Technical notes Experiments in Fluids 22 (1997) 261—264 ( Springer-Verlag 1997

Refractive index matching and marking methods for highly concentratedsolid—liquid flows

M. M. Cui, R. J. Adrian

Received: 4 March 1996/Accepted: 14 June 1996

M. M. Cui, R. J. AdrianDepartment of Theoretical and Applied MechanicsUniversity of IllinoisUrbana, IL 61801 USA

Correspondence to: R. J. Adrian

The research was supported by the Department of Energy throughArgonne National Laboratory.

Abstract Two index-matched systems of solid particles inliquid have been developed to enable the study of velocityand concentration distributions in the highly concentratedsolid—liquid flows. The mixtures have excellent optical trans-parency up to depths exceeding 80 mm at concentrations upto 50% solids by volume. Highly visible marker particles withnearly the same mechanical properties as the index-matchedparticles are formed by metal plating or substitution. Goodquality images of marker particles are obtained in bothstationary and moving two-phase mixtures, and permit accu-rate tracking of the individual markers.

1IntroductionConcentrated solid—liquid flow occurs when the mean volumeconcentration of suspended solids exceeds 5—10%. It is cha-racterized by momentum and energy transfer due to thetranslation of particles from one layer to another and collisionsamong the particles. Continuum descriptions require consti-tutive equations that relate the concentration of solids, therate-of-strain, and the stress, energy and dissipation of themixture to micro-mechanical aspects of particle motionand material properties of the particles. In addition to themacroscopic velocity and concentration of the mixture, the‘‘granular temperature’’, defined as the mean square of therandom particle velocity, is a fundamental and often difficult topredict dependent variable that should be measured (Savage1984; Campbell 1990). Important physical properties thatshould be controlled experimentally are the ratio of solid andfluid densities, the shape and mechanical properties of thesolid particles, and the viscosity of the fluid.

Experimental studies of concentrated two-phase flows suchas slurries and rapid granular flows are hindered by the highopacity of the real solid-in-fluid mixtures. Even at solidsfractions of 0.1, the mixtures are difficult to penetrate optically,

and when the concentration approaches close packing, theycannot be penetrated more than a few particle diameters.Magnetic resonance imaging and acoustical scattering tech-niques are useful methods for measuring some aspects of theflows, but it is desirable to be able also to bring the powerfuloptical techniques of laser Doppler velocimetry and particleimage velocimetry (cf. Adrian 1991) to bear on the experi-mental study of these flows.

A well known method of achieving optical transparencyin model systems of solid—liquid mixtures is to match therefractive indices of the solids and the liquid by careful choiceof both. While this approach should, in principle, render themixture perfectly transparent, in practice the depth to whichone can image into the mixture is limited by imperfections inthe solid particles such as fine bubbles, by variations of therefractive index within the solids, and by variations of therefractive index of the liquid caused by temperature sensitivityand/or changing properties of the liquid mixture. For example,Zisselmar and Molerus (1978) report penetration of 50 mminto a 5.6% mixture of 55 lm glass beads, and Nouri et al.(1986) report penetration of 25.4 mm into a 14% mixture of116—212 lm Diakon particles in a mixture of tetraline andturpentine. By using silica gel particles Abbas and Crowe(1987) were able to increase the concentration to 30% with17.5 mm penetration using 96—210 lm particles, and Chen andKadambi (1990) achieved 25.4 mm penetration through 50%concentrations of 40 lm silica in a sodium iodide solution.Park et al. (1989) used 1—2 lm silica gel particles in a 51 mmpipe at 14% volume concentration, but reported that someof the other brands of silica gel particles that they tried gavelimited penetration at high concentrations due to refractiveindex variations within the particles.

This Note describes two new refractive index-matched sys-tems of solid particles in liquids. These suspensions extendthe repertoire of model systems available for experimentalstudy by providing penetration depths and maximum con-centrations that are significantly greater than those reportedheretofore. The high transparencies achieved make possibleexperimental investigations in relatively large scale apparatus,of order 100 mm in thickness. The liquids used in thesesystems have also been selected to have viscosity and densitynear that of water, making them suitable as models ofcoal—water slurries. A new aspect of the technique describedhere is the introduction of special marker particles into thetransparent mixture to make the motion and concentration ofthe solids visible. Instead of relying on uncontrolled impuritiesin the primary population of solids to scatter light, the marking

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Fig. 1. a Photograph of styrene/divinylbenzene particles (250 lmmean diameter); b optical transparency of a 50% suspension ofstyrene/divinyl benzene particles in index-matched liquids. The depthof the layer of suspended particles is 15 mm; c nickel plated styrene/divinylbenzene particles (250 lm mean diameter)

is controlled making possible improved accuracy of velocitymeasurements and the measurement concentration.

