Technical notes
Experiments in Fluids 22 (1997) 261—264 ( Springer-Verlag 1997
Refractive index matching and marking methods for highly concentrated
solid—liquid flows
M. M. Cui, R. J. Adrian
261
Abstract Two index-matched systems of solid particles in
liquid have been developed to enable the study of velocity
and concentration distributions in the highly concentrated
solid—liquid flows. The mixtures have excellent optical transparency up to depths exceeding 80 mm at concentrations up
to 50% solids by volume. Highly visible marker particles with
nearly the same mechanical properties as the index-matched
particles are formed by metal plating or substitution. Good
quality images of marker particles are obtained in both
stationary and moving two-phase mixtures, and permit accurate tracking of the individual markers.
1
Introduction
Concentrated solid—liquid flow occurs when the mean volume
concentration of suspended solids exceeds 5—10%. It is characterized by momentum and energy transfer due to the
translation of particles from one layer to another and collisions
among the particles. Continuum descriptions require constitutive equations that relate the concentration of solids, the
rate-of-strain, and the stress, energy and dissipation of the
mixture to micro-mechanical aspects of particle motion
and material properties of the particles. In addition to the
macroscopic velocity and concentration of the mixture, the
‘‘granular temperature’’, defined as the mean square of the
random particle velocity, is a fundamental and often difficult to
predict dependent variable that should be measured (Savage
1984; Campbell 1990). Important physical properties that
should be controlled experimentally are the ratio of solid and
fluid densities, the shape and mechanical properties of the
solid particles, and the viscosity of the fluid.
Experimental studies of concentrated two-phase flows such
as slurries and rapid granular flows are hindered by the high
opacity of the real solid-in-fluid mixtures. Even at solids
fractions of 0.1, the mixtures are difficult to penetrate optically,
Received: 4 March 1996/Accepted: 14 June 1996
M. M. Cui, R. J. Adrian
Department of Theoretical and Applied Mechanics
University of Illinois
Urbana, IL 61801 USA
Correspondence to: R. J. Adrian
The research was supported by the Department of Energy through
Argonne National Laboratory.
and when the concentration approaches close packing, they
cannot be penetrated more than a few particle diameters.
Magnetic resonance imaging and acoustical scattering techniques are useful methods for measuring some aspects of the
flows, but it is desirable to be able also to bring the powerful
optical techniques of laser Doppler velocimetry and particle
image velocimetry (cf. Adrian 1991) to bear on the experimental study of these flows.
A well known method of achieving optical transparency
in model systems of solid—liquid mixtures is to match the
refractive indices of the solids and the liquid by careful choice
of both. While this approach should, in principle, render the
mixture perfectly transparent, in practice the depth to which
one can image into the mixture is limited by imperfections in
the solid particles such as fine bubbles, by variations of the
refractive index within the solids, and by variations of the
refractive index of the liquid caused by temperature sensitivity
and/or changing properties of the liquid mixture. For example,
Zisselmar and Molerus (1978) report penetration of 50 mm
into a 5.6% mixture of 55 lm glass beads, and Nouri et al.
(1986) report penetration of 25.4 mm into a 14% mixture of
116—212 lm Diakon particles in a mixture of tetraline and
turpentine. By using silica gel particles Abbas and Crowe
(1987) were able to increase the concentration to 30% with
17.5 mm penetration using 96 —210 lm particles, and Chen and
Kadambi (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 mm
pipe at 14% volume concentration, but reported that some
of the other brands of silica gel particles that they tried gave
limited penetration at high concentrations due to refractive
index variations within the particles.
This Note describes two new refractive index-matched systems of solid particles in liquids. These suspensions extend
the repertoire of model systems available for experimental
study by providing penetration depths and maximum concentrations that are significantly greater than those reported
heretofore. The high transparencies achieved make possible
experimental investigations in relatively large scale apparatus,
of order 100 mm in thickness. The liquids used in these
systems have also been selected to have viscosity and density
near that of water, making them suitable as models of
coal—water slurries. A new aspect of the technique described
here is the introduction of special marker particles into the
transparent mixture to make the motion and concentration of
the solids visible. Instead of relying on uncontrolled impurities
in the primary population of solids to scatter light, the marking
is controlled making possible improved accuracy of velocity
measurements and the measurement concentration.
