Brazilian Journal
of Chemical ISSN 0104-6632 Printed in Brazil Engineering www.abeq.org.br/bjche
Vol. 25, No. 04, pp. 697 - 711, October - December, 2008
BEHAVIOR AND FLUIDIZATION OF THE COHESIVE POWDERS: AGGLOMERATES SIZES APPROACH D. Turki1* and N. Fatah2
1Université Ibn-Khaldoun de Tiaret, Laboratoire de Chimie et Environnement, BP 78, 14000 Tiaret, Algeria. 2Unité de Catalyse et de Chimie du Solide, UMR CNRS 8181, ENSC Lille, bat. C7, 59655, Villeneuve d’Ascq Cedex, France. E-mail: [email protected]
(Received: August 01, 2007 ; Accepted: November 01, 2007)
Abstract - This work focuses on the fluidization of three types of TiO2 powders: Anatase (99% TiO2), Rutile 1 (95% TiO2 and 5% Al) and Rutile 2 (96.5% TiO2 and 3.5% Al and Si); the average diameters of the powders are 204 nm, 159 nm and 167 nm, respectively. These powders belong to group C of the Geldart classification and are characterized as cohesive powders with a non-free flow and a difficult fluidization. The fluidization of the powders was carried out in a glass column of 103 mm inner diameter and 1500 mm height. The experiments and analysis performed included measurements of the physical properties of the powders such as the particle size, density, specific surface area and the flow properties of the powders like the Hausner’s index, the angle of repose, the angle of slide, consolidation and shearing (via shear cell testing). The results obtained with the nanometric TiO2 powders show a more complex behavior than the micronic powders; with a low strength value (Hausner index, angle of repose and angle of slide), the TiO2 powders have a free flow or intermediate-flow and a non-free-flow for higher strength intensities (consolidation and shearing). This behavior is related to the structure of the nanometric particles in the packed bed; the evolution of this structure is made up of individualized and spherical agglomerate shapes and is not perturbed by stresses of low intensities. Indeed, the latter seems to modify the structure of the powder (group C of Geldart classification) to acquire a behavior typical of group A, B or D in the Geldart classification. With high stress values, the individualized agglomerates are disintegrated and the powder is reduced to a more compact structure. The fluidization of TiO2 powders seems to evolve in a more homogeneous way than the micronic powders. This behavior is related to the initial structure being made up of stable agglomerates. Thus, this fluidization is made by agglomerates with a gas velocity of 3×106 to 4.6×106 times the gas velocity for fluidizing the primary particles.A numerical approach based on a force balance in agglomerating fluidized beds was developed in order to estimate the agglomerates sizes. Keywords: Fluidization; Cohesive powder; Agglomerate; Nanometric powder; Interparticle Forces.
INTRODUCTION powders (cohesive powder), micronic and nanometric powders. Many industrial processes In the last years, fluidization has progressed require the use of fine powders in the manufacture of through systematic research, with various specialized catalysts for reactors, ceramics, pharmaceuticals, functions such as: combustion, mixing, chemical paints and cosmetics. reaction, heat and mass transfer, coating, granulation, According to research performed for nearly fifty encapsulation and CVD (Chemical Vapor Deposition) years, the fluidization of fine powders (diameter of processes. This research development persuaded the the primary particles less than 50 µm) is complex. researchers to become interested in the use of fine The difficulty of putting these powders in suspension
*To whom correspondence should be addressed 698 D. Turki and N. Fatah in the fluidizing gas is related to the cohesive between two solids depends on the size, the shape structure and, in particular, to the physical forces and the roughness of the particles, as well as the between the primary particles. In general, the distance between the particles. These forces are experiments are complex during the handling or calculated starting from the Derjaguin approximation fluidizing of these powders. This is due to the (Derjaguin, 1934) and the theory of Lifshitz unpredictable behaviors of the cohesive powders. (Lifshitz, 1956). The estimation of the van der Waals This category of powders belongs to group C of forces is defined as the sum of all interactions Geldart’s classification (Geldart, 1973). The between molecules held on the surface of the complexity of this behavior is due to the small size particles face to face. The magnitude of these forces of the fine particles, i.e., the micronic or nanometric increases with the size reduction of the particles and particles. These tend to form agglomerates (self- becomes dominating compared to the weight of the agglomeration) of completely random size and shape particles. by the action of the interparticle forces between the In many industrial processes, the cohesive primary particles. This is related to the high ratio powders are fluidized in the form of agglomerates. between the surface and the volume of the particles For this, it is necessary to apply either a high gas and to the short distance between the particles. This velocity (Fatah and Cavrois, 