Viscosity of concentrated suspensions of sphere/rod mixtures Page: 1 of 3
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February 13, 1996 02:05 PM
VISCOSITY OF CONCENTRATED SUSPENSIONS OF SPHERE/ROD MIXTURES
R. Mor', M. Gottlieb', A.L. Graham-, and L.A. Monday
'Department of Chemical Engineering, Ben Gurion University, Beer Sheva, 84105 ISRAEL
2 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA
'Sandia National Laboratorics. Albuquerquc. Ncw Mexico 87185-0834 USA
* To whom correspondence should be addressedINTRODUCTION
Most investigations on the theology of concentrated suspensions have
focused on monodisperse suspensions of either spherical or rodlike
particles. In practice, suspensions contain panicles that are polydisperse
both in size and in shape. Only a limited number of studies have been
devoted to the problem of size polydispersity and even less is known
about the behavior of suspensions composed of particles of different
shapes. In this paper we provide experimental data for the low shear rate
viscosity of concentrated suspensions of neutrally buoyant, rod-sphere
mixtures and develop a simple phenomenological model for the
viscosity of such systems.
Farris [1] developed a model for the viscosity of multimodal
suspensions of spheres. In his model, for each fraction of a given
particle size. the smaller particles in the suspension do not jitract with
the larger particles and are 'sensed' by the large particles as part of a
continuous Newtonian suspending fluid. In what follows, we use
Faris's concepts to develop an equation for the viscosity of a
suspension of a mixture of rodlike and spherical particles. If the rods
are large enough relative to the spheres, we may consider the spherical
particles as part of the homogeneous suspending continuum. Let us
define an apparent sphere volume fraction 0, = V, /(Vo+V,) = , / (1+)
where V is volume. is the volume fraction. and the subscripts 0. r. s. T
stand for the fluid, rods, spheres, and total solids respectively. If we
assume the viscosity of a suspension composed of spheres and rods is
the same as the viscosity of a suspension of rods suspended in a
Newtonian homogeneous fluid of viscosity identical to the viscosity of
an equivalent susepensitni of spheres with a vumhnne frAciio n', we may
write:(1)
(2)
(3)IHere we adopt the Thomas relations for spheres [2] and Milliken's for
randomly oriented rods with aspect ratio of 20 [3]. The relative viscosity
of a mixed suspension may now be calculated for any combination of
rods (of aspect ratio 20) and spheres.
EXPERIMENTAL
The experineiral apparatus, materials. and methods have been described
in great detail elsewhere [3-5]. Suspensions composed of mixtures of
poly(methyl methacrylate) spheres with diameter of 3.175 mm and rods
with length of 31.65 mm and diameter of 1.587 mm were used. The rod-
sphere mixtures were suspended in a three-main-components Newtonian
fluid with 50%wt alkylayl polycther alcohol 35%wt polyalkylene glycol,
and 15%wt tetrabromoethane. The quantity of tetrabromoethane in the
mixture was adjmsted tsi tha. (lie densily and the refractive index of the
fluid would match those of the PMMA particles. The falling balls withdiameters between 6.35 mm and 15.88 mm were either chrome-plated
steci ball bearings, moneL or tungsten carbide. The trajectories of the
falling balls were recorded on a high-speed digitizing video system. An
average velocity was determined by measuring the elapsed time for the
ball to settle a known distance on the screen. Up to 40 individual drops
were required for each data point.
RESULTS AND DISCUSSION
The relative viscosity is obtained from the dimensionless ratio of the
measured Stokes viscosity of the suspension, incorporating the Faxen
boundary correction [3-5], to the viscosity of the suspending fluid. The
average relative viscosity for each suspension is obtained by averaging
up to 120 separate ball drops for any given suspension. In Fig. 1 the
measured average viscosities symbolss) arc compared to the theory
described in the first section (lines). The agreement between the limited
number of available experimental points and the calculated lines is very
good. This agreement seems to validate the assumption that, in a
suspension in which two populations of solid particles with large size
diffcrcnce coexist. the larger particles 'sense' the smaller particles only as
part of an effective suspending continuum.25
$ 20
*2 15
> 10
0
0.0.1 0.2 0.3 0.4
Total Solids Volume Fraction0.5
Fig 1. The relative viscosity of the mixed suspension as function of the
.t1l solids vumTte lfrAciinm. The liTIes represent te clctlateld theoretical
values and the points represent the average experimental values for any
given composition.
REFERENCES
1. R.J. Faris, Trans. Soc. Rheol., 12, 281(1968).
2. D.G.Thomas, J. Col/oidSci. , 20, 267 (1965).
3. W.J. Milliken, L.A. Mondy. M. Gottlieb, AL. Graham, and R.L.
Powell, J. Fluid Mech., 202, 217 (1989).
4. W.J Milliken, L.A. Mandy, M. (httllieb, A.L. Gahomm, and R.L.
Powell, Phys. Chem. Hydro., 11. 341 (1989).
5. R. Mor, M. Gottlieb, AL. Graham. L.A Mondy, Chem. Eng. Comm.
in press (1996).Vi~J)
r~
- rods (Ld=20) /
- *15% 7
- sheres
- -From: Prof. Moshe Gottlieb
Fax #: 972-7-472916
Page 2 of 2
P pia ) = 9MWpcrs ,14 ) 91, W,
/e)mwe6)mtd)0
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Mor, R.; Gottlieb, M.; Graham, A. L. & Mondy, L. A. Viscosity of concentrated suspensions of sphere/rod mixtures, article, May 1, 1996; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc666039/m1/1/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.