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Experimental and theoretical study on the agglomeration arising from fluidization of cohesive particles—effects of mechanical vibration
Chemical Engineering Science 60 (2005) 6529 – 6541 www.elsevier.com/locate/ces
Experimental and theoretical study on the agglomeration arising from fluidization of cohesive particles—effects of mechanical vibration Chunbao Xu, Jesse Zhu∗ Particle Technology Research Centre, Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada Received 28 July 2004; received in revised form 2 May 2005; accepted 15 May 2005 Available online 11 July 2005
Abstract A novel technique that can prevent the disruption of agglomerates when sampling the agglomerates from a fluidized bed has been developed and has been applied to the investigation of the agglomeration behaviour of cohesive particles during fluidization with and without mechanical vibration. A new model for the prediction of agglomerate size has also been established on the basis of the energy balance between the agglomerate collision energy, the energy due to cohesive forces and the energy generated by vibration. The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the present work and in the literature. Effects of gas velocity and mechanical vibration on agglomeration for two cohesive (Geldart group C) powders in fluidization are examined experimentally and theoretically. The experimental results prove that mechanical vibration can significantly reduce both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed. However, the experiments also reveal that the mean agglomerate size decreases initially with the vibration intensity, but increases gradually as the vibration intensity exceeds a critical value. This suggests that the vibration cannot only facilitate breaking the agglomerates due to the increased agglomerate collision energy but can also favour the growth of the agglomerates due to the enhanced contacting probability between particles and/or agglomerates. Both the experimental and theoretical results show that a higher gas velocity leads to a smaller agglomerate size. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Cohesive particles; Fluidization; Mechanical vibration; Agglomeration; Modelling
1. Introduction The significance of particle technology is apparent in that approximately one-half of the products in the chemical industry and at least three-quarters of the raw materials are in granular form (Nedderman, 1992) and it is estimated that sales of $61 billion per annum in the chemical industry are linked to particle technology (Ennis et al., 1994). The high surface area-to-volume ratio and other special characteristics of fine particles make them very attractive in the industries of advanced materials, food and pharmaceuticals, etc. However, handling of these fine powders becomes much more difficult as their sizes become smaller. Fine particles, ∗ Corresponding author.
E-mail address: [email protected] (J. Zhu). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.05.062
30 m or smaller in size, classified as group C (cohesive) particles by Geldart (1973), are generally believed to be unsuitable for fluidization since they tend to form agglomerates as a consequence of strong interparticle forces (Baerns, 1966; Chaouki et al., 1985; Pacek and Nienow, 1990; Ushiki, 1995; Horio et al., 1996). Although for submicron- or nanoparticles where the interparticle force is much stronger than the gravitational forces, the bed of particles may exhibit a state of self-agglomerating fluidization due to the formation of stable and roughly mono-sized agglomerates (Molerus, 1982; Geldart et al., 1984; Rietema, 1984; Jaraiz et al., 1992; Chaouki et al., 1985; Morooka et al., 1988), for most of the group C particles where the interparticle forces are not strong enough, the agglomerates formed in fluidization are unstable and normally have a severe size segregation, leading to partial fluidization or even de-fluidization (Pacek and
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Nienow, 1990; Wang et al., 1998; Xu et al., 2004). It thus suggests that the fluidization behaviour of cohesive particles strongly depends on the properties (e.g., strength, size and size distribution, etc.) of the agglomerates arising from fluidization and the agglomeration behaviours during fluidization (Chaouki et al., 1985; Chirone et al., 1993). Several previous experimental works (Kono et al., 1990; Li et al., 1990; Wank et al., 2001; Xu et al., 2004) have demonstrated that the size/size distribution of agglomerates arising from fluidization of cohesive particles is dependent not only on the properties of the primary particles but also on the fluidization conditions such as parameters of fluidizing gas (gas type, humidity and velocity) and the application of fluidization aids (e.g., mechanical vibration). Mechanical vibration has proved to be an effective means to help fluidization of cohesive solids due to the breaking of channels and agglomerates (Mori et al., 1990; Dutta and Dullea, 1991; Mujumdar, 1983; Wank et al., 2001; Xu et al., 2004). Consequently, vibro-fluidized beds are commonly used in powder processing such as mixing, granulation, drying and coating. So far, however, a comprehensive study on the agglomeration behaviours of cohesive particles during fluidization and the effects of mechanical vibration are still unavailable in the literature. Due to the fragile structures of the agglomerates, the biggest challenge in studying the agglomeration during fluidization is the agglomerate–sampling techniques (Noda et al., 1998; Wang et al., 1998; Venkatesh et al., 1998; Castellanos et al., 1999; Wank et al., 2001; Xu et al., 2004). A “freezing” method has been developed by Pacek and Nienow (1990), in which the agglomerate granules were frozen by spraying of a binder solution of wax from the top of the bed before sampling. Another technique, called particle/droplet image analysis, has been recently reported for direct measurement of the agglomerate size in the free board and the region close to the upper surface of the solid bed (Wank et al., 2001). However, there exists an obvious limitation for these two techniques in that they are only capable of the size measurement for the agglomerates in the top bed. It is thus of a great significance to develop other techniques, which are capable of sampling the agglomerates, without disrupting them in either sizes or structures, from any parts of the bed (top, middle or bottom bed). In the present study, a novel “on-line sampling” technique has been developed, the details of which will be described later in the experimental section. It is well accepted that theoretical study is a very useful means for exploring the mechanism governing the processes of interest. Several theoretical studies on the prediction of agglomerate size have been reported since 1985 (Chaouki et al., 1985; Morooka et al., 1988; Iwadate and Horio, 1998; Zhou and Li, 1999), where most of the models are based on the principle of force balance. Bergstrom (1997) proposed a very simple model, where the agglomerate size was estimated from the force balance between the drag force due to the gas flow and the interparticle force (van der Waals force).
Similarly, Iwadate and Horio (1998) predicted the agglomerate size simply by balancing the bubble-causing expansion force and the cohesive force between agglomerates. Zhou and Li (1999) assumed that the drag force due to gas flow and the collision force between agglomerates are balanced with the buoyant gravity and the cohesive force. The predictions using these force-balance-based models have shown various degrees of agreement with the experimental data. On the other hand, Morooka et al. (1988) came up with a model based on an energy balance, in which it is assumed that the agglomerate tends to disintegrate when the energy generated by laminar shear stress and the kinetic energy of the agglomerate are equal to the energy required to break the agglomerate (i.e., the energy due to the cohesive forces). However, in their model, the minimum fluidization velocity (umf ) rather than the superficial gas velocity was used in calculating the energy generated by laminar shear stress and the kinetic energy of agglomerates, which makes the reliability of the model very questionable. Obviously, more studies are needed to ameliorate these models for precise prediction of agglomerate size in fluidization of cohesive particles. In order to clarify the mechanism governing the formation and failure of agglomerates during fluidization of fine particles under mechanical vibration, the present study will deal with both the measurement and the modelling of the size of agglomerates arising from the fluidization of cohesive particles with and without vibration. A new model for the prediction of agglomerate size is developed based on the energy balance between the agglomerate collision energy, the energy due to cohesive forces and the energy generated by vibration.
2. Theoretical analysis The phenomenon of size-segregation of agglomerates is often observed in fluidization of cohesive powders, resulting in a layered structure along the bed height: the smaller and usually more stable agglomerates exist at the top, while the larger and looser ones are present at the bottom (Xu et al., 2004). In this regard, the efforts on modelling of the agglomerate size are only meaningful for the top-bed stable agglomerates. To simplify the analysis, the following assumptions are made: (1) the agglomerates formed are all spherical in shape, same in size with a mean diameter of da , and of the same properties, (2) the wall effect is neglected and (3) the van der Waals force dominates over other types of the interparticle cohesive forces. It is also assumed that the agglomerate tends to disrupt or break when the total energy due to collision plus external vibration (if applied) is greater than that due to the cohesive forces. Accordingly, the following energy balance may be attained at the breaking point for the agglomerate Ecoll + Evib,eff = Ecoh ,
(1)
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
where the subscripts “coll”, “vib”, “eff” and “coh” denote “collision”, “effective vibration” and “cohesion”, respectively. 2.1. Collision energy Similar to the work by Zhou and Li (1999), the agglomerates are assumed to be elastic bodies, and the maximum compression displacement can be calculated from the elasticity theory (Timoshenko and Goodier, 1970) 2/5 1.25V 2 = , (2) nm where V is the relative velocity between two agglomerates in a collision, and n and m are given by 8 da1 da2 n= , (3) 2 d +d 2 9 (k1 + k2 ) a1 a2 m=
m1 + m2 , m1 m 2
(4)
where m1 and m2 represent the mass of the two agglomerates in the collision and k is a function of Poisson’s ratio and Young’s modulus E, defined as k=
1 − 2 . E
(5)
According to the assumptions made, m1 = m2 = m = 1/6da3 a , k1 = k2 = k and da1 = da2 = da , then one has
= (0.313V 2 2 k a )2/5 da .
(6)
The collision force between the two agglomerates is (Zhou and Li, 1999) Fcoll = n3/2 .
(7)
Assuming the collision force remains constant during the collision, the collision energy Ecoll is then obtained as Ecoll = Fcoll = n5/2 .
(8)
Substituting n and through Eqs. (3) and (6) into Eq. (8) gives Ecoll = 0.104a da3 V 2 .
(9)
Since all the agglomerates in the bed are moving around within the bed at certain unknown velocities, to determine the relative velocity V between the two agglomerates in collision becomes more difficult. In the studies of Iwadate and Horio (1998) and Zhou and Li (1999), the relative velocity V was estimated by the following correlation: V = (1.5Ps,n Db g b )0.5 ,
(10)
where Ps,n is the dimensionless average particle pressure, b is the bed voidage and Db is the bubble diameter. However, the calculation based on the above correlation show
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that the relative velocity is as high as the superficial gas velocity (ug ), and in some cases the calculated V is even much higher than ug , which is obviously too large to be practical. On the other hand, Morooka et al. (1988) adopted umf of the agglomerates as the relative velocity V , but this approximation is also questionable since it overlooks the effect of the superficial gas velocity (ug ) on the agglomerate size, while this effect is significant as will be discussed later. Since the two agglomerates in collision are more likely moving in a same direction along with the fluidizing gas or bubbles within the bed, a more reasonable understanding is that the relative velocity V should be small. Thus, in this study, V is assumed to lie between 0 and the geometric average of ug and umf , i.e., √ V = ug umf ,
(11)
where is the factor whose value is between 0 and 1.0. By comparing the predictions with the experimental results, is fixed at 0.1 in this study. umf of agglomerates (generally with a large size) can be estimated with the conventional correlation by Leva (1959) umf =
9.23 × 10−3 da1.82 (a − g )0.94 0.06 0.88 g g
,
(12)
where g and g are the viscosity and density of the fluidizing gas. 2.2. Vibration energy As well known, the application of an external vibration to the fluidization will help breaking the agglomerates down to small ones, so the contribution of the vibration should be properly taken into account. However, a quantitatively study in this regard is not yet available in the literature. For a mass ms oscillating with a simple harmonic motion of an amplitude A and a frequency f, it possesses an oscillating energy of (2ms f 2 A2 ) (Morse and Ingard, 1968). Where, it should be noted that the oscillating energy of an agglomerate, during collision with the other one, will dissipate only partially since its oscillation sustains after collision but with a slightly decreased amplitude or frequency due to the damping effect of the collision. In order to account for the effective part of the oscillating energy that contributes to break the agglomerates, the effective factor, i.e., , is adopted, and the effective energy due to vibration may be assumed as Evib,eff = 2ms f 2 A2 .