2
Model system for suspensions of spherical, neutrally
buoyant particles
262
Theoretical analyses and numerical simulations of solid—liquid
suspensions commonly treat simplified conditions in which
the particles are monodisperse, spherical and neutrally buoyant, the latter condition permitting the neglect of gravitational force. Since the primary concern is with characteristics that
arise predominantly from transport by the particulates, it is
also desirable for the fluid viscosity to be small. (To model
dry granular flow it is also necessary for the fluid density to
be small compared to the particle density, but this is not
compatible with achieving refractive index matching.) By using
a combination of three liquids it is possible to adjust both the
liquid refractive index and the liquid density independently, so
as to achieve good refractive index matching and neutrally
buoyant particles.
The system reported here consists of a liquid mixture of
tetraline, 1-methanaphthalene and 1-chloronaphthalene and
styrene/divinylbenzene particles (Bangs Laboratories, Inc.). As
shown in Fig. 1a, the shape of styrene/divinylbenzene particles
is perfectly spherical, and they are available in a range of sizes.
Table 1 summarizes the properties of tetraline, 1-methanaphthalene, 1-chloronaphthalene and styrene/divinylbenzene
particles. The neutrally buoyant solid/liquid mixture is a combination of 41% tetraline, 28% 1-methanaphthalene and 31%
1-chloronaphthalene by volume. In this combination the
refractive index is 1.5903, and the density is 1050 kg m~3,
matching the values listed for the particles in Table 1. The
dynamic viscosity is 2.547]10~3 kg m~1 s~1, and the kinematic viscosity is 2.426]10~6 m2 s~1, about two and one-half
times that of water.
The transparency of each refractive index-matched mixture
and the visibility of marker particles have been studied in both
stationary and moving suspensions. Figure 1b demonstrates
the transparency of a 15 mm deep layer of a 50% by volume
suspension styrene/divinylbenzene particles in a laboratory
dish resting on a ruled pattern. The visibility of the pattern
seen looking through the suspension is excellent.
By controlling the percentage of different chemicals one
can also obtain index-matched liquid mixtures with different
densities which can be used to study the influence of solid/
liquid density ratio on the behavior of the two-phase flow.
2.1
Spherical, neutral buoyancy marker particles
Unlike previous LDV techniques which used air bubbles in the
solid particles (Nouri et al. 1986) or index mismatch of solid
and fluid (Abbas and Crowe 1987), the present idea is to match
the indices of solid and liquids as well as possible, and then
to seed the suspension with a selected number of marker particles that are made visible by special treatment. The number
of marker particles is chosen to permit measurements with
acceptable data rate while maintaining satisfactory transparency. The independent selection of index-matched particles
and marker particles provides valuable freedom which can
be used to maximize the penetration depth at a given con-
Fig. 1. a Photograph of styrene/divinylbenzene particles (250 lm
mean diameter); b optical transparency of a 50% suspension of
styrene/divinyl benzene particles in index-matched liquids. The depth
of the layer of suspended particles is 15 mm; c nickel plated styrene/
divinylbenzene particles (250 lm mean diameter)
centration of solid particles in which the measurements can
be done.
Ideally, the marker particles should have the same mechanical properties as the unmarked particles, and their scattering
Table 1. Basic properties of
1-methanaphthalene, 1chloronathalene, tetraline and
styrene/divinylbenzene particles
Property
1-Methanaphthalene
1-Chloronaphthalene
Tetraline
Styrene-divinylbenzene particle
Density (kg m~3)
Refractive index
(20°C)
Boiling point
(0°C)
Viscosity at
(20°C (kg m~1 s~1)
1001
1.615
1194
1.632
967—970
1.546
1050
1.5903
240—243
111—113
207.2
—
3]10~3
3.5]10~3
2.2]10~3
—
263
characteristics should produce enough light to give clear
images. An ideal method of meeting these criteria is to plate
a mechanically thin but optically thick layer of metal onto
the same particles as those used in the suspension. For the
styrene/divinylbenzene particles nickel plating by precipitation proved successful in creating very bright particles that
produced excellent images, Fig. 1c. The marker particles retain
the sphericity of the original particles, and because of the
thinness of the plating they have the same mechanical properties as the unplated particles, including essentially the same
density.