2Model system for suspensions of spherical, neutrallybuoyant particlesTheoretical analyses and numerical simulations of solid—liquidsuspensions commonly treat simplified conditions in whichthe particles are monodisperse, spherical and neutrally buo-yant, the latter condition permitting the neglect of gravitatio-nal force. Since the primary concern is with characteristics thatarise predominantly from transport by the particulates, it isalso desirable for the fluid viscosity to be small. (To modeldry granular flow it is also necessary for the fluid density tobe small compared to the particle density, but this is notcompatible with achieving refractive index matching.) By usinga combination of three liquids it is possible to adjust both theliquid refractive index and the liquid density independently, soas to achieve good refractive index matching and neutrallybuoyant particles.

The system reported here consists of a liquid mixture oftetraline, 1-methanaphthalene and 1-chloronaphthalene andstyrene/divinylbenzene particles (Bangs Laboratories, Inc.). Asshown in Fig. 1a, the shape of styrene/divinylbenzene particlesis perfectly spherical, and they are available in a range of sizes.Table 1 summarizes the properties of tetraline, 1-methanaph-thalene, 1-chloronaphthalene and styrene/divinylbenzeneparticles. The neutrally buoyant solid/liquid mixture is a com-bination of 41% tetraline, 28% 1-methanaphthalene and 31%1-chloronaphthalene by volume. In this combination therefractive index is 1.5903, and the density is 1050 kg m~3,matching the values listed for the particles in Table 1. Thedynamic viscosity is 2.547]10~3 kg m~1 s~1, and the kin-ematic viscosity is 2.426]10~6 m2 s~1, about two and one-halftimes that of water.

The transparency of each refractive index-matched mixtureand the visibility of marker particles have been studied in bothstationary and moving suspensions. Figure 1b demonstratesthe transparency of a 15 mm deep layer of a 50% by volumesuspension styrene/divinylbenzene particles in a laboratorydish resting on a ruled pattern. The visibility of the patternseen looking through the suspension is excellent.

By controlling the percentage of different chemicals onecan also obtain index-matched liquid mixtures with differentdensities which can be used to study the influence of solid/liquid density ratio on the behavior of the two-phase flow.

2.1Spherical, neutral buoyancy marker particlesUnlike previous LDV techniques which used air bubbles in thesolid particles (Nouri et al. 1986) or index mismatch of solidand fluid (Abbas and Crowe 1987), the present idea is to matchthe indices of solid and liquids as well as possible, and thento seed the suspension with a selected number of marker parti-cles that are made visible by special treatment. The numberof marker particles is chosen to permit measurements withacceptable data rate while maintaining satisfactory transpar-ency. The independent selection of index-matched particlesand marker particles provides valuable freedom which canbe used to maximize the penetration depth at a given con-

centration of solid particles in which the measurements canbe done.

Ideally, the marker particles should have the same mechan-ical properties as the unmarked particles, and their scattering

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Table 1. Basic properties of1-methanaphthalene, 1-chloronathalene, tetraline andstyrene/divinylbenzene particles

Property 1-Metha- 1-Chloro- Tetraline Styrene-divinyl-naphthalene naphthalene benzene particle

Density (kg m~3) 1001 1194 967—970 1050Refractive index 1.615 1.632 1.546 1.5903(20°C)Boiling point 240—243 111—113 207.2 —(0°C)Viscosity at 3]10~3 3.5]10~3 2.2]10~3 —(20°C (kg m~1 s~1)

Table 2. Properties of alcohols and silica gel particles

Property Benzyl alcohol Ethyl alcohol Silica gel

Density (kg m~3) 1045 800—888 2100Refractive index 1.540 1.360—1.362 1.452(20°C)Boiling point (°C) 205 78—79 —Viscosity at 2.0]10~3 1.2]10~3 —20°C (kg m~1 s~1)

characteristics should produce enough light to give clearimages. An ideal method of meeting these criteria is to platea mechanically thin but optically thick layer of metal ontothe same particles as those used in the suspension. For thestyrene/divinylbenzene particles nickel plating by precipita-tion proved successful in creating very bright particles thatproduced excellent images, Fig. 1c. The marker particles retainthe sphericity of the original particles, and because of thethinness of the plating they have the same mechanical pro-perties as the unplated particles, including essentially the samedensity.