(13)
Substituting the expression ms = 1/6da3 a into Eq. (13) gives Evib = 13 3 a f 2 A2 da3 .
(14)
By comparing the predictions with the experimental results, is assumed as 0.01 in this model.
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2.3. Cohesion energy Practically, the agglomerates in collision may break up unevenly into larger parts and smaller parts, but the average volume of the two portions in the bed should be equal, so we have assumed that the agglomerate breaks into two equal parts to simplify the modelling process. To break an agglomerate into half-and-half, the tensile strength due to cohesive forces within the agglomerate must be overcome, and the energy required for this process is the cohesion energy Ecoh . Assuming the cohesive forces remain constant during the breaking of the agglomerate, Ecoh can be calculated as Z 2 da d , (15) Ecoh = Z0 4 where is the tensile strength of the agglomerate, is the displacement of the two parts of the agglomerate at the breakage or the distance between the two departing particles, Z0 is the initial distance between the two adjacent particles and Z is the displacement within which the tensile strength of the agglomerate remains in effect. According to Molerus (1982),
=
1 − a Fc , a dp2
(16)
where a is the voidage of agglomerates and Fc is the interparticle forces. As has been thoroughly discussed in the literature (Krupp, 1967; Hartley et al., 1985; Staniforth, 1985; Seville et al., 2000), the interparticle forces that lead to agglomeration of fine particles may be of several types including the van der Waals forces, electrostatic forces, interfacial forces due to solid bridges and liquid bridges, as well as mechanical forces resulting from static frictional contact or interlocking of irregular particle surfaces. Any of these forces may be dominant in a particular circumstance. Although the relative importance of a particular form of interparticle forces is strongly dependent on the fluidized bed set-up, the original properties of the particles and the fluidization conditions (such as moisture level), it is generally believed that the van der Waals force is much more significant than the electrostatic force and other types of interparticle forces for finer particles of a diameter < 100 m in the absence of liquid bridges (Baerns, 1966; Visser, 1989; Wang and Li, 1995). In our experiments, tribo-electrostatic charge was not observed for all the powders tested. Furthermore, in another study by the same authors (Xu et al., 2005), we have also tested the effect of adding very fine metal particles as flow conditioners to fine polyester powders (10–20 m), and it turned out that the addition of these electro-conductive metal particles did not give better results on reducing the cohesiveness of the host particles, compared with the operations of other types of non-conductive flow conditioners (Al2 O3 , silica or TiO2 ). This thus suggests that even for the polyester particles, a material very favourable for build-up of electrostatic charge, the electrostatic force is not the dom-
inant force among the interparticle forces in the fluidized bed. Therefore, it is reasonable in this study to assume that van der Waals forces dominate, as stated in the previous assumptions for the modelling. According to Krupp (1967), Fvan between two particles can be estimated as h¯ R, (17) 8 2 where h¯ is the Lifshitz–van der Waals constant, and R is defined by rp1 rp2 R= , (18) rp1 + rp2 Fvan =
where rp1 and rp2 are the asperity radii for the two particles in contact. By assuming the particles to be with smooth surfaces, rp1 and rp2 can be radii of the particles, i.e., rp1 = rp2 = ra = dp /2 (Krupp, 1967; Morooka et al., 1988) and R=dp /4. By taking the number of contact points per particle (nc =1.61−1.48 ) (Jaraiz et al., 1992) into account, the overall a cohesive forces per particle (Fc ) becomes Fc = nc Fvan = 1.61−1.48 a
h¯
R. (19) 8 2 Substituting R = dp /4 into Eq. (19) and the substituting Eq. (19) into Eq. (16), one has
= 1.61−1.48 a
1 − a 1 h¯ . a dp 32 2
(20)
Replacing h¯ with the Hamaker constant AH (h¯ = (4/3)/AH ) (Krupp and Sperling, 1966; Krupp, 1967) gives
= 1.61−1.48 a
1 − a 1 A H . a dp 24 2
Substituting Eq. (21) into Eq. (15) Z 2 1 − a Ecoh = da 1.61−1.48 a a Z0 4 2 1 − a AH = da 1.61−1.48 a 96 a dp
(21) gives 1 AH d
dp 24 2 1 1 − . Z0 Z
(22)
The distance of maximum attraction or the initial distance between two particles at the point of contact, Z0 , is normally ˚ chosen as 4 A(=4 × 10−10 m). This value can be justified by the fact that Z0 = 4 A˚ is slightly larger than the lattice constant of weekly van der Waals-bonded molecular crystals (Krupp and Sperling, 1966; Krupp, 1967). Consequently, Z0 is assumed as 4 A˚ in this work, and Z is arbitrarily assumed to be far larger than Z0 , i.e., Z Z0 . With this hypothesis, Eq. (22) can be reduced to Ecoh =
2 1 − a A H 1 da 1.61−1.48 . a 96 a d p Z0
(23)
The Hamaker constant AH can be estimated by the following equation (Israelachvili, 1992): 2 1 − 0 2 3 3hv e n21 − n20 + √ , (24) AH = kB T 4 1 + 0 16 2 (n21 + n20 )3/2
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
where kB is Boltzmann’s constant (kB =1.381×10−23 J/K), T is the absolute temperature and 1 (0 ) and n1 (n0 ) are the dielectric constant and refractive index of the particulate materials (the medium where the particles are present) (for vacuum or air, 0 = n0 = 1.0). Here, h is Planck’s constant (=6.626×10−34 J s) and e is the main electronic absorption frequency in the UV region, typically at around 3×1015 s−1 . Hence, for the particulate materials fluidized in air, Eq. (24) is rewritten as 1 − 0 2 AH = 1.036 × 10−23 T 1 + 0 (n2 − n2 )2 + 2.635 × 10−19 21 20 3/2 . (25) (n1 + n0 ) The agglomerate voidage (a ) can be determined indirectly from the agglomerate density (a ) and the particle density (p )
a = 1 − a /p .
(26)
Here, the value of a can be obtained by direct measurement, but the experimental results of Zhou and Li (1999) have demonstrated that a for cohesive particles is approximately between 1.15 times the aerated density (ba ) and 0.85 times the tapped density (bt ) of the primary particles, depending the bonding strength of the agglomerate. To simplify, a in this study is approximated by bt of the primary particles. Substituting Eqs. (9), (14) and (23) into Eq. (1) results in da =
−1.48 1−a AH 1 96 1.61a a dp Z0 . 0.104a V 2 + 13 3 a f 2 A2
(27)
It should be noted that the relative velocity of agglomerates (V ) is of da dependence, referring to Eqs. (10)–(12), so that Eq. (27) must be solved by an iterative approach.
3. Experimental The vibro-fluidized bed setup used in this study consists of a fluidized bed column made of Plexiglas (38 mm i.d. and 500 mm tall), a vibration generation system, a data
6533
acquisition system, and a gas flow control system. Compressed air stripped of trace humidity through a fixed bed of silica gel is used as the fluidizing gas, whose flow rate is controlled by a series of rotameters (Omega Engineering Inc.) and a digital mass flow controller (Fathom Technologies, GR series). All the flowmeters are carefully calibrated with a Wet Test Meter (GCA/Precision Scientific) before using. A porous polymer plate serves as the gas distributor. Pressure drops across the whole bed are measured with a differential pressure transducer (Omega PX163 series). Mechanical vibration is generated by a pair of vibrators driven by an ABB inverter with a vibration frequency (f) varying from 0 to 50 Hz. Through changing the unbalanced weights of the vibrator, various amplitudes (A) between 0 and 3 mm (depending on the frequency used) can be obtained. In the present work, the vibration frequency and amplitude are set at 50 Hz and 0.3 mm, respectively, unless specified otherwise. The fine particulate materials used are cohesive fine particles of Talc (4.1 m) and CaCO3 (5.5m), which are typical Geldart group C powders, whose key physical properties are listed in Table 1. The particles are loaded to the bed to a fixed height of about 100 mm, and the whole particle bed is first loosened by a gas flow at 2.0 cm/s for 10 min before the experiments start. In the case of no vibration, when the fluidization is attempted by slowly increasing the gas velocity, the bed first behaves as that typical of group C particles, i.e., plugging and channelling, until a certain bed pressure builds up causing the particle bed to fracture. As the gas velocity increases further, the bed comes to a transition region during which the particles at the top-bed start to fluidize and self-agglomeration develops gradually, leading to the eventual fluidization and agglomeration of the whole bed. On the other hand, the application of the vibration significantly improves the fluidization, e.g., the plugging, channelling and fracturing of the bed disappear and the agglomerate size decreases, leading to smoother fluidization and higher pressure drops. In order to sample the agglomerates out of the bed for characterization while avoiding disrupting their size, shape and structures, a novel “online sampling” technique that is illustrated in Fig. 1 has been developed and applied to this
Table 1 Fine powders used for fluidization experiments Powders
CaCO3 Talc
dp a
Density (kg/m3 )
RH b
(m)
p
bl d
ba d
5.5 4.1
2700 2710
1160 360
520 170
a The volume-weighted mean diameter by laser diffraction (Malvern Mastersizer 2000). b R (Hausner ratio) = / . H bt ba cAOR, angle of repose. dAnalyzed by a Hosokawa Powder Tester.
AORc ,d
Geldart group
(deg) 2.23 2.12
50.0 48.4
C C
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
Talc(4.1µm)
450
No vibration
da (µm)
400
With vibration (30Hz/0.3mm)
350
300 20
40
60
80 t (min)
100
120
140
Fig. 2. Changes in mean diameters of the top-bed agglomerates of Talc (4.1 m) with fluidization time in air at 9.4 cm/s.