1998) compared to the strong interaction between the powders affects the velocity necessary for fluidizing primary particles, or flow properties of the powders. a lower velocity but with addition of external energy. The smooth fluidization of gas-solid particles is (Chirone et al., 1993) drew up a list of techniques the result of equilibrium between the hydrodynamic, used as additional energy (vibration, magnetic gravitational and interparticle forces. However, in pulsation and acoustic energy) to disintegrate the the case of cohesive powders, the interparticle forces cohesive structure and to facilitate the fluidization of are considerable and they control the behavior of a the agglomerates. The mechanism of agglomerate bed composed of fine particles. Thus, during fluidization supposes the passage from group C to a fluidization, the bed of powder cracks into large group A powder or even a group B powder of the portions and the gas tends to flow into the gap Geldart classification. (Leu and Huang, 1994) note a between the fissures. Then, channeling occurs in the clear improvement of the quality of fluidization and bed and, eventually, the gas-solid contact is very low expansion of the bed for powders with low particle and any heat and mass transfer operation is size under the effect of the acoustic pressure. weakened. Indeed, this seems to modify (Russo and al., 1995) The powders are generally presented in the form the structure of the fluidized bed (group C of of heterogeneous structures in particle size, size Geldart) and to acquire a behavior typical of group A distribution, morphology (shape) and physical of Geldart. (Nezzal, 1996) describes that the use of properties (density, specific surface area and mechanical agitation (intrusive method) modifies the porosity). These characteristics are related to the hydrodynamic behavior of the bed powder. This local structure of the particulate system and the type provides a better aeration of the bed particles and of gas flowing around these particles. In the case of homogenizes the fluidization in the form of the cohesive powders, this particulate system appears agglomerates. Thus, the size of the agglomerates to be very complex and uncontrollable. The decreases when the agitating velocity increases. interparticle forces are considerable and control the The aim of this work is to study an important micronic and nanometric particle behavior of the feature of powder structure and the use of different bed. This physical attraction is the effect of the great measurement techniques that can help to understand intensity of internal forces between primary the behavior of fine particles. The experiments and particles. In the case where the particulate system is analysis performed included measurements of the handled in air and when the size and the distance physical properties of the powders such as the between the particles are very small, the van der particle size, density, specific surface area and the Waals forces are controlling rather than the other flow properties of the powders like the Hausner’s interactions forces (capillary and electrostatic index, the angle of repose, the angle of slide, the forces). The particle-particle interactions are consolidation and the shearing (via annular shear achieved primarily by contact. If the particles are not cell). in contact, no force is exerted between them. The The flowability and the physical properties of the van der Waals forces between two macroscopic powders seem to be an interesting way of describing bodies are calculated in a different way from the the hydrodynamic behavior of the very cohesive microscopic one. Indeed, the force of interaction structure.
Brazilian Journal of Chemical Engineering
Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 699 The interparticle forces for the cohesive interaction percentage undersize curve (in volume) and defined are determined by a force balance (kinetic, van der by the following equation: Waals, collision, gravitational and buoyancy forces). A numerical approach based on a force balance in d C= i 60% (2) agglomerating fluidized beds was developed in order to u d estimate the agglomerate’s sizes. i 10% The experimental results indicate that there is a close correlation between the hydrodynamics and the Cu < 2: The particle size distribution is known as local structure of the powder bed. uniform. Cu > 2: The particle size distribution is known as non-uniform or large. MATERIALS AND METHODS di60% and di10% are defined as dimensions of the particles corresponding respectively to 60% and 10% of the particle size distribution of the cumulative In this work three types of TiO2 powders of the Kronos company were studied: curve. The density (p) and the BET surface area (Ss) of . Anatase (99% TiO2): labeled TiO2 (A); powders were, respectively, measured by helium gas . Rutile1 (95% TiO2 and 5% Al): labeled TiO2 (R1); pycnometer (Micromeritics, AccuPyc 1330) and nitrogen gas adsorption (Micromeritics, Asap 2000). . Rutile2 (96.5% TiO2 and 3.5% Al and Si): labeled TiO2 (R2). The powder size distribution was measured with MEASUREMENTS OF FLOW PROPERTIES the light-scattering laser instrument (Beckman- Coulter, LS230). This experiment measures the