductant can be added to inhibit oxidation-reduction reactions(5)For RIM fluids containing solids, more attention should be paid to the effect of the operating temperature on solubility and avoid using saturated or near-saturated solutions as RIM fluid(6)For RIM fluids that contain flammable, explosive, irritating, or toxic substances, there should be equipped with appropriate purification and treatment equipment, protective appliances, and install instruments with explosion-proof functions, and safety awareness and experimental skills training of experimenter should be strengthened. Miller et al. [187] have systematically organized the flammability and toxicity of plenty of RIM fluids(7)When formulating a new RIM fluid, the transmittance, compatibility, and stability tests of the mixed substances should be fully carried out while considering the factors of RI, density, dynamic viscosity, and experimental cost. When doing compatibility testing, the effect of stress and unstressed corrosion is very different, so it is necessary to simulate the situation under real experimental conditions as much as possible. Fan et al. [110] found that the RI, density, and dynamic viscosity of a mixed solution decreased the temperature increase. Since the physical properties of RIM fluids are greatly affected by temperature, temperature control shall be done well during physical property measurement(8)No matter what RIM fluid is chosen, researchers should first procure a small number of samples for the tests mentioned above and confirm that they meet the requirements before injecting them into the loop

5. Conclusions

This review summarizes the measurement techniques in flow field visualization experiments, preparation principles, schemes, and usage suggestions of RIM fluids, and the following conclusions can be drawn: (1)Sodium iodide solution and p-Cymene are the two most used RIM fluids of PMMA. Among them: sodium iodide solution is expensive, easily oxidized to yellow, and will corrode metal parts; p-Cymene has a corrosive effect on organic materials and is irritating and needs to be equipped with waste gas and liquid treatment equipment. For experiments with small loop volume, sodium iodide solution can be used; for experiments with large-scale test sections or with minor stress in test sections, p-Cymene can be used. p-Cymene is cheap and has simple and stable physical properties, but if the cost of waste gas and liquid treatment equipment is considered, there would have a higher cost(2)Although PMMA has the advantages of high transmittance, good mechanical properties, easy processing, and stable chemical properties, it is susceptible to organic compounds such as Triton X-100, ethanol, p-Cymene, and tetralin, resulting in cracks or even fractures on the contact surface. When there is stress inside the PMMA, this fracture will be more evident and rapid. Therefore, after the PMMA model is manufactured, it should be annealed to eliminate internal stress as much as possible. When the PMMA model is stored for a long time, it should be placed in a dry, light-proof, and suitable temperature environment to slow down aging of PMMA(3)There are two ways to formulate a new RIM fluid: (a) using a pure liquid with an RI close to that of the model material; (b) mixing two or more substances. The latter method involves more substances and factors affecting the RIM fluid’s physical properties and also requires no reactions between the substances that affect the physical properties, so it is more complicated. Finally, the physical properties of the new RIM fluid, especially compatibility, stability, and safety, need to be considered to ensure the smooth conduct of the experiment(4)As far as we know, no RIM fluid is perfect without any defects. We should choose a suitable RIM fluid by comprehensively considering the experimental characteristics, requirements, costs, and other factors

Roman Letters

:	Acceleration of the working fluid (m/s²)
D:	Diameter (m)
:	Hydraulic diameter of the flow channel (m)
:	Diameter of the tracer particles (m)
L:	Tube length (m)
n:	Refractive index (–)
:	Mass fraction (–)
:	Reynolds number (–)
:	Velocity lag of the tracer particle (m/s)
V:	Velocity (m/s).

Greek Letters

:	Volume fraction (–)
:	Dynamic viscosity (Pa·s)
:	Density of a working fluid (kg/m³)
:	Density of the tracer particle (kg/m³).

Abbreviations and Acronyms

CCD:	Charge-coupled device
CFD:	Computational fluid dynamics
COSTALD:	Corresponding state liquid density
FEP:	Fluorinated ethylene propylene
LDA:	Laser Doppler anemometry
NMRI:	Nuclear magnetic resonance imaging
PDA:	Phase Doppler anemometer
PIV:	Particle image velocimetry
PLIF:	Planar laser-induced fluorescence
PMMA:	Polymethyl methacrylate
PS:	Polystyrene
PTV:	Particle-tracking velocimetry
PVAc:	Polyvinyl acetate
RI:	Refractive index
RIM:	Refractive index matching
TDLAS:	Tunable diode laser absorption spectroscopy
UDV:	Ultrasonic Doppler velocimetry.

Data Availability

The data will be available on request from the authors. The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 12122512), the National Key Research and Development Program of China (No. 2020YFB1902100), and the Basic and Applied Basic Research Foundation of Guangdong Province (No. 2020B1515120035).

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