Fig. 1. Diagram of the “online agglomerate sampling” technique: (a) sampling the agglomerates from the top layer of the bed; (b) removing the agglomerates from the upper layer by vacuum prior to the sampling for the agglomerates on the lower layer.
study. The agglomerates are sampled in situ, without stopping the fluidizing gas or making any other changes to the fluidization conditions (e.g. gas velocity and vibration if applicable), and with a sampling ladle from the top of the column. To sample the agglomerates in the upper region of the bed, the ladle is used to pick up the agglomerates directly. As for the agglomerates in the middle and bottom regions, an intensity-controllable vacuum is used to remove all the particulate materials very carefully above the sampling plane. More particles are removed as the measure-
ments are continued further to the lower planes of the bed. In the experiments, the operations of both the agglomerate sampling and the vacuum agglomerate removal were manually but carefully performed. In sampling the agglomerates from the top layer of the bed with the ladle, particular care was taken to avoid breaking the agglomerates during the sampling. In removing the agglomerates with the vacuum probe, the suction intensity was controlled (by adjusting either the suction flow rate or the working distance between the tip of vacuum probe and the suction objects) to be high enough to “pick up” all the agglomerates in the upper layer but low enough to avoid removing the agglomerates in the layer below. The agglomerates captured in the sampling ladle were poured carefully onto a metal disk (4 cm in diameter), followed by gold plating and measurement of their shape/size by scanning electronic microscopy (Hitachi SEM S-2600N). The mean agglomerate size is obtained by taking the arithmetic average of over 100 agglomerates from one sample. In the present study, two experimental runs were carried out for each given condition. The error of the average agglomerate diameter between two tests with the same powder under the same fluidization conditions was within the range of ±(10.15)%, giving acceptable reproducibility for this technique. Since the self-agglomeration of fine particles during fluidization is a dynamic process governed by the growing of the agglomerates due to the cohesive forces and the fracturing of the agglomerates due to the breaking forces, it may take a certain length of time to achieve stabilization of the agglomerates in size and shape under certain fluidization conditions (gas velocity, vibration intensity, etc.). The stable
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
sizes of agglomerates are particularly important and more meaningful for the modelling of the self-agglomeration of cohesive particles in fluidization. It is thus highly necessary to first determine the stabilization time for the agglomeration process. Upon obtaining the stabilization time, one can further determine the sampling time, i.e., the fluidization time for the particles before sampling the formed agglomerates out for characterization. The sampling time should be equal to or longer than the stabilization time for the agglomeration process. In this regard, experiments are carried out using the Talc (4.1m) powder fluidized in air at 9.44 cm/s with and without vibration (30 Hz/0.3 mm). The agglomerates formed during fluidization are sampled from the top-bed after various lengths of time. The mean diameters of the agglomerates at the fluidization time of 30, 60 and 120 min are illustrated in Fig. 2. The results show that the sizes of the agglomerates attain a stable value after about 60 min of fluidization no matter whether the vibration is applied or not. It is thus safe to set the sampling time at 120 min in every case.
6535
4. Results Fig. 3 shows the overhead and the close-up pictures of the top-bed agglomerates for CaCO3 (5.5 m) and Talc (4.1 m) powders at specific superficial gas velocities in air without vibration. Clearly, with the new “online sampling” technique, the original shapes and structures of the agglomerate samples are well maintained. From the overhead pictures for the agglomerates of the two powders, it can be seen that the agglomerates formed at the top-bed are in a good spherical shape with a diameter of 200–500 m under the fluidization conditions stated above. In particular, the sphericity of the agglomerates of Talc (4.1 m) is almost perfect. On the other hand, the microstructures of the agglomerate surfaces are clearly shown in the close-up pictures. The surfaces of both agglomerates show the structures of floc or dendrite, which may reveal one of the possible mechanisms governing the self-agglomerate formation during fluidization as has also been proposed in other previous works by
Fig. 3. Microphotographs of the top-bed agglomerates of (a) CaCO3 at 18.88 cm/s and (b) Talc at 9.4 cm/s in air for 2 h without vibration: scale bars are 1 mm and 50 m for the overhead views and close-up views, respectively.
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
Fig. 4. Segregation for the agglomerates along the bed height for Talc (4.1 m) powder fluidized at 9.4 cm/s in air for 2 h (a) without and (b) with vibration.
Princen (1968), Vold (1960) and Wang (1995). The agglomerate formation in fluidization may be associated with the following sequential steps: growing of the individual chains from the seed particles, growing of the dendrites from the individual chains, and formation of an agglom-
erate by folding of the dendrites due to collision and the binding forces between dendrite/dendrite, agglomerate/agglomerate or dendrite/agglomerate. Despite the wide application of the fine particles in industries and the growing interest of the research in fluidization of fine particles,
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
100
Top
6537
Talc(4.1µm)
3000
80 2500 60 40 No vibration With vibration (30Hz/0.3mm)
20
Number% under size
0 100
(a)
da (µm)
2000
No vibration
1500
Middle 1000
80 60
500
40
With vibration (30Hz/0.3mm) 0
20 0 100
0.0 Bottom-bed
(b) Bottom
0.5 z/Z0 (-)
1.0 Top-bed
Fig. 6. Changes in mean diameters of the agglomerates sampled in different positions along the bed height for Talc (4.1 m) powder fluidized in air at 9.4 cm/s for 2 h with and without vibration.
80 60 40 20 (c) 0 100
500
2000
5000
da (µm) Fig. 5. Size distributions of the agglomerates sampled at (a) the top-bed; (b) middle-bed and (c) bottom-bed for Talc (4.1 m) powder fluidized at 9.4 cm/s in air for 2 h with and without vibration.
the mechanisms governing the self-agglomeration for cohesive particles during fluidization remain poorly understood, and more studies are obviously necessary in this regard. Fig. 4 shows the microscopic photos of the agglomerates sampled from the top, medium and bottom of the bed of the Talc particles (4.1 m) after being fluidized in air at 9.4 cm/s for 2 h with and without mechanical vibration (30 Hz/0.3 mm). Under no vibration, the maximum size of the top-bed agglomerates is around 600 m and the bottombed agglomerates around 6000 m. Under vibration, however, the maximum sizes of the top-bed and the bottombed agglomerates are significantly reduced to around 500 and 550 m, respectively. This observation shows a much more severe segregation of agglomerate size along the bed height without vibration than that with vibration. The statistical size distributions of the agglomerate samples in Fig. 4 can be illustrated in Fig. 5. It is found that the size distri-
bution of the agglomerates sampled at any position of the bed is narrowed when applying the vibration, which indicates a reduced degree of the size-segregation. Moreover, the mean diameters of the agglomerates, calculated from Fig. 5, are plotted in Fig. 6 against the different sampling positions along the bed height. Clearly, both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed are significantly reduced due to the vibration, the latter of which may be particularly important for improving the fluidization quality of cohesive particles. With the mathematical model (Eq. (27)) developed in the previous section, the agglomerate sizes for cohesive powders can be calculated through the iterative approach. For the Talc (4.1 m) powder, for example, the calculated sizes of the top-bed agglomerates are 390 and 247 m, respectively, at a fluidizing gas velocity of 9.4 cm/s in air without and with vibration (30 Hz/0.3 mm). The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the current work and in the literature, as shown in Table 2. The experimental conditions and the related parameters used in modelling are listed in Table 3. For the Talc and CaCO3 powders investigated in this work, the calculated results are in an acceptable agreement with the experimental data regardless of whether or not the vibration is applied. For the other powders including TiO2 (0.6 m), SiO2 (4.6 m) and SiC (1.82 m) by Zhou and Li (1999) and TiO2 (0.27 m) by Iwadate and Horio (1998), the calculation results are also in a reasonable agreement with the experimental data.
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Table 2 Comparison between modelling results and experimental data of agglomerate size Authors
da (m)
Powder
This work
Talc CaCO3 TiO2 SiO2 SiC TiO2
Zhou/Li (1999)
Iwadate/Horio (1998)
da,c a ,b (m)
No vibr.
With vibr.c
No vibr.
With vibr.c
425 362 482 300 597 441
382 326 n.a.d n.a. n.a. n.a.
390 230 415 252 330 560
247 (−35%) 190 (−42%) n.a. n.a. n.a. n.a.
(−8%) (−36%) (−14%) (−16%) (−45%) (+27%)
a Modelling (calculated) results. b The number in the parenthesis is the % error between the calculation and the experimental data. c f = 30 Hz, A = 0.28 mm. d Not applicable.
Table 3 Experimental conditions and parameters used in modelling Authors
Powder
This work Zhou/Li (1999)
Iwadate/Horio (1998)
Talc CaCO3 TiO2 SiO2 SiC TiO2
p
dp (m)
n1 a
(kg/m3 )
1 a
2720 2700 3880 2000 3210 4250
4.1 5.5 0.6 4.6 1.82 0.27
1.79 1.64 2.46 1.54 2.56 2.46
1.0 8.0 114 3.7 10.2 114
a
Dc (m)
u (m/s)
(kg/m3 )
0.038 0.038 0.033 0.033 0.033 0.044
0.094 0.189 0.52 0.32 0.52 0.46
357 1164 1229 217 1068 1700
a From Bergstrom (1997).
5. Discussion
800 Talc(4.1µm)
5.1. Effect of gas velocity 600 15Hz/0.3mm da (µm)
The velocity of the fluidizing gas is generally believed to be one of the most important factors affecting the agglomeration of fine particles during fluidization. However, the effect of the gas velocity on agglomeration is still debatable. On the one hand, it has been suggested that the fluidizing gas velocity has little effect on the agglomerate diameter (Chaouki et al., 1985; Kono et al., 1987; Morooka et al., 1988); and on the other hand, the models proposed by Iwadate and Horio (1998) and by Zhou and Li (1999) suggest that a reduction in agglomerate diameter should occur with increasing gas velocity. Clarifying the effect of gas velocity on agglomeration is significant for understanding the agglomerating behaviour of cohesive particles in fluidization or for exploring the mechanisms governing the formation and failure of agglomerates during fluidization. In this regard, experimental and theoretical studies are carried out using Talc (4.1 m) powder fluidized under a mild vibration condition (15 Hz/0.3 mm) in air at a varying gas velocity of 6.5, 9.4 and 14.2 cm/s. The mean diameters of the agglomerates sampled at the top bed are plotted against the gas velocity in Fig. 7, wherein the modelling results are also illustrated comparatively. Although with noticeable deviation between the experimental data and the simulation, the model can predict a same trend that was observed by experiments,
Experimental Modelling
400
200
0 0
5
10
15
20 25 30 ug (cm/s)
35
40
45
50
Fig. 7. Effect of gas velocity on mean diameters of top-bed agglomerates for Talc (4.1 m) powder fluidized in air under vibration (15 Hz/0.3 mm).
i.e., the agglomerate size decreases with increasing gas velocity. This result strongly supports the previous conclusion made by Iwadate and Horio (1998) and Zhou and Li (1999).
