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Ind. Eng. Chem. Res. 2004, 43, 4434-4437
Effect of Fluid Viscosity on Liquid-Solid Fluidization Ou Qiu, Hongzhong Li,* and Hua Tong Multiphase Reaction Laboratory, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100080, China
Four kinds of solid particles were fluidized and tested in aqueous solutions of glycerol ranging in viscosity from 7 to 1400 cP. Two trends in which the fluidization behavior of particles is significantly affected by fluid viscosity were observed, and a physical model was proposed based on these phenomena. On the one hand, increasing the fluid viscosity could decrease the bubble size, which results in smoother fluidization. On the other hand, because of the effect of the laminar layer, particle agglomeration could occur when the fluid viscosity is high enough, which results in heterogeneous behavior in the fluidized bed. At the critical point, these two trends balance each other, and the best fluid quality is observed. For all particles in this work, although the values of optimal viscosity are different, the values of the particle terminal Reynolds number are about 0.004 at the critical point. Introduction
Table 1. Properties of Experimental Materials
Heterogeneous behavior, which means gas bubbling or particle agglomerating, is normally associated with a gas fluidized bed. A liquid fluidized bed, on the other hand, in general shows homogeneous behavior with a spatially uniformly distributed concentration of solid particles. Geldart1 found that the particle diameter and particle-fluid density difference dominate the behavior of gas-solid fluidization, and therefore he classified solid particles into four groups of A, B, C, and D, according to the particle diameter and particle-fluid density difference. Yates,2 Knowlton,3 and Liu et al.4 studied the effects of temperature and pressure on gassolid fluidization. While the effects of the particle diameter, particle-fluid density difference, temperature, and pressure on fluidization have been quantitatively determined, precise knowledge of the dependence of fluidization quality on liquid viscosity is far from being a matter of consensus. So far most reported investigations were confined to restricted ranges of viscosity, and different views have been presented on the relationship between liquid viscosity and fluidization quality. Harrison et al.5 found that elevating liquid viscosity in a lead shot/liquid system resulted in smoother fluidization, and fluid viscosity was a dominant factor in determining the fluidization type of fine powders. Also, Martin6 introduced viscosity as the third dimension into Geldart’s diagram of powder classification,1 inferring that viscous forces always dominate particulate beds. Although there was evidence on improving the quality of liquid fluidization by raising the viscosity,5 there is an evident tendency toward an arrangement of particles with extensive aggregation in very viscous fluids because particle clustering or aggregation reflects drag forces on particles, and the drag coefficient changes significantly at low Reynolds numbers of flow.7 A deduction of the EMMS model8 indicated that when a two-phase structure was formed at low Reynolds number, a decrease of the fluid kinematics viscosity would * To whom correspondence should be addressed. Tel.: (86) 010-62558002. Fax: (86) 010-62536108. E-mail: hzli@ home.ipe.ac.cn.
particles Fp
(kg/m3)
aqueous solutions of glycerol dp (mm)
C1
8900
0.55
C2
8900
0.15
S1
2300
0.55
S2
2300
0.15
G1 G2 G3 G4 G5 G6 G7 G8 G9
Ff (kg/m3)
µ (cP)
1256 1248 1246 1238 1230 1222 1203 1181 1126
982 552 450 237 172 97 65 25 7
be beneficial to reduce the difference between the structures of the dense phase and the dilute phase. Therefore, it was expected that reducing the viscosity would be beneficial to uniform fluidization. The object of this paper is to report some experimental results on this subject in the hope of shedding some light on the above controversy. Experimental Section Fluidized particles included copper powders (C1 and C2) and sand (S1 and S2), covering fully aggregate and particulate zones in fluidization with ambient water,9,10 whereas fluidizing media consisted of 12 kinds of aqueous solutions of glycerol with viscosity from 7 to 1400 cP. The properties of the particles (C1, C2, S1, and S2) and the 9 kinds of aqueous solutions of glycerol (G1G9) are listed in Table 1. The liquid-solid fluidized bed was a 80-mm-i.d. and 1.2-m-height glass tube, with a sintered glass plate as the liquid distributor. Figure 1 shows the schematic drawing of the experimental apparatus. A local solids fraction signal was collected via an optical fiber probe installed at a point 165 mm above the liquid distributor, and by using a computer for online data processing, then local solids fraction signals were measured at different radial positions by traversing the probe horizontally. A fluctuating local solids fraction signal time series s, sampled by the optical fiber probe, can yield a standard deviation σ, which can
10.1021/ie034207n CCC: $27.50 © 2004 American Chemical Society Published on Web 06/05/2004
Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4435
Figure 3. Transient signals of a local solids fraction of the C2 particle in fluids with various viscosities. Figure 1. Liquid-solid fluidized bed: 1, fluidized bed; 2, liquid tank; 3, gear pump; 4, cooler; 5, optical fiber; 6, A/D converter; 7, computer.