3
Model system for suspensions of irregular, heavy particles
The rheology of dense suspensions of heavy, irregularly shaped
particles is of interest because of the technological importance
of coal slurries and slurries from mining operations. Silica gel
particles have irregular shape which is qualitatively similar to
coal particles. In the present system refractive index matching
is achieved using a mixture of 45% benzyl alcohol and 55%
ethyl alcohol by volume.
The properties of the alcohols and silica gel particles are
listed in Table 2. The data varies slightly depending upon the
manufacturer and the purity. The refractive index of liquid is
measured by a refractometer (ATAGO R5000). The liquid
temperature was controlled within 0.1°C. The refractive index
of the alcohol mixture is not sensitive to change of temperature, making the mixture easy to use. There is no special
requirement to control the temperature of the test section as
long as the room temperature is stable to within ^2°C.
Naturally, the tolerance for temperature variation decreases
with increasing depth of penetration.
The viscosity of the mixture of benzyl and ethyl alcohols
has been measured as a function of temperature with a standard viscometer (Brookfield synchro-lectric viscometer model
LVT) and temperature-dependent data can be found in Cui
(1994). At 20°C the density is 974.4 kg m~3, the dynamic
viscosity is 2.0]10~3 kg m~1 s~1, and the kinematic viscosity
is 2.05 m2 s~1, close to that of water. Because of the irregular
particle shape and the distribution of sizes over the range
75—580 lm, close packing of the silica gel particles (after
immersion in the alcohol mixture) occurs at a concentration of
83.3% by volume, rather higher than for spherical particles.
The silica gel can be sieved to obtain different size distributions, and the volume concentration at which close packing
occurs would vary with the size distribution.
The most useful property of this suspension is its extreme
clarity. Figure 2b shows a 1 mm rectangular grid viewed
Table 2. Properties of alcohols and silica gel particles
Property
Benzyl alcohol
Ethyl alcohol
Silica gel
Density (kg m~3)
Refractive index
(20°C)
Boiling point (°C)
Viscosity at
20°C (kg m~1 s~1)
1045
1.540
800—888
1.360—1.362
2100
1.452
205
2.0]10~3
78—79
1.2]10~3
—
—
through an 80 mm deep layer of 50% by volume suspension
of the 75—580 lm silica particles. The present silica system
possess exceptional transparency and penetration depth,
making it suitable for large-scale simulation. In comparison,
a suspension of the same solid particles with 5% concentration
by volume in water is totally opaque. The improved transparency is due, in part, to the use of high purity silica (‘Chromatographic Silica Media’, Davis Chemical).
Attempts to plate nickel onto the silica gel were not as
successful as for the styrene/divinylbenzene particles. Application of the plating was irregular, even after etching the silica
surfaces with acid, and the resulting images of the markers
were weak. As an alternative, magnesium/aluminum 50/50
alloy particles (Reade Mfgr. Co.) of equal sieve size have been
used to mark the silica gel/alcohol mixture. These particles
possess irregular shapes not dissimilar from the silica gel, cf.
Fig. 2c. The images of the magnesium/aluminum particles are
very clear, even in close packed silica gel particles, as shown in
Fig. 3.
Images of marker particles moving within the suspension
have also been obtained by using a video camera. The multiple
exposed particle images shown in Fig. 4 illustrate the images
obtained after thresh holding. Since the intensity of the light
scattered by the marker particles is significantly stronger than
the background noise, threshold values that accurately isolate
the marked particles from the background are easily chosen.
These bilevel images can be used to calculate the locations of
the centroids, sizes and distribution of the marker particles.
4
Concluding Remarks
Refractive index matching of two systems of solid particles and
liquids has been achieved. The transparency of the mixtures is
excellent at large depth-of-field and close-packing of particles.
The best result is obtained by developing the index matched
two-phase mixtures and proper marker particles separately.
264
Fig. 3. Magnesium/aluminum powder in a 20 mm thick close-packed
layer of silica gel particles with refractive index matching alcohols
Fig. 4. Multiple exposed particle images in a refractive index matched
layer of silica gel/alcohol mixture with 60% concentration. The layer
thickness is 25 mm.
Fig. 2. a The shape of silica gel particles (250— 425 lm); b optical
transparency of a 50% suspension of silica gel particles in a refractive
index matching liquid. The particles are 75—585 lm in size and
the thickness of the suspension is 80 mm. The scale of the grid is
1 mm/division; c the shape of magnesium/aluminium particles with
300 lm mean diameter.
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