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
700
CaCO3 (5.5µm)
600 da (µm)
It is well accepted that the self-agglomeration of fine particles during fluidization is a dynamic process between growing of the agglomerates due to the cohesive forces and fracturing of the agglomerates due to the breaking forces such as the collision force between particles and/or agglomerates generated by the fluidizing gas. A higher gas velocity therefore tends to generate larger breaking forces, which may result in a smaller agglomerate size.
6539
500
Experimental Modelling
400 300 200
In general, as has been shown in Figs. 4–6 and Table 2 in the previous section, the effect of vibration on agglomeration is evident, i.e., the vibration significantly reduces both the average size and the degree of the size-segregation of the agglomerates in the whole bed. Another factor that may affect the agglomeration behaviour of cohesive particles in fluidization under vibration would be the vibration intensity, which is closely related with the vibration frequency (f) or amplitude (A). To quantify the vibration intensity, the vibration strength, , defined as the ratio of acceleration of vibration to that of gravity, i.e., = A(2f )2 /g, is used. From the present model (Eq. (27)), it may be concluded that a larger vibration intensity by increasing either f or A may lead to a smaller agglomerate size. However, this is never the case from the experimental data obtained, as shown in Fig. 8. In this figure, the experimental and modelling results of the mean agglomerate size da for CaCO3 (5.5 m) at 18.9 cm/s and Talc (4.1 m) at 9.4 cm/s are plotted against the vibration strength . A reasonable agreement of the modelling results and the experimental data is shown for lower than 0.25, showing a similar trend that da decreases with . When the vibration intensity increases further, however, the experiments show that the mean agglomerate size does not decrease but increases gradually with the vibration intensity. Discrepancy between the modelling and experimental results becomes larger at a higher . This suggests that precise prediction of agglomerate size for fluidization of cohesive particles under mechanical vibration is difficult because the effect of vibration on agglomeration appears to never be monotonic. The following gives a possible explanation: as has been discussed in the previous sections, the self-agglomeration of fine particles during fluidization is a dynamic process between growing of the agglomerates and fracturing of the agglomerates. The experimental data shown in Fig. 8 suggest that the effect of vibration on agglomeration is two-sided. On the one hand, the additional energy introduced to the bed due to the vibration can help to break the agglomerates, leading to a smaller agglomerate diameter. On the other hand, the vibration increases the contacting probability between particles and/or agglomerates, which thus favour the growth of the agglomerates in fluidization of the cohesive particles where the interparticle forces are very strong. These two contrary effects compete with each other during the process of self-agglomeration in fluidization.
(a)
100
700
Talc (4.1µm)
600 da (µm)
5.2. Effect of vibration intensity
500 400 300 200 100 0.0
0.5
(b)
1.0
1.5 (-)
2.0
2.5
3.0
Fig. 8. Effect of vibration intensity on mean diameters of top-bed agglomerates (a) for the 5.5 m particles of CaCO3 at 18.9 cm/s and (b) for the 4.1 m particles of Talc at 9.4 cm/s.
Under these circumstances, the experimental data regarding the effect of vibration intensity on agglomerate size can thus be accountable: at lower vibration intensities the former effect can be predominant, while the latter may become predominant at higher intensities.
6. Conclusions Due to the strong inter-particle forces, the handling of cohesive powders in industries always suffers from the severe problem of agglomeration, which often leads to poor fluidization or even complete de-fluidization when attempting to fluidize these particles. Mechanical vibration proves to be an effective means to help fluidization of the cohesive solids. However, a comprehensive study on the self-agglomeration of cohesive particles during fluidization, and the effect of mechanical vibration on agglomeration behaviours did not receive enough attention previously. In this study, a novel “on-line sampling” technique, which is able to prevent the agglomerates from being disrupted during sampling, has been developed. Effects of gas velocity and mechanical vibration on the self-agglomeration during fluidization of cohesive particles have been examined experimentally and theoretically using Talc (4.1m) and CaCO3 (5.5 m) powders. A new model for prediction of agglomerate size has also been established on the basis of on an energy balance,
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where the collision energy between agglomerates, the energy due to cohesive forces and the energy generated by vibration are taken into account. The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the present work and in the literature. For the two powders investigated in this work, the calculated results agree satisfactorily with the experimental data regardless of whether or not the vibration is applied. The results of the calculations are also within reasonable agreement with the experimental data by others. Without vibration, a severe segregation of agglomerate size along the bed height has been observed with small agglomerates existing at the top and bigger ones at the bottom. When the vibration is applied, both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed are significantly reduced. Both experimental and theoretical studies show that a higher gas velocity leads to a smaller agglomerate size. Meanwhile, it is found that the effect of vibration is much more complicated. The mean agglomerate size decreases initially with the vibration intensity, but increases gradually when the vibration intensity exceeds a critical value. It thus suggests that the effect of vibration on agglomeration in fluidization of the cohesive particles is two-sided: it can help to break the agglomerates due to the additional vibrational energy, and it can also favour the growth of the agglomerates due to the enhanced contacting probability between particles and/or agglomerates. These two sides of the effect are competing during the self-agglomeration process in fluidization of cohesive particles under vibration, one of which may become dominant depending on the vibration intensity.
kB L0 m ms mi n0 n1 n Ps,n rpi ra R RH T ug umf V Z0 Z
Greek letters
b a 0 1
Notation A AOR AH dp dai Db Dc E Evib Ecoll Ecoh f Fc Fcoll Fvan g h ki
amplitude of vibration, m Angle of repose, deg Hamaker constant, J mean-particle size, m diameter of agglomerate i (i = 1, 2), m bubble diameter, m diameter of fluidized bed, m Young’s modulus, Pa energy generated by vibration, J collision energy between agglomerates, J cohesion energy of agglomerates, J frequency of vibration, Hz cohesive force, N collision force, N the van der Waals force, N gravity acceleration, 9.81 m/s2 Planck’s constant (=6.626 × 10−34 J s) function of Poisson’s ratio and Young’s modulus, Pa−1
boltzmann’s constant (=1.381 × 10−23 J/K) static (unexpanded) bed height, m function defined by Eq. (4) average mass of agglomerate, kg mass of agglomerate i (i = 1, 2), kg refractive index of medium, dimensionless refractive index of the solids, dimensionless function defined by Eq. (3) dimensionless average particle pressure asperity radii for particle i (i = 1, 2), m asperity radius for particle, m parameter used in Fvan calculation, dimensionless Hausner ratio (=bt /ba ), dimensionless absolute temperature, K superficial gas velocity, m/s minimum fluidization velocity, m/s relative velocity of agglomerates, m/s initial distance between two particles, m the maximum displacement within which the tensile strength of the agglomerate remains in effect, m
g e ba bt p g a h¯
maximum compression displacement, m the displacement of the two parts of the agglomerate at the breakage, m average bed voidage, dimensionless agglomerate voidage, dimensionless dielectric constant of medium, dimensionless dielectric constant of the solids, dimensionless the effective factor for vibration energy, dimensionless vibration strength, dimensionless gas viscosity, kg/m/s Poisson’s ratio main electronic absorption frequency in the UV region the dimensionless factor in Eq. (11), dimensionless aerated bulk density, kg/m3 tapped bulk density, kg/m3 apparent particle density, kg/m3 gas density,kg/m3 agglomerate density, kg/m3 tensile strength of the agglomerate, Pa Lifshitz–van der Waals constant, eV
Acknowledgements The authors are grateful to the Ontario Research and Development Challenge Fund for supporting this study.
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
References Baerns, M., 1966. Effect of interparticle adhesive forces on fluidization of fine particles. Industrial & Engineering Chemistry Fundamentals 5, 508–516. Bergstrom, L., 1997. Hamaker constants of inorganic materials. Advances in Colloid and Interface Science 70, 125–169. Castellanos, A., Valverde, J.M., Perez, A.T., Ramos, A., Watson, P.K., 1999. Flow regimes in fine cohesive powders. Physical Review Letters 82, 1156–1159. Chaouki, J., Chavarie, C., Klvana, D., 1985. Effect of interparticle forces on the hydrodynamic behaviour of fluidized aerogels. Power Technology 43, 117–125. Chirone, R., Massimilla, L., Russo, S., 1993. Bubble-free fluidization of a cohesive powder in an acoustic field. Chemical Engineering Science 48, 41–52. Dutta, A., Dullea, L.V., 1991. Effects of external vibration and the addition of fibers on the fluidization of a fine powder. A.I.Ch.E. Symposium Series 87 (281), 38–46. Ennis, B.J., Green, J., Davies, R., 1994. The legacy of neglect in the U.S. Chemical Engingeering Progress 904, 32–43. Geldart, D., 1973. Types of gas fluidization. Powder Technology 7, 285–297. Geldart, D., Harnby, N., Wong, A.C., 1984. Fluidization of cohesive powders. Powder Technology 37, 25–37. Hartley, P.A., Parfitt, G.D., Pollack, L.B., 1985. The role of the van der Waals force in the agglomeration of powders containing submicron particles. Powder Technology 42, 35–46. Horio, M., Saito, A., Unou, K., Nakazono, H., Shibuya, N., 1996. Synthesis of diamond particles with an acetylene circulating fluidized bed. Chemical Engineering Science 51, 3033–3038. Israelachvili, J.N., 1992. Intermolecular and Surface Forces. second ed. Academic Press, London. Iwadate, Y., Horio, M., 1998. Prediction of agglomerate sizes in bubbling fluidized beds of group C powders. Powder Technology 100, 223–236. Jaraiz, E., Kiruma, S., Levenspiel, O., 1992. Vibrating beds of fine particles: estimation of interparticle forces from expansion and pressure drop experiments. Powder Technology 72, 23–30. Kono, H.O., Huang, C.C., Morimoto, E., Nakayama, T., Hikosaka, T., 1987. Segregation and agglomeration of type C powders from homogeneously aerated type A-C powder mixtures during fluidization. Powder Technology 53, 163–168. Kono, H.O., Matsuda, C., Tian, D.C., 1990. Agglomeration cluster formation of fine powders in gas–solid two phase flow. A.I.Ch.E. Symposium Series 86 (276), 72–77. Krupp, H., 1967. Particle adhesion theory and experiment. Advances in Colloid and Interface Science 1, 111–239. Krupp, H., Sperling, G., 1966. Theory of adhesion of small particles. Journal of Applied Physics 37, 4176–4180. Leva, M., 1959. Fluidization. McGraw-Hill, New York, p. 69. Li, H., Legros, R., Brereton, C.H.M., Grace, J.R., Chaouki, J., 1990. Hydrodynamic behaviour of aerogel powders in high velocity fluidized beds. Powder Technology 60, 121–129. Molerus, O., 1982. Interpretation of Geldart’s type A, B, C and D powders by taking into account interparticle cohesion forces. Powder Technology 33, 81–87. Morooka, S., Kusakabe, K., Kobata, A., Kato, Y., 1988. Fluidization state of ultrafine powders. Journal of Chemical Engineering of Japan 21, 41–46.