Measurements were carried out under the same particle size. It should be noted that, due to the working conditions, i.e., with a relative humidity complexity of this experiment, each batch of powder ranging between 40% and 53% and at ambient was analyzed according to a suitable protocol that temperature. The tests were carried out according to gives the primary particle size and not the size of a specific protocol in order to preserve the agglomerate. During these experiments, the optimal reproducibility of the results. With regard to the conditions obtained to reach the lowest size of TiO2 following techniques: particles without degrading the powder structure, are . Ensuring that the initial structure of particles is as follows: the cohesive powders were dispersed in homogeneous during filling. In this test, the loading demineralised water with addition of 0.5% of powder is carried out with a vibrating sieve of 1 tetrasodium diphosphate as dispersant in a flask. mm in aperture. Before the introduction of this suspension into the . Using a smooth and clean cell wall to decrease laser instrument and for a better dispersion of the friction forces and contamination of the powder. primary particles, a manual mixing of TiO2 (R1) . Controlling humidity related to each test, to avoid powders and the use of ultrasound for TiO2 (A) and capillary interactions. TiO2 (R2) was carried out in a flask. The average For most measured flow properties, the average of diameter of the three powders of TiO2 was calculated 10 successive measurements was recorded except for according to the diameter definition “surface- the test of shearing, where measurements were volume” or Sauter diameter: repeated three times. Table 1 shows the average flow measurements and the standard deviation representing
3 the average error of these measurements. Ndii (1) d=p Hausner’s Index Nd2 ii The Hausner index (HR) is defined as the ratio of bulk density of fine powders after prolonged where N is the number of particles in class i and d t i i tapping to aerated density . the average diameter of the particle in this class. ae The range of the particle size distribution was ρt quantified using the index of uniformity Cu HR= (3) (Schlosser, 1998) obtained from the cumulative ρae
Brazilian Journal of Chemical Engineering Vol. 25, No. 04, pp. 697 - 711, October - December, 2008 700 D. Turki and N. Fatah HR describes the powder flowability. The hinge of 0° to 180° from a fixed support (Figure 1). various flows can be classified as follows: After depositing a uniform particle layer 5 mm HR > 1.4 characterizes cohesive powders (non- thick, gradually we inclined the plate at a free flowing), HR < 1.2 indicates a free flowing practically constant velocity until no particle is on (non-cohesive powders) and 1.2 < HR < 1.4 shows the surface plate (or covered of a mono-layer of an intermediate behavior of the powders. This test particles that adhere to the wall). The slide angle is measures the reduction of the volume of packed bed the angle formed by the plate and the fixed support. of particles. This is carried out in a graduated The flow is known as free for < 30° and non-free cylinder of 100 ml. The initial volume of the for > 30°. particles is fixed at 40 ml. Finally, the cylinder is subjected to vertical tapping until no change in the Consolidation Test volume related to time is observed. The packed volume of the powders is recorded when that volume The consolidation test shows the aptitude that a remains constant with time. The tapping technique powder has to consolidate, i.e., to decrease the was achieved using two methods: manual (manual volume of the packed bed of powder under the effect tapping of the powder in a test-tube) and automatic of an increasing normal stress (). A known mass of with an ERWEKA SVM22 device. powder (M) is introduced into a graduated 5.3 cm diameter cylinder. The base of the cylinder is closed Angle of Repose Measurement by a porous plate to allow the evacuation of the air stored in the powder during consolidation. A twister The angle of repose () was measured by is introduced into the cylinder to homogenize the applying the flow procedure through a funnel. This surface of the powder. A glass piston is applied on measurement consists of passing a known mass of the powder and the variation of volume is measured powder through a funnel with a sieve of 1mm in according to the force (F) related to the cylinder aperture and 35 mm in diameter, the funnel is (Figure 2). The solid fraction (1- ) related to the submitted to a mechanical vibration to form a strain is noted as: uniform powder heap on a glass base of 40 mm in diameter. The funnel is fixed at a distance of 45 mm M from the base. The angle of repose is the constant 1-ε= (4) V angle formed by the base and the tangent to the heap ρPt formed by the powder. The flow is known as free M and V are the mass and the total volume of the flowing for < 40° and non-free for > 40°. t packed bed of particles, respectively. Angle of Slide Measurement F = (5) The device for measurement of the angle of slide S () is composed of a glass plate 40 mm in width, 145 mm in length and 5 mm thick revolving around a S is the cross-sectional area of the glass piston.