3Model system for suspensions of irregular, heavy particlesThe rheology of dense suspensions of heavy, irregularly shapedparticles is of interest because of the technological importanceof coal slurries and slurries from mining operations. Silica gelparticles have irregular shape which is qualitatively similar tocoal particles. In the present system refractive index matchingis achieved using a mixture of 45% benzyl alcohol and 55%ethyl alcohol by volume.

The properties of the alcohols and silica gel particles arelisted in Table 2. The data varies slightly depending upon themanufacturer and the purity. The refractive index of liquid ismeasured by a refractometer (ATAGO R5000). The liquidtemperature was controlled within 0.1°C. The refractive indexof the alcohol mixture is not sensitive to change of temper-ature, making the mixture easy to use. There is no specialrequirement to control the temperature of the test section aslong as the room temperature is stable to within ^2°C.Naturally, the tolerance for temperature variation decreaseswith increasing depth of penetration.

The viscosity of the mixture of benzyl and ethyl alcoholshas been measured as a function of temperature with a stan-dard viscometer (Brookfield synchro-lectric viscometer modelLVT) and temperature-dependent data can be found in Cui(1994). At 20°C the density is 974.4 kg m~3, the dynamicviscosity is 2.0]10~3 kg m~1 s~1, and the kinematic viscosityis 2.05 m2 s~1, close to that of water. Because of the irregularparticle shape and the distribution of sizes over the range75—580 lm, close packing of the silica gel particles (afterimmersion in the alcohol mixture) occurs at a concentration of83.3% by volume, rather higher than for spherical particles.The silica gel can be sieved to obtain different size distribu-tions, and the volume concentration at which close packingoccurs would vary with the size distribution.

The most useful property of this suspension is its extremeclarity. Figure 2b shows a 1 mm rectangular grid viewed

through an 80 mm deep layer of 50% by volume suspensionof the 75—580 lm silica particles. The present silica systempossess exceptional transparency and penetration depth,making it suitable for large-scale simulation. In comparison,a suspension of the same solid particles with 5% concentrationby volume in water is totally opaque. The improved trans-parency is due, in part, to the use of high purity silica (‘Chro-matographic Silica Media’, Davis Chemical).

Attempts to plate nickel onto the silica gel were not assuccessful as for the styrene/divinylbenzene particles. Applica-tion of the plating was irregular, even after etching the silicasurfaces with acid, and the resulting images of the markerswere weak. As an alternative, magnesium/aluminum 50/50alloy particles (Reade Mfgr. Co.) of equal sieve size have beenused to mark the silica gel/alcohol mixture. These particlespossess irregular shapes not dissimilar from the silica gel, cf.Fig. 2c. The images of the magnesium/aluminum particles arevery clear, even in close packed silica gel particles, as shown inFig. 3.

Images of marker particles moving within the suspensionhave also been obtained by using a video camera. The multipleexposed particle images shown in Fig. 4 illustrate the imagesobtained after thresh holding. Since the intensity of the lightscattered by the marker particles is significantly stronger thanthe background noise, threshold values that accurately isolatethe marked particles from the background are easily chosen.These bilevel images can be used to calculate the locations ofthe centroids, sizes and distribution of the marker particles.

4Concluding RemarksRefractive index matching of two systems of solid particles andliquids has been achieved. The transparency of the mixtures isexcellent at large depth-of-field and close-packing of particles.The best result is obtained by developing the index matchedtwo-phase mixtures and proper marker particles separately.

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Fig. 2. a The shape of silica gel particles (250—425 lm); b opticaltransparency of a 50% suspension of silica gel particles in a refractiveindex matching liquid. The particles are 75—585 lm in size andthe thickness of the suspension is 80 mm. The scale of the grid is1 mm/division; c the shape of magnesium/aluminium particles with300 lm mean diameter.

Fig. 3. Magnesium/aluminum powder in a 20 mm thick close-packedlayer of silica gel particles with refractive index matching alcohols

Fig. 4. Multiple exposed particle images in a refractive index matchedlayer of silica gel/alcohol mixture with 60% concentration. The layerthickness is 25 mm.

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