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Mori, S., Yamamoto, A., Iwata, S., Haruta, T., Yamada, I., 1990. Vibro-fluidization of group-C particles and its industrial applications. A.I.Ch.E. Symposium Series 86 (276), 88–94. Morse, P.M., Ingard, K.U., 1968. Theoretical Acoustics. McGraw-Hill, New York. Mujumdar, A.S., 1983. Aerodynamics, hat transfer and dying in vibrated fluidized beds. American Journal of Heat Mass Transfer 7, 99–110. Nedderman, R.M., 1992. Statics and Kinematics of Granular Materials. Cambridge University Press, Cambridge. Noda, K., Mawatani, Y., Uchida, S., 1998. Flow pattern of fine particles in a vibrated fluidized bed under atmospheric or reduced pressure. Powder Technology 99, 11–14. Pacek, A.W., Nienow, A.W., 1990. Fluidization of fine and very dense hard metal powders. Powder Technology 60, 145–158. Princen, H.M., 1968. The effect of capillary liquid on the force of adhesion between spherical solid particles. Journal of Colloid Interface Science 26, 249–253. Rietema, K., 1984. Powders, what are they? Powder Technology 37, 5–23. Seville, J.P.K., Willett, C.D., Knight, P.C., 2000. Interparticle forces in fluidization: a review. Powder Technology 113, 261–268. Staniforth, J.N., 1985. Ordered mixing or spontaneous granulation. Powder Technology 45, 73–77. Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity. McGraw-Hill, New York. Ushiki, H., 1995. Non-uniformity space time concept in condensed matters. Kobunshi 44, 726–731. Venkatesh, R.D., Grmela, M., Chaouki, J., 1998. Fluidization of cryogels in a conical column. Powder Technology 100, 211–222. Visser, J., 1989. An invited review—van der Waals and other cohesive forces affecting powder fluidization. Powder Technology 58, 1–10. Vold, M.J., 1960. The sediment volume in dilute dispersions of spherical particles. Journal of Physical Chemistry 64, 1616–1619. Wang, Z. 1995., Fluidization of fine particles and effects of additive particles. Ph.D. Thesis, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, p. 77. Wang, Z., Li, H., 1995. A new criterion for prejudging the fluidization behaviour of powders. Powder Technology 84, 191–195. Wang, Z., Kwauk, M., Li, H., 1998. Fluidization of fine particles. Chemical Engineering Science 53, 377–395. Wank, J.R., George, S.M., Weimer, A.W., 2001. Vibro-fluidization of fine boron nitride powder at low pressure. Powder Technology 121, 195– 204. Xu, C., Cheng, Y., Zhu, J., 2004. Fine particle fluidization-effects of mechanical/acoustic vibration. In: Arena, L., Chirone, R., Miccio, M., Salatino, P. (Eds.), Fluidization XI. Present and Future for Fluidization Engineering. ECI, New York, USA, pp. 627–634. Xu, C., Zhang, H., Zhu, J., 2005. Improving fluidizability of cohesive particles by surface coating with flow conditioners. Chemical Engineering Science, submitted. Zhou, T., Li, H., 1999. Estimation of agglomerate size for cohesive particles during fluidization. Powder Technology 101, 57–62.
Further reading Mori, S., Wen, C.Y., 1975. Estimation of bubble diameter in gaseous fluidized Beds. A.I.Ch.E. Journal 21, 109.
Experimental and theoretical study on the agglomeration arising from fluidization of cohesive particles—effects of mechanical vibration Chunbao Xu, Jesse Zhu∗ Particle Technology Research Centre, Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada Received 28 July 2004; received in revised form 2 May 2005; accepted 15 May 2005 Available online 11 July 2005
Abstract A novel technique that can prevent the disruption of agglomerates when sampling the agglomerates from a fluidized bed has been developed and has been applied to the investigation of the agglomeration behaviour of cohesive particles during fluidization with and without mechanical vibration. A new model for the prediction of agglomerate size has also been established on the basis of the energy balance between the agglomerate collision energy, the energy due to cohesive forces and the energy generated by vibration. The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the present work and in the literature. Effects of gas velocity and mechanical vibration on agglomeration for two cohesive (Geldart group C) powders in fluidization are examined experimentally and theoretically. The experimental results prove that mechanical vibration can significantly reduce both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed. However, the experiments also reveal that the mean agglomerate size decreases initially with the vibration intensity, but increases gradually as the vibration intensity exceeds a critical value. This suggests that the vibration cannot only facilitate breaking the agglomerates due to the increased agglomerate collision energy but can also favour the growth of the agglomerates due to the enhanced contacting probability between particles and/or agglomerates. Both the experimental and theoretical results show that a higher gas velocity leads to a smaller agglomerate size. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Cohesive particles; Fluidization; Mechanical vibration; Agglomeration; Modelling
1. Introduction The significance of particle technology is apparent in that approximately one-half of the products in the chemical industry and at least three-quarters of the raw materials are in granular form (Nedderman, 1992) and it is estimated that sales of $61 billion per annum in the chemical industry are linked to particle technology (Ennis et al., 1994). The high surface area-to-volume ratio and other special characteristics of fine particles make them very attractive in the industries of advanced materials, food and pharmaceuticals, etc. However, handling of these fine powders becomes much more difficult as their sizes become smaller. Fine particles, ∗ Corresponding author.
E-mail address: [email protected] (J. Zhu). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.05.062
30 m or smaller in size, classified as group C (cohesive) particles by Geldart (1973), are generally believed to be unsuitable for fluidization since they tend to form agglomerates as a consequence of strong interparticle forces (Baerns, 1966; Chaouki et al., 1985; Pacek and Nienow, 1990; Ushiki, 1995; Horio et al., 1996). Although for submicron- or nanoparticles where the interparticle force is much stronger than the gravitational forces, the bed of particles may exhibit a state of self-agglomerating fluidization due to the formation of stable and roughly mono-sized agglomerates (Molerus, 1982; Geldart et al., 1984; Rietema, 1984; Jaraiz et al., 1992; Chaouki et al., 1985; Morooka et al., 1988), for most of the group C particles where the interparticle forces are not strong enough, the agglomerates formed in fluidization are unstable and normally have a severe size segregation, leading to partial fluidization or even de-fluidization (Pacek and
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
Nienow, 1990; Wang et al., 1998; Xu et al., 2004). It thus suggests that the fluidization behaviour of cohesive particles strongly depends on the properties (e.g., strength, size and size distribution, etc.) of the agglomerates arising from fluidization and the agglomeration behaviours during fluidization (Chaouki et al., 1985; Chirone et al., 1993). Several previous experimental works (Kono et al., 1990; Li et al., 1990; Wank et al., 2001; Xu et al., 2004) have demonstrated that the size/size distribution of agglomerates arising from fluidization of cohesive particles is dependent not only on the properties of the primary particles but also on the fluidization conditions such as parameters of fluidizing gas (gas type, humidity and velocity) and the application of fluidization aids (e.g., mechanical vibration). Mechanical vibration has proved to be an effective means to help fluidization of cohesive solids due to the breaking of channels and agglomerates (Mori et al., 1990; Dutta and Dullea, 1991; Mujumdar, 1983; Wank et al., 2001; Xu et al., 2004). Consequently, vibro-fluidized beds are commonly used in powder processing such as mixing, granulation, drying and coating. So far, however, a comprehensive study on the agglomeration behaviours of cohesive particles during fluidization and the effects of mechanical vibration are still unavailable in the literature. Due to the fragile structures of the agglomerates, the biggest challenge in studying the agglomeration during fluidization is the agglomerate–sampling techniques (Noda et al., 1998; Wang et al., 1998; Venkatesh et al., 1998; Castellanos et al., 1999; Wank et al., 2001; Xu et al., 2004). A “freezing” method has been developed by Pacek and Nienow (1990), in which the agglomerate granules were frozen by spraying of a binder solution of wax from the top of the bed before sampling. Another technique, called particle/droplet image analysis, has been recently reported for direct measurement of the agglomerate size in the free board and the region close to the upper surface of the solid bed (Wank et al., 2001). However, there exists an obvious limitation for these two techniques in that they are only capable of the size measurement for the agglomerates in the top bed. It is thus of a great significance to develop other techniques, which are capable of sampling the agglomerates, without disrupting them in either sizes or structures, from any parts of the bed (top, middle or bottom bed). In the present study, a novel “on-line sampling” technique has been developed, the details of which will be described later in the experimental section. It is well accepted that theoretical study is a very useful means for exploring the mechanism governing the processes of interest. Several theoretical studies on the prediction of agglomerate size have been reported since 1985 (Chaouki et al., 1985; Morooka et al., 1988; Iwadate and Horio, 1998; Zhou and Li, 1999), where most of the models are based on the principle of force balance. Bergstrom (1997) proposed a very simple model, where the agglomerate size was estimated from the force balance between the drag force due to the gas flow and the interparticle force (van der Waals force).
Similarly, Iwadate and Horio (1998) predicted the agglomerate size simply by balancing the bubble-causing expansion force and the cohesive force between agglomerates. Zhou and Li (1999) assumed that the drag force due to gas flow and the collision force between agglomerates are balanced with the buoyant gravity and the cohesive force. The predictions using these force-balance-based models have shown various degrees of agreement with the experimental data. On the other hand, Morooka et al. (1988) came up with a model based on an energy balance, in which it is assumed that the agglomerate tends to disintegrate when the energy generated by laminar shear stress and the kinetic energy of the agglomerate are equal to the energy required to break the agglomerate (i.e., the energy due to the cohesive forces). However, in their model, the minimum fluidization velocity (umf ) rather than the superficial gas velocity was used in calculating the energy generated by laminar shear stress and the kinetic energy of agglomerates, which makes the reliability of the model very questionable. Obviously, more studies are needed to ameliorate these models for precise prediction of agglomerate size in fluidization of cohesive particles. In order to clarify the mechanism governing the formation and failure of agglomerates during fluidization of fine particles under mechanical vibration, the present study will deal with both the measurement and the modelling of the size of agglomerates arising from the fluidization of cohesive particles with and without vibration. A new model for the prediction of agglomerate size is developed based on the energy balance between the agglomerate collision energy, the energy due to cohesive forces and the energy generated by vibration.