Figure 1: Device measurement of the angle of slide
Brazilian Journal of Chemical Engineering
Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 701
Figure 2 : Consolidation test
Annular Shearing Cell flow, the value of is noted and the second point (, ) is obtained. The whole procedure is repeated The annular shear cell (RST-XS) (Schulze, 1995) for three or four other points. The curve, called yield is an alternative version of Jenike’s cell (Jenike, locus (Figure 4), is obtained. This illustrates the limit 1954). The illustration follows the same procedure between two zones corresponding to the pressures and theory as Jenike’s cell (Jenike, 1954), where the applied: the zone in the lower part of the yield locus yield locus is obtained starting from at least four corresponds to an impossible flow of the powders characteristic points of rupture for a given and the zone above the yield locus curve represents consolidation state. With the annular shearing cell, a the collapse of the powder and flow. complete yield locus is usually measured with one From the yield locus two properties of flow can sample (in contrast to the Jenike shear tester where be obtained: only one point can be measured with one sample). . The cohesion C is the value of the ordinate at the This cell is automatic and less time consuming. origin (=0). This parameter gives the true cohesion The shearing test (annular cell) is composed of an between the particles apart from particle-particle annular channel, carefully filled with the powders. A friction. For C=0, the powder shows a free flow; for lid is placed on the annular channel and the unit is C > 0 the powder is said to have a non-free flow. then placed on a revolving plate. Then a piston is . The compressive resistance Fc is obtained from lowered on the lid. The lid has as the role of Mohr’s circle passing through the origin and tangent transmitting at the normal strain () and the shear to the yield locus. stress () simultaneously to the powder. Only the . The principal stress corresponds to the lower plate is in rotation and engages the annular maximum stress that the powder has undergone for channel (Figure 3). The upper part, i.e., the lid, is the first time. It is obtained from Mohr’s circle maintained fixed using two tie rods transmitting the passing through the point (sf,sf) and tangent to the shearing force to the sensors. The first stage consists yield locus. of shearing the powder until a stationary state From the values of 1 and Fc, the parameter corresponding to a plate marking the flow, then the FFc =1/Fc can be defined and this characterizes the cell returns to its initial state. In this case the critical flow property of the powders according to the following classification: point (stationary flow) is reached (sf,sf) in the coordinate system (, ) (Figure 4), i.e., the limiting . FFc < 2: very cohesive powder, non-free flow. point of flow. The second point in this same system . 2 < FFc < 4: cohesive powder, difficult flow. . 4 < FF < 10: intermediate flow. is obtained by applying and the powder is c sf . 10 < FF : non cohesive powder and free flow. sheared until rupture that corresponds to the start of c
Brazilian Journal of Chemical Engineering Vol. 25, No. 04, pp. 697 - 711, October - December, 2008 702 D. Turki and N. Fatah
Figure 3: Annular shearing cell (Schulze, 1995)
Figure 4: Determination of the yield locus
EXPERIMENTAL APPARATUS: the bed is measured using a pressure probe made up FLUIDIZATION COLUMN of a stainless steel tube of 1mm inner diameter, immersed in the column and placed just above the The tests of fluidization were carried out in a distributor. To avoid clogging the pressure probe by glass column of 103 mm inner diameter and 1500 fine powders, the end of this tube is protected by a mm height (Figure 5). Air was used as the fluidizing double steel sheet of 50 µm in aperture. The tube is gas; the flow was controlled by a set of rotameters. connected to a differential pressure sensor (Societé The diffusion of air through the bed of particles is Sedeme) where the second pressure probe corresponds ensured by using a porous stainless steel plate (gas to atmospheric pressure. The fluctuation of the distributor) placed at the base of the column. The recorded pressure drop (P) with time and velocity of filtering capacity of the porous plate is 98 % and the gas are achieved using a Sefram recorder. A 99.9 % to stop particles of 1.2 µm and 3.6 µm in cyclone is connected to the top of the column to collect size, respectively. The pressure drop (P) through the fine particles elutriated during fluidization.