Figure 4. Transient signals of a local solids fraction of the S1 particle in fluids with various viscosities. Figure 2. Transient signals of a local solids fraction of the C1 particle in fluids with various viscosities.
be used for evaluating the fluidization quality4
σ)
x∑ 1
n
ni)1
(si - js)2
(1)
where n is the number of samples. Results and Discussion Particles C1, C2, S1, and S2 were first fluidized with a glycerol solution (1400 cP). The liquid was then progressively diluted with water to reduce its viscosity, down to 7 cP. All of the particles suffered serious channeling in the viscosity above 1000 cP, and measurement with the optical fiber probe became impossible. Figures 2-5 show transient signals of a local solids fraction in fluids with various viscosities. Figure 6 shows a standard deviation for signals, indicating that
heterogeneity of fluidization varies with fluid viscosity. It is obvious for all particles that there exist two fluidization regions: a high-viscosity region and a lowviscosity region. Also, there is a critical value of fluid viscosity between these two regions. Above the critical value, the heterogeneity of fluidization increases with an increase of the fluid viscosity in the high-viscosity region, and below the critical value, the increase of fluid viscosity results in smoother fluidization in the lowviscosity region. Heterogeneity of fluidization is the smallest at the critical value of fluid viscosity, which is defined as the optimal viscosity. When the value of fluid viscosity is lower than the optimal viscosity, the fluid bubbles would dominate the heterogeneous behavior of the fluidized bed, and when the value of fluid viscosity is higher than the optimal viscosity, particle agglomerates would dominate the heterogeneous behavior of the fluidized bed, instead of fluid bubbles. According to Harrison’s theory on the stability of the roof of a spherical cap of bubble,5 if the diameter of a bubble is allowed to be De and the diameter of a particle
4436 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004
The thickness of the laminar fluid layer δ1 surrounding a particle can be expressed as a function of the particle Reynolds number
δ1 ) f1(Ret)
(3)
The distance between adjacent particles δ2 would be expressed as a function of the particle Reynolds number, δ2 ) f2(Ret); when δ2 e 2δ1, clustering between adjacent particles could occur, implying that agglomeration would appear when
f1(Ret) f2(Ret)
g
1 2
(4)
Equation 4 implies that, at the critical point, the particle Reynolds number may be a constant. The force balance for a particle in fluid flow gives
( )
πdp2 2 π 3 1 ut dp (Fp - Ff)g ) CDFf 6 2 4
Figure 5. Transient signals of a local solids fraction of the S2 particle in fluids with various viscosities.
(5)
where ut is the terminal velocity of the particle, or
3 Ar ) CDRet2 4
(6)
where Ar is the Archimedes number
Ar ) dp3Ff(Fp - Ff)g/µ2
(7)
Ret is the particle Reynolds number
Ret ) dputFf/µ
Figure 6. Standard deviation of transient solids fraction signals in fluids with various viscosities.
is allowed to be dp, then
( )(
)[(
Fs - 0 2 De F µ s - Ff ) 71.3 dp gdpFf 1 - 0
In eq 6, CD is the drag coefficient. For liquid fluidization, the drag coefficient on a single particle in the intermediate flow is provided by Dallavalle12 as follows:
CD )
) ] 1/2
2
-1
[( ) 23.04 Ret
1/2
]
+ 0.3971/2
2
(9)
To express the effect of the particle concentration on the drag force on a particle in a multiparticle system, the following equation is proposed,13
gdp3Ff 1+ (Fs 54µ2 Ff)
(8)
(2)
For a fluidized bed, when the fluid viscosity increases, the bubble size would be of the same order of magnitude as the particle diameter, and thus the bed would appear homogeneous. The behavior of two spherical particles settling in a viscous fluid was first studied by Happel and Pfeffer,11 which revealed that when the particle Reynolds number, Ret, was less than 0.25, the particle maintained a creeping flow with no relative motion between the particles. However, as soon as the particle Reynolds number exceeded 0.25, relative motion between particles occurred and the particles moved away from each other. On the basis of the above experimental observation and theoretical analysis, the following physical model could be proposed. Particle agglomeration in a viscous fluid is caused by the laminar layer next to the surface of the particles.
CD )
24 0.413 (1 + 0.173Ret0.657) + (10) Ret 1 + 16300Re -1.09 t
when Ret is small,
CD )
24 (1 + 0.173Ret0.657) Ret
(11)
Combining eqs 6 and 11 gives
3.114Ret1.657 + 18Ret - Ar ) 0
(12)
On the basis of experimental values of the optimal viscosity, values of the particle Reynolds number at the critical points could be calculated from eq 12 as shown in Table 2. It can be seen from Table 2 that all values of the particle Reynolds number at the critical points are nearly equal to 0.004, which just verified the physical model proposed by this work.
Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4437 Table 2. Values of the Particle Reynolds Number at the Optimal Viscosity particles
µopt (cP) Ret
C1
C2
S1
S2
450 4.237 × 10-3
65 4.031 × 10-3
172 4.013 × 10-3
25 3.868 × 10-3
Combining eqs 6 and 7 gives
µ)
x
1.5
4dp 3
xFfg(Fp - Ff) xCDRet
(13)
Because Ret is 0.004 at the critical point, the optimal fluid viscosity can be given by substituting 0.004 for Ret into eqs 11 and 13 as follows:
µopt ) 3.718dp1.5xFfg(Fp - Ff)
(14)
Conclusion (1) Fluidization behavior of particles is significantly affected by fluid viscosity in two trends. On the one hand, increasing the fluid viscosity could decrease the bubble size, which results in smoother fluidization. On the other hand, because of the effect of the laminar layer, particle agglomeration could occur when the fluid viscosity is high enough, which results in heterogeneous behavior in the fluidized bed. At the critical point, these two trends balance each other, and the best fluid quality is reached. (2) A physical model for predicting the optimal fluid viscosity at the critical point was proposed, and a rule was tentatively found that the value of the particle Reynolds number at the critical point is about 0.004 for all particle-fluid systems in this work. This rule should be further verified by more experimental data. Acknowledgment The authors are grateful to the National Natural Science Foundation of China for financial support with contract No. 20221603 and the President Fund of the Chinese Academy of Sciences for special financial support with contract No. 799 to this work. Nomenclature Ar ) Archimedes number CD ) drag coefficient De ) bubble diameter, m dp ) particle diameter, m
r ) radial coordinate, m R ) fluidized-bed inner radius, m Ret ) particle Reynolds number t ) time, s u ) fluid velocity, m/s umf ) incipient fluidization velocity, m/s ut ) terminal velocity of the particle, m/s δx ) thickness of the laminar fluid layer, m s ) local solids fraction 0 ) bed voidage fraction at incipient fluidization σ ) standard deviation µ ) fluid viscosity, kg/(m s) µopt ) optimal fluid viscosity, kg/(m s) Ff ) fluid density, kg/m3 Fp ) particle density, kg/m3
Literature Cited (1) Geldart, D. Types of Gas Fluidization. Powder Technol. 1973, 7, 285. (2) Yates, J. G. Effects of Temperature and Pressure on GasSolid Fluidization. Chem. Eng. Sci. 1996, 51, 167. (3) Knowlton, T. M. Pressure and Temperature Effects in Fluid-Particle Systems. In Fluidization VII; Potter, O. E., Nicklin, D. J., Eds.; Engineering Foundation: New York, 1992; p 27. (4) Liu, D.; Kwauk, M.; Li, H.-z. Aggregative and Particulate FluidizationsThe Two Extremes of a Continuous Spectrum. Chem. Eng. Sci. 1996, 51, 4045. (5) Harrison, D.; Davidson, J. F.; De Kcok, J. W. On the Nature of Aggregative and Particulate Fluidization. Trans. Inst. Chem. Eng. 1961, 39, 202. (6) Martin, P. D. On the ‘Particulate’ and ‘Delayed Bubbling’ Regimes in Fluidization. Chem. Eng. Res. Des. 1983, 61, 318. (7) Gunn, D. J.; Malik, A. A. The Structure of Fluidized Beds in Particulate Fluidization. Proceedings of the International Symposium on Fluidization; Drinkenburg, Ed.; Netherlands University Press: Eindhoven, The Netherlands, 1967; p 52. (8) Li, J.; Kwauk, M. Particle-Fluid Two-Phase FlowsThe Energy Minimization Multi-Scale Method; Metallurgical Industry Press: Beijing, 1993. (9) Foscolo, P. U.; Gibilaro, L. G. A Fully Predictive Criterion for the Transition between Particulate and Aggregate Fluidization. Chem. Eng. Sci. 1984, 39, 1667. (10) Gibilaro, L. G.; Hossain, I.; Foscolo, P. U. Aggregate Behavior of Liquid Fluidized Bed. Can. J. Chem. Eng. 1986, 64, 9. (11) Happel, J.; Pfeffer, R. The Motion of Two Spheres Following Each Other in a Viscous Fluid. AIChE J. 1960, 6, 129. (12) Dallavalle, J. M. Micromerities: The Technology of Fine Particles, 2nd ed.; Pitman: London, 1948. (13) Turton, R.; Levenspiel, O. A Short Note on the Drag Correlation for Spheres. Powder Technol. 1986, 47, 83.
Received for review October 25, 2003 Revised manuscript received March 11, 2004 Accepted March 17, 2004 IE034207N