2. Theoretical analysis The phenomenon of size-segregation of agglomerates is often observed in fluidization of cohesive powders, resulting in a layered structure along the bed height: the smaller and usually more stable agglomerates exist at the top, while the larger and looser ones are present at the bottom (Xu et al., 2004). In this regard, the efforts on modelling of the agglomerate size are only meaningful for the top-bed stable agglomerates. To simplify the analysis, the following assumptions are made: (1) the agglomerates formed are all spherical in shape, same in size with a mean diameter of da , and of the same properties, (2) the wall effect is neglected and (3) the van der Waals force dominates over other types of the interparticle cohesive forces. It is also assumed that the agglomerate tends to disrupt or break when the total energy due to collision plus external vibration (if applied) is greater than that due to the cohesive forces. Accordingly, the following energy balance may be attained at the breaking point for the agglomerate Ecoll + Evib,eff = Ecoh ,
(1)
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
where the subscripts “coll”, “vib”, “eff” and “coh” denote “collision”, “effective vibration” and “cohesion”, respectively. 2.1. Collision energy Similar to the work by Zhou and Li (1999), the agglomerates are assumed to be elastic bodies, and the maximum compression displacement can be calculated from the elasticity theory (Timoshenko and Goodier, 1970) 2/5 1.25V 2 = , (2) nm where V is the relative velocity between two agglomerates in a collision, and n and m are given by 8 da1 da2 n= , (3) 2 d +d 2 9 (k1 + k2 ) a1 a2 m=
m1 + m2 , m1 m 2
(4)
where m1 and m2 represent the mass of the two agglomerates in the collision and k is a function of Poisson’s ratio and Young’s modulus E, defined as k=
1 − 2 . E
(5)
According to the assumptions made, m1 = m2 = m = 1/6da3 a , k1 = k2 = k and da1 = da2 = da , then one has
= (0.313V 2 2 k a )2/5 da .
(6)
The collision force between the two agglomerates is (Zhou and Li, 1999) Fcoll = n3/2 .
(7)
Assuming the collision force remains constant during the collision, the collision energy Ecoll is then obtained as Ecoll = Fcoll = n5/2 .
(8)
Substituting n and through Eqs. (3) and (6) into Eq. (8) gives Ecoll = 0.104a da3 V 2 .
(9)
Since all the agglomerates in the bed are moving around within the bed at certain unknown velocities, to determine the relative velocity V between the two agglomerates in collision becomes more difficult. In the studies of Iwadate and Horio (1998) and Zhou and Li (1999), the relative velocity V was estimated by the following correlation: V = (1.5Ps,n Db g b )0.5 ,
(10)
where Ps,n is the dimensionless average particle pressure, b is the bed voidage and Db is the bubble diameter. However, the calculation based on the above correlation show
6531
that the relative velocity is as high as the superficial gas velocity (ug ), and in some cases the calculated V is even much higher than ug , which is obviously too large to be practical. On the other hand, Morooka et al. (1988) adopted umf of the agglomerates as the relative velocity V , but this approximation is also questionable since it overlooks the effect of the superficial gas velocity (ug ) on the agglomerate size, while this effect is significant as will be discussed later. Since the two agglomerates in collision are more likely moving in a same direction along with the fluidizing gas or bubbles within the bed, a more reasonable understanding is that the relative velocity V should be small. Thus, in this study, V is assumed to lie between 0 and the geometric average of ug and umf , i.e., √ V = ug umf ,
(11)
where is the factor whose value is between 0 and 1.0. By comparing the predictions with the experimental results, is fixed at 0.1 in this study. umf of agglomerates (generally with a large size) can be estimated with the conventional correlation by Leva (1959) umf =
9.23 × 10−3 da1.82 (a − g )0.94 0.06 0.88 g g
,
(12)
where g and g are the viscosity and density of the fluidizing gas. 2.2. Vibration energy As well known, the application of an external vibration to the fluidization will help breaking the agglomerates down to small ones, so the contribution of the vibration should be properly taken into account. However, a quantitatively study in this regard is not yet available in the literature. For a mass ms oscillating with a simple harmonic motion of an amplitude A and a frequency f, it possesses an oscillating energy of (2ms f 2 A2 ) (Morse and Ingard, 1968). Where, it should be noted that the oscillating energy of an agglomerate, during collision with the other one, will dissipate only partially since its oscillation sustains after collision but with a slightly decreased amplitude or frequency due to the damping effect of the collision. In order to account for the effective part of the oscillating energy that contributes to break the agglomerates, the effective factor, i.e., , is adopted, and the effective energy due to vibration may be assumed as Evib,eff = 2ms f 2 A2 .
(13)
Substituting the expression ms = 1/6da3 a into Eq. (13) gives Evib = 13 3 a f 2 A2 da3 .
(14)
By comparing the predictions with the experimental results, is assumed as 0.01 in this model.
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
2.3. Cohesion energy Practically, the agglomerates in collision may break up unevenly into larger parts and smaller parts, but the average volume of the two portions in the bed should be equal, so we have assumed that the agglomerate breaks into two equal parts to simplify the modelling process. To break an agglomerate into half-and-half, the tensile strength due to cohesive forces within the agglomerate must be overcome, and the energy required for this process is the cohesion energy Ecoh . Assuming the cohesive forces remain constant during the breaking of the agglomerate, Ecoh can be calculated as Z 2 da d , (15) Ecoh = Z0 4 where is the tensile strength of the agglomerate, is the displacement of the two parts of the agglomerate at the breakage or the distance between the two departing particles, Z0 is the initial distance between the two adjacent particles and Z is the displacement within which the tensile strength of the agglomerate remains in effect. According to Molerus (1982),
=
1 − a Fc , a dp2
(16)
where a is the voidage of agglomerates and Fc is the interparticle forces. As has been thoroughly discussed in the literature (Krupp, 1967; Hartley et al., 1985; Staniforth, 1985; Seville et al., 2000), the interparticle forces that lead to agglomeration of fine particles may be of several types including the van der Waals forces, electrostatic forces, interfacial forces due to solid bridges and liquid bridges, as well as mechanical forces resulting from static frictional contact or interlocking of irregular particle surfaces. Any of these forces may be dominant in a particular circumstance. Although the relative importance of a particular form of interparticle forces is strongly dependent on the fluidized bed set-up, the original properties of the particles and the fluidization conditions (such as moisture level), it is generally believed that the van der Waals force is much more significant than the electrostatic force and other types of interparticle forces for finer particles of a diameter < 100 m in the absence of liquid bridges (Baerns, 1966; Visser, 1989; Wang and Li, 1995). In our experiments, tribo-electrostatic charge was not observed for all the powders tested. Furthermore, in another study by the same authors (Xu et al., 2005), we have also tested the effect of adding very fine metal particles as flow conditioners to fine polyester powders (10–20 m), and it turned out that the addition of these electro-conductive metal particles did not give better results on reducing the cohesiveness of the host particles, compared with the operations of other types of non-conductive flow conditioners (Al2 O3 , silica or TiO2 ). This thus suggests that even for the polyester particles, a material very favourable for build-up of electrostatic charge, the electrostatic force is not the dom-
inant force among the interparticle forces in the fluidized bed. Therefore, it is reasonable in this study to assume that van der Waals forces dominate, as stated in the previous assumptions for the modelling. According to Krupp (1967), Fvan between two particles can be estimated as h¯ R, (17) 8 2 where h¯ is the Lifshitz–van der Waals constant, and R is defined by rp1 rp2 R= , (18) rp1 + rp2 Fvan =
where rp1 and rp2 are the asperity radii for the two particles in contact. By assuming the particles to be with smooth surfaces, rp1 and rp2 can be radii of the particles, i.e., rp1 = rp2 = ra = dp /2 (Krupp, 1967; Morooka et al., 1988) and R=dp /4. By taking the number of contact points per particle (nc =1.61−1.48 ) (Jaraiz et al., 1992) into account, the overall a cohesive forces per particle (Fc ) becomes Fc = nc Fvan = 1.61−1.48 a
h¯
R. (19) 8 2 Substituting R = dp /4 into Eq. (19) and the substituting Eq. (19) into Eq. (16), one has
= 1.61−1.48 a
1 − a 1 h¯ . a dp 32 2
(20)
Replacing h¯ with the Hamaker constant AH (h¯ = (4/3)/AH ) (Krupp and Sperling, 1966; Krupp, 1967) gives
= 1.61−1.48 a
1 − a 1 A H . a dp 24 2
Substituting Eq. (21) into Eq. (15) Z 2 1 − a Ecoh = da 1.61−1.48 a a Z0 4 2 1 − a AH = da 1.61−1.48 a 96 a dp
(21) gives 1 AH d
dp 24 2 1 1 − . Z0 Z
(22)
The distance of maximum attraction or the initial distance between two particles at the point of contact, Z0 , is normally ˚ chosen as 4 A(=4 × 10−10 m). This value can be justified by the fact that Z0 = 4 A˚ is slightly larger than the lattice constant of weekly van der Waals-bonded molecular crystals (Krupp and Sperling, 1966; Krupp, 1967). Consequently, Z0 is assumed as 4 A˚ in this work, and Z is arbitrarily assumed to be far larger than Z0 , i.e., Z Z0 . With this hypothesis, Eq. (22) can be reduced to Ecoh =
2 1 − a A H 1 da 1.61−1.48 . a 96 a d p Z0
(23)
The Hamaker constant AH can be estimated by the following equation (Israelachvili, 1992): 2 1 − 0 2 3 3hv e n21 − n20 + √ , (24) AH = kB T 4 1 + 0 16 2 (n21 + n20 )3/2
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
where kB is Boltzmann’s constant (kB =1.381×10−23 J/K), T is the absolute temperature and 1 (0 ) and n1 (n0 ) are the dielectric constant and refractive index of the particulate materials (the medium where the particles are present) (for vacuum or air, 0 = n0 = 1.0). Here, h is Planck’s constant (=6.626×10−34 J s) and e is the main electronic absorption frequency in the UV region, typically at around 3×1015 s−1 . Hence, for the particulate materials fluidized in air, Eq. (24) is rewritten as 1 − 0 2 AH = 1.036 × 10−23 T 1 + 0 (n2 − n2 )2 + 2.635 × 10−19 21 20 3/2 . (25) (n1 + n0 ) The agglomerate voidage (a ) can be determined indirectly from the agglomerate density (a ) and the particle density (p )
a = 1 − a /p .
(26)
Here, the value of a can be obtained by direct measurement, but the experimental results of Zhou and Li (1999) have demonstrated that a for cohesive particles is approximately between 1.15 times the aerated density (ba ) and 0.85 times the tapped density (bt ) of the primary particles, depending the bonding strength of the agglomerate. To simplify, a in this study is approximated by bt of the primary particles. Substituting Eqs. (9), (14) and (23) into Eq. (1) results in da =
−1.48 1−a AH 1 96 1.61a a dp Z0 . 0.104a V 2 + 13 3 a f 2 A2
(27)
It should be noted that the relative velocity of agglomerates (V ) is of da dependence, referring to Eqs. (10)–(12), so that Eq. (27) must be solved by an iterative approach.