Brazilian Journal of Chemical Engineering
Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 703
1. cylindrical fluidized bed 2. gas distributor 3. cyclone 4. collecting bottle 5. pressure probe 6. differential pressure sensor 7. recorder
Figure 5: Fluidization column
RESULTS AND DISCUSSION are given in Figure 6. The average sizes of the particles are dp=204 nm, dp=159 nm and dp=167 nm The studies of the cohesive powders (Fatah et al., for TiO2 (A), TiO2 (R1) and TiO2 (R2), respectively. 1998; Fatah and Sanchez, 2004) reveal the existence The Cu index is obtained from the cumulative of two categories of powders: micronic particles percentage curve and defined by equation (2). This (diameter of the particle varying between a value of parameter indicates a broad size distribution 500 nm and 50 µm) and nanometric particles corresponding to Cu= 3.6, Cu=3 and Cu= 3 for the (diameter of the particle less than 500 nm). The three TiO2 powders (TiO2 (A), TiO2 (R1) and TiO2 nanometric particles are more complex and show a (R2)), respectively. This large interval is due to the different behavior from the micronic particles under presence of agglomerates, as shown in Figure 6. For the action of the variation of the external forces. the three powders, a first mode towards 225 nm is Thus, this present work is concentrated on the study observed, that seems rather close to the average of the behavior of nanometric powders. diameter calculated. 3 The particle size distributions of the three TiO2 The particle density (ρp) is 3900 kg/m , 4200 3 3 powders were obtained according to an optimal kg/m and 4200 kg/m for TiO2 (A), TiO2 (R1) and procedure of dispersion in order to measure the size TiO2 (R2), respectively. The BET surface area seems of the primary particles and not that of agglomerates. to be identical for the three powders and is about 9 2 The particle size distributions of the TiO2 powders m /g.
Table 1: Flow property values and standard deviation of TiO2 powders
Powder Hausner index HR Angle of repose Angle of slide Standard deviation automatic manual α(°) β(°) HR αβ automatic manual TiO2 (A) 1.27 1.60 51.0 37.4 0.014 0.059 1.26 6.75 TiO2 (R1) 1.28 1.77 43.5 43.8 0.020 0.050 1.00 6.80 TiO2 (R2) 1.23 1.65 41.7 37.7 0.050 0.050 1.22 2.42 7 TiO2 (A) 6 Volume 5 TiO2 (R1) 4 TiO2 (R2) 3 2 1 0 0.01 0.1 1 10 100 1000 10000 Size of particle ( µm )
Figure 6: Size distribution of TiO2 (A), TiO2 (R1) and TiO2 (R2)
Brazilian Journal of Chemical Engineering Vol. 25, No. 04, pp. 697 - 711, October - December, 2008 704 D. Turki and N. Fatah
The study of TiO2 powder flows shows a free to higher values of , the transition zone is reached, intermediary flow under the action of low strength, corresponding to the load held by the solid structure; i.e., in the case of using the automatic tapping test then packing and rearrangement of the particles measurement (Hausner’s index, angle of repose and occurs. Beyond this zone, the load is spread out on angle of slide) (Figures 7, 8 and 9) and Table 1. The the solid; thus, there is consolidation of the packed values of HR seem to be identical and slightly higher bed of powder. Low solid fraction values (in the case than 1.2. It is the same for the angle of repose and of TiO2 (A)) show a very cohesive behavior of the the angle of slide, which are close to 41°-51° and powders. However, TiO2 (R1) powder seems to be 37°-43°, respectively. This behavior is related to the less cohesive than TiO2 (A) and TiO2 (R2) powders. initial structure of the nanometric powder in the In the same way, Figure 11 represents experimental packed bed that appears to be (visually) made up of results obtained from the annular shear cell, where stable agglomerates with different diameters and the FFc value characterizes the type of flow close to a spherical shape. This structure seems to (deformation of the powder’s packed bed) and C depend on the history of the packed bed (self- indicates cohesion between particles. For all agglomeration) and the process of micro- powders, the results indicate a non-free flow (FFc < 2 consolidation. This phenomenon is due to the great and C > 0). The TiO2 (A) and TiO2 (R2) powders intensity of the interparticle forces and to the very show higher degrees of cohesion than TiO2 (R1). short distance between primary particles. Such a These results are in perfect agreement with those structure generates a number of agglomerates with a obtained with the test of consolidation. However, large size distribution that can be classified in group they seem to be in contradiction with the results A, B or D of Geldart’s