3. Experimental The vibro-fluidized bed setup used in this study consists of a fluidized bed column made of Plexiglas (38 mm i.d. and 500 mm tall), a vibration generation system, a data
6533
acquisition system, and a gas flow control system. Compressed air stripped of trace humidity through a fixed bed of silica gel is used as the fluidizing gas, whose flow rate is controlled by a series of rotameters (Omega Engineering Inc.) and a digital mass flow controller (Fathom Technologies, GR series). All the flowmeters are carefully calibrated with a Wet Test Meter (GCA/Precision Scientific) before using. A porous polymer plate serves as the gas distributor. Pressure drops across the whole bed are measured with a differential pressure transducer (Omega PX163 series). Mechanical vibration is generated by a pair of vibrators driven by an ABB inverter with a vibration frequency (f) varying from 0 to 50 Hz. Through changing the unbalanced weights of the vibrator, various amplitudes (A) between 0 and 3 mm (depending on the frequency used) can be obtained. In the present work, the vibration frequency and amplitude are set at 50 Hz and 0.3 mm, respectively, unless specified otherwise. The fine particulate materials used are cohesive fine particles of Talc (4.1 m) and CaCO3 (5.5m), which are typical Geldart group C powders, whose key physical properties are listed in Table 1. The particles are loaded to the bed to a fixed height of about 100 mm, and the whole particle bed is first loosened by a gas flow at 2.0 cm/s for 10 min before the experiments start. In the case of no vibration, when the fluidization is attempted by slowly increasing the gas velocity, the bed first behaves as that typical of group C particles, i.e., plugging and channelling, until a certain bed pressure builds up causing the particle bed to fracture. As the gas velocity increases further, the bed comes to a transition region during which the particles at the top-bed start to fluidize and self-agglomeration develops gradually, leading to the eventual fluidization and agglomeration of the whole bed. On the other hand, the application of the vibration significantly improves the fluidization, e.g., the plugging, channelling and fracturing of the bed disappear and the agglomerate size decreases, leading to smoother fluidization and higher pressure drops. In order to sample the agglomerates out of the bed for characterization while avoiding disrupting their size, shape and structures, a novel “online sampling” technique that is illustrated in Fig. 1 has been developed and applied to this
Table 1 Fine powders used for fluidization experiments Powders
CaCO3 Talc
dp a
Density (kg/m3 )
RH b
(m)
p
bl d
ba d
5.5 4.1
2700 2710
1160 360
520 170
a The volume-weighted mean diameter by laser diffraction (Malvern Mastersizer 2000). b R (Hausner ratio) = / . H bt ba cAOR, angle of repose. dAnalyzed by a Hosokawa Powder Tester.
AORc ,d
Geldart group
(deg) 2.23 2.12
50.0 48.4
C C
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
Talc(4.1µm)
450
No vibration
da (µm)
400
With vibration (30Hz/0.3mm)
350
300 20
40
60
80 t (min)
100
120
140
Fig. 2. Changes in mean diameters of the top-bed agglomerates of Talc (4.1 m) with fluidization time in air at 9.4 cm/s.
Fig. 1. Diagram of the “online agglomerate sampling” technique: (a) sampling the agglomerates from the top layer of the bed; (b) removing the agglomerates from the upper layer by vacuum prior to the sampling for the agglomerates on the lower layer.
study. The agglomerates are sampled in situ, without stopping the fluidizing gas or making any other changes to the fluidization conditions (e.g. gas velocity and vibration if applicable), and with a sampling ladle from the top of the column. To sample the agglomerates in the upper region of the bed, the ladle is used to pick up the agglomerates directly. As for the agglomerates in the middle and bottom regions, an intensity-controllable vacuum is used to remove all the particulate materials very carefully above the sampling plane. More particles are removed as the measure-
ments are continued further to the lower planes of the bed. In the experiments, the operations of both the agglomerate sampling and the vacuum agglomerate removal were manually but carefully performed. In sampling the agglomerates from the top layer of the bed with the ladle, particular care was taken to avoid breaking the agglomerates during the sampling. In removing the agglomerates with the vacuum probe, the suction intensity was controlled (by adjusting either the suction flow rate or the working distance between the tip of vacuum probe and the suction objects) to be high enough to “pick up” all the agglomerates in the upper layer but low enough to avoid removing the agglomerates in the layer below. The agglomerates captured in the sampling ladle were poured carefully onto a metal disk (4 cm in diameter), followed by gold plating and measurement of their shape/size by scanning electronic microscopy (Hitachi SEM S-2600N). The mean agglomerate size is obtained by taking the arithmetic average of over 100 agglomerates from one sample. In the present study, two experimental runs were carried out for each given condition. The error of the average agglomerate diameter between two tests with the same powder under the same fluidization conditions was within the range of ±(10.15)%, giving acceptable reproducibility for this technique. Since the self-agglomeration of fine particles during fluidization is a dynamic process governed by the growing of the agglomerates due to the cohesive forces and the fracturing of the agglomerates due to the breaking forces, it may take a certain length of time to achieve stabilization of the agglomerates in size and shape under certain fluidization conditions (gas velocity, vibration intensity, etc.). The stable
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
sizes of agglomerates are particularly important and more meaningful for the modelling of the self-agglomeration of cohesive particles in fluidization. It is thus highly necessary to first determine the stabilization time for the agglomeration process. Upon obtaining the stabilization time, one can further determine the sampling time, i.e., the fluidization time for the particles before sampling the formed agglomerates out for characterization. The sampling time should be equal to or longer than the stabilization time for the agglomeration process. In this regard, experiments are carried out using the Talc (4.1m) powder fluidized in air at 9.44 cm/s with and without vibration (30 Hz/0.3 mm). The agglomerates formed during fluidization are sampled from the top-bed after various lengths of time. The mean diameters of the agglomerates at the fluidization time of 30, 60 and 120 min are illustrated in Fig. 2. The results show that the sizes of the agglomerates attain a stable value after about 60 min of fluidization no matter whether the vibration is applied or not. It is thus safe to set the sampling time at 120 min in every case.
6535
4. Results Fig. 3 shows the overhead and the close-up pictures of the top-bed agglomerates for CaCO3 (5.5 m) and Talc (4.1 m) powders at specific superficial gas velocities in air without vibration. Clearly, with the new “online sampling” technique, the original shapes and structures of the agglomerate samples are well maintained. From the overhead pictures for the agglomerates of the two powders, it can be seen that the agglomerates formed at the top-bed are in a good spherical shape with a diameter of 200–500 m under the fluidization conditions stated above. In particular, the sphericity of the agglomerates of Talc (4.1 m) is almost perfect. On the other hand, the microstructures of the agglomerate surfaces are clearly shown in the close-up pictures. The surfaces of both agglomerates show the structures of floc or dendrite, which may reveal one of the possible mechanisms governing the self-agglomerate formation during fluidization as has also been proposed in other previous works by
Fig. 3. Microphotographs of the top-bed agglomerates of (a) CaCO3 at 18.88 cm/s and (b) Talc at 9.4 cm/s in air for 2 h without vibration: scale bars are 1 mm and 50 m for the overhead views and close-up views, respectively.
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
Fig. 4. Segregation for the agglomerates along the bed height for Talc (4.1 m) powder fluidized at 9.4 cm/s in air for 2 h (a) without and (b) with vibration.
Princen (1968), Vold (1960) and Wang (1995). The agglomerate formation in fluidization may be associated with the following sequential steps: growing of the individual chains from the seed particles, growing of the dendrites from the individual chains, and formation of an agglom-
erate by folding of the dendrites due to collision and the binding forces between dendrite/dendrite, agglomerate/agglomerate or dendrite/agglomerate. Despite the wide application of the fine particles in industries and the growing interest of the research in fluidization of fine particles,
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
100
Top
6537
Talc(4.1µm)
3000
80 2500 60 40 No vibration With vibration (30Hz/0.3mm)
20
Number% under size
0 100
(a)
da (µm)
2000
No vibration
1500
Middle 1000
80 60
500
40
With vibration (30Hz/0.3mm) 0
20 0 100
0.0 Bottom-bed
(b) Bottom
0.5 z/Z0 (-)
1.0 Top-bed
Fig. 6. Changes in mean diameters of the agglomerates sampled in different positions along the bed height for Talc (4.1 m) powder fluidized in air at 9.4 cm/s for 2 h with and without vibration.
80 60 40 20 (c) 0 100
500
2000
5000
da (µm) Fig. 5. Size distributions of the agglomerates sampled at (a) the top-bed; (b) middle-bed and (c) bottom-bed for Talc (4.1 m) powder fluidized at 9.4 cm/s in air for 2 h with and without vibration.
the mechanisms governing the self-agglomeration for cohesive particles during fluidization remain poorly understood, and more studies are obviously necessary in this regard. Fig. 4 shows the microscopic photos of the agglomerates sampled from the top, medium and bottom of the bed of the Talc particles (4.1 m) after being fluidized in air at 9.4 cm/s for 2 h with and without mechanical vibration (30 Hz/0.3 mm). Under no vibration, the maximum size of the top-bed agglomerates is around 600 m and the bottombed agglomerates around 6000 m. Under vibration, however, the maximum sizes of the top-bed and the bottombed agglomerates are significantly reduced to around 500 and 550 m, respectively. This observation shows a much more severe segregation of agglomerate size along the bed height without vibration than that with vibration. The statistical size distributions of the agglomerate samples in Fig. 4 can be illustrated in Fig. 5. It is found that the size distri-
bution of the agglomerates sampled at any position of the bed is narrowed when applying the vibration, which indicates a reduced degree of the size-segregation. Moreover, the mean diameters of the agglomerates, calculated from Fig. 5, are plotted in Fig. 6 against the different sampling positions along the bed height. Clearly, both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed are significantly reduced due to the vibration, the latter of which may be particularly important for improving the fluidization quality of cohesive particles. With the mathematical model (Eq. (27)) developed in the previous section, the agglomerate sizes for cohesive powders can be calculated through the iterative approach. For the Talc (4.1 m) powder, for example, the calculated sizes of the top-bed agglomerates are 390 and 247 m, respectively, at a fluidizing gas velocity of 9.4 cm/s in air without and with vibration (30 Hz/0.3 mm). The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the current work and in the literature, as shown in Table 2. The experimental conditions and the related parameters used in modelling are listed in Table 3. For the Talc and CaCO3 powders investigated in this work, the calculated results are in an acceptable agreement with the experimental data regardless of whether or not the vibration is applied. For the other powders including TiO2 (0.6 m), SiO2 (4.6 m) and SiC (1.82 m) by Zhou and Li (1999) and TiO2 (0.27 m) by Iwadate and Horio (1998), the calculation results are also in a reasonable agreement with the experimental data.
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
Table 2 Comparison between modelling results and experimental data of agglomerate size Authors
da (m)
Powder
This work
Talc CaCO3 TiO2 SiO2 SiC TiO2
Zhou/Li (1999)
Iwadate/Horio (1998)
da,c a ,b (m)
No vibr.
With vibr.c
No vibr.
With vibr.c
425 362 482 300 597 441
382 326 n.a.d n.a. n.a. n.a.
390 230 415 252 330 560
247 (−35%) 190 (−42%) n.a. n.a. n.a. n.a.
(−8%) (−36%) (−14%) (−16%) (−45%) (+27%)
a Modelling (calculated) results. b The number in the parenthesis is the % error between the calculation and the experimental data. c f = 30 Hz, A = 0.28 mm. d Not applicable.
Table 3 Experimental conditions and parameters used in modelling Authors
Powder
This work Zhou/Li (1999)
Iwadate/Horio (1998)
Talc CaCO3 TiO2 SiO2 SiC TiO2
p
dp (m)
n1 a
(kg/m3 )
1 a
2720 2700 3880 2000 3210 4250
4.1 5.5 0.6 4.6 1.82 0.27
1.79 1.64 2.46 1.54 2.56 2.46
1.0 8.0 114 3.7 10.2 114
a
Dc (m)
u (m/s)
(kg/m3 )
0.038 0.038 0.033 0.033 0.033 0.044
0.094 0.189 0.52 0.32 0.52 0.46
357 1164 1229 217 1068 1700
a From Bergstrom (1997).
5. Discussion
800 Talc(4.1µm)
5.1. Effect of gas velocity 600 15Hz/0.3mm da (µm)
The velocity of the fluidizing gas is generally believed to be one of the most important factors affecting the agglomeration of fine particles during fluidization. However, the effect of the gas velocity on agglomeration is still debatable. On the one hand, it has been suggested that the fluidizing gas velocity has little effect on the agglomerate diameter (Chaouki et al., 1985; Kono et al., 1987; Morooka et al., 1988); and on the other hand, the models proposed by Iwadate and Horio (1998) and by Zhou and Li (1999) suggest that a reduction in agglomerate diameter should occur with increasing gas velocity. Clarifying the effect of gas velocity on agglomeration is significant for understanding the agglomerating behaviour of cohesive particles in fluidization or for exploring the mechanisms governing the formation and failure of agglomerates during fluidization. In this regard, experimental and theoretical studies are carried out using Talc (4.1 m) powder fluidized under a mild vibration condition (15 Hz/0.3 mm) in air at a varying gas velocity of 6.5, 9.4 and 14.2 cm/s. The mean diameters of the agglomerates sampled at the top bed are plotted against the gas velocity in Fig. 7, wherein the modelling results are also illustrated comparatively. Although with noticeable deviation between the experimental data and the simulation, the model can predict a same trend that was observed by experiments,
Experimental Modelling
400
200
0 0
5
10
15
20 25 30 ug (cm/s)
35
40
45
50
Fig. 7. Effect of gas velocity on mean diameters of top-bed agglomerates for Talc (4.1 m) powder fluidized in air under vibration (15 Hz/0.3 mm).
i.e., the agglomerate size decreases with increasing gas velocity. This result strongly supports the previous conclusion made by Iwadate and Horio (1998) and Zhou and Li (1999).
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
700
CaCO3 (5.5µm)
600 da (µm)
It is well accepted that the self-agglomeration of fine particles during fluidization is a dynamic process between growing of the agglomerates due to the cohesive forces and fracturing of the agglomerates due to the breaking forces such as the collision force between particles and/or agglomerates generated by the fluidizing gas. A higher gas velocity therefore tends to generate larger breaking forces, which may result in a smaller agglomerate size.
6539
500
Experimental Modelling
400 300 200
In general, as has been shown in Figs. 4–6 and Table 2 in the previous section, the effect of vibration on agglomeration is evident, i.e., the vibration significantly reduces both the average size and the degree of the size-segregation of the agglomerates in the whole bed. Another factor that may affect the agglomeration behaviour of cohesive particles in fluidization under vibration would be the vibration intensity, which is closely related with the vibration frequency (f) or amplitude (A). To quantify the vibration intensity, the vibration strength, , defined as the ratio of acceleration of vibration to that of gravity, i.e., = A(2f )2 /g, is used. From the present model (Eq. (27)), it may be concluded that a larger vibration intensity by increasing either f or A may lead to a smaller agglomerate size. However, this is never the case from the experimental data obtained, as shown in Fig. 8. In this figure, the experimental and modelling results of the mean agglomerate size da for CaCO3 (5.5 m) at 18.9 cm/s and Talc (4.1 m) at 9.4 cm/s are plotted against the vibration strength . A reasonable agreement of the modelling results and the experimental data is shown for lower than 0.25, showing a similar trend that da decreases with . When the vibration intensity increases further, however, the experiments show that the mean agglomerate size does not decrease but increases gradually with the vibration intensity. Discrepancy between the modelling and experimental results becomes larger at a higher . This suggests that precise prediction of agglomerate size for fluidization of cohesive particles under mechanical vibration is difficult because the effect of vibration on agglomeration appears to never be monotonic. The following gives a possible explanation: as has been discussed in the previous sections, the self-agglomeration of fine particles during fluidization is a dynamic process between growing of the agglomerates and fracturing of the agglomerates. The experimental data shown in Fig. 8 suggest that the effect of vibration on agglomeration is two-sided. On the one hand, the additional energy introduced to the bed due to the vibration can help to break the agglomerates, leading to a smaller agglomerate diameter. On the other hand, the vibration increases the contacting probability between particles and/or agglomerates, which thus favour the growth of the agglomerates in fluidization of the cohesive particles where the interparticle forces are very strong. These two contrary effects compete with each other during the process of self-agglomeration in fluidization.
(a)
100
700
Talc (4.1µm)
600 da (µm)
5.2. Effect of vibration intensity
500 400 300 200 100 0.0
0.5
(b)
1.0
1.5 (-)
2.0
2.5
3.0
Fig. 8. Effect of vibration intensity on mean diameters of top-bed agglomerates (a) for the 5.5 m particles of CaCO3 at 18.9 cm/s and (b) for the 4.1 m particles of Talc at 9.4 cm/s.
Under these circumstances, the experimental data regarding the effect of vibration intensity on agglomerate size can thus be accountable: at lower vibration intensities the former effect can be predominant, while the latter may become predominant at higher intensities.
6. Conclusions Due to the strong inter-particle forces, the handling of cohesive powders in industries always suffers from the severe problem of agglomeration, which often leads to poor fluidization or even complete de-fluidization when attempting to fluidize these particles. Mechanical vibration proves to be an effective means to help fluidization of the cohesive solids. However, a comprehensive study on the self-agglomeration of cohesive particles during fluidization, and the effect of mechanical vibration on agglomeration behaviours did not receive enough attention previously. In this study, a novel “on-line sampling” technique, which is able to prevent the agglomerates from being disrupted during sampling, has been developed. Effects of gas velocity and mechanical vibration on the self-agglomeration during fluidization of cohesive particles have been examined experimentally and theoretically using Talc (4.1m) and CaCO3 (5.5 m) powders. A new model for prediction of agglomerate size has also been established on the basis of on an energy balance,
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C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
where the collision energy between agglomerates, the energy due to cohesive forces and the energy generated by vibration are taken into account. The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the present work and in the literature. For the two powders investigated in this work, the calculated results agree satisfactorily with the experimental data regardless of whether or not the vibration is applied. The results of the calculations are also within reasonable agreement with the experimental data by others. Without vibration, a severe segregation of agglomerate size along the bed height has been observed with small agglomerates existing at the top and bigger ones at the bottom. When the vibration is applied, both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed are significantly reduced. Both experimental and theoretical studies show that a higher gas velocity leads to a smaller agglomerate size. Meanwhile, it is found that the effect of vibration is much more complicated. The mean agglomerate size decreases initially with the vibration intensity, but increases gradually when the vibration intensity exceeds a critical value. It thus suggests that the effect of vibration on agglomeration in fluidization of the cohesive particles is two-sided: it can help to break the agglomerates due to the additional vibrational energy, and it can also favour the growth of the agglomerates due to the enhanced contacting probability between particles and/or agglomerates. These two sides of the effect are competing during the self-agglomeration process in fluidization of cohesive particles under vibration, one of which may become dominant depending on the vibration intensity.
kB L0 m ms mi n0 n1 n Ps,n rpi ra R RH T ug umf V Z0 Z
Greek letters
b a 0 1
Notation A AOR AH dp dai Db Dc E Evib Ecoll Ecoh f Fc Fcoll Fvan g h ki
amplitude of vibration, m Angle of repose, deg Hamaker constant, J mean-particle size, m diameter of agglomerate i (i = 1, 2), m bubble diameter, m diameter of fluidized bed, m Young’s modulus, Pa energy generated by vibration, J collision energy between agglomerates, J cohesion energy of agglomerates, J frequency of vibration, Hz cohesive force, N collision force, N the van der Waals force, N gravity acceleration, 9.81 m/s2 Planck’s constant (=6.626 × 10−34 J s) function of Poisson’s ratio and Young’s modulus, Pa−1
boltzmann’s constant (=1.381 × 10−23 J/K) static (unexpanded) bed height, m function defined by Eq. (4) average mass of agglomerate, kg mass of agglomerate i (i = 1, 2), kg refractive index of medium, dimensionless refractive index of the solids, dimensionless function defined by Eq. (3) dimensionless average particle pressure asperity radii for particle i (i = 1, 2), m asperity radius for particle, m parameter used in Fvan calculation, dimensionless Hausner ratio (=bt /ba ), dimensionless absolute temperature, K superficial gas velocity, m/s minimum fluidization velocity, m/s relative velocity of agglomerates, m/s initial distance between two particles, m the maximum displacement within which the tensile strength of the agglomerate remains in effect, m
g e ba bt p g a h¯
maximum compression displacement, m the displacement of the two parts of the agglomerate at the breakage, m average bed voidage, dimensionless agglomerate voidage, dimensionless dielectric constant of medium, dimensionless dielectric constant of the solids, dimensionless the effective factor for vibration energy, dimensionless vibration strength, dimensionless gas viscosity, kg/m/s Poisson’s ratio main electronic absorption frequency in the UV region the dimensionless factor in Eq. (11), dimensionless aerated bulk density, kg/m3 tapped bulk density, kg/m3 apparent particle density, kg/m3 gas density,kg/m3 agglomerate density, kg/m3 tensile strength of the agglomerate, Pa Lifshitz–van der Waals constant, eV
Acknowledgements The authors are grateful to the Ontario Research and Development Challenge Fund for supporting this study.
C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529 – 6541
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Further reading Mori, S., Wen, C.Y., 1975. Estimation of bubble diameter in gaseous fluidized Beds. A.I.Ch.E. Journal 21, 109.