classification. Finally, this obtained when using the manual tapping test, due to powder system does not seem to evolve under the the fact that the stress applied with this test still action of forces with low intensities. remains low compared to the test of consolidation However the application of higher forces by and shearing. This phenomenon shows that the study manual tapping test, consolidation test and annular of nanometric powders should be carried out with shear cell, indicates a non-free flow (Figures 7, 10 care. Thus, it is sensible to link several tests. and 11). The values of HR are much higher than 1.4 In this work, the TiO2 powder structure loses its (results more coherent for this type of powders) and individualized character (formation of dispersed do not seem to evolve identically for powders when agglomerates) under the action of high values of using automatic tapping. It is more advisable to link external force. Thus, there is a rupture of this test with consolidation and shearing tests to agglomerates and the structure changes to a more categorize the powders Thus, it is noted that the compact powder system, identical to a dense bulk powders do not present the same degree of cohesion. that makes the handling of these powders very Figure 10 shows the variation of the solid fraction complex. The cohesive character of these powders is (1-ε) according to the normal strain () (test of detectable only under high external forces that consolidation). In the initial state, a high rate of overcome the effect of the internal forces between aeration is noted, indicating a solid fraction of about particles that form agglomerates. 15%, 18% and 19% for TiO2 (A), TiO2 (R1) and TiO2 Thus, to fluidize the TiO2 powders, an important (R2), respectively, and formation of porous energy must be applied not only to disintegrate the agglomerates with an internal porosity ξ. cohesive structure but also to set in suspension the Experimental error for the calculation of the solid agglomerates. Referring to these results the TiO2 fractions came from the estimation of the standard (R1) powder should be fluidized with a gas velocity deviation. Thus, values of 0.029, 0.0419 and 0.050 lower than the two other powders. are obtained for TiO2 (A), TiO2 (R1) and TiO2 (R2) The suspension of the TiO2 powders was carried powders, respectively. Then, for a low consolidation, out with air and at ambient temperature. The (1-ε) increases with , according to a slightly linear disintegration of the cohesive structure in the evolution. This corresponds to the diffusion of air in fluidized bed was carried out under high gas velocity the structure of the packed bed of particles. For (≈ 0.5m/s).
Brazilian Journal of Chemical Engineering
Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 705
2.2 55 HR automatic tapping Angle of repose (°) 2.0 manuel tapping 50 1.8
1.6 45
1.4 40 1.2
1.0 35 TiO2 (A) TiO2 (R1) TiO2 (R2) TiO2 (A) TiO2 (R1) TiO2 (R2)
Figure 7: HR evolution for the three TiO2 Figure 8: Evolution of the angle of repose powders: automatic and manual tapping for the three TiO2 powders
60 Angle of slide (°)
50
40
30 TiO2 (A) TiO2 (R1) TiO2 (R2)
Figure 9: Evolution of the angle of slide for the three TiO2 powders 0.40 (1-ε) TiO2 (R1) 0.35 TiO2 (R2) TiO2 (A) 0.30
0.25
0.20 σ 0.15 0 20000 40000 60000
Figure 10: Variation of the solid fraction according to the normal strain for the three TiO2 powders 3 16000 C (Pa) FFc FFc
2.5 C 12000
2 8000
1.5 4000
1 0 00.511.522.533.5 TiO2 (R1) TiO2 (R2) TiO2 (A)
Figure 11: Evolution of FFc (flow characteristic) and C (cohesion) for the three TiO2 powders
Brazilian Journal of Chemical Engineering Vol. 25, No. 04, pp. 697 - 711, October - December, 2008 706 D. Turki and N. Fatah
During the fluidization of Geldart’s group C the apparent minimum fluidization velocity (Umfa) of powders, the following phases often observed can be TiO2 (A). Values of 0.176 m/s, 0.11 m/s and 0.175 listed below: m/s for the TiO2 (A), TiO2 (R1) and TiO2 (R2) 1) For low gas velocity, the fluid crosses the powders are noted, respectively. The results are cohesive structure by creating a preferential passage compared with those of references to calculate the (channeling). The totality of the gas passes through a fluidization index defined as the ratio between U mfa channel, observed especially for beds that are not and the fluidization velocity calculated (U ) from deep enough (the static height of the bed of particles mfc the (Wen and Yu, 1966) correlation. lower or equal to the diameter of the column). For deep beds, the channeling is preceded by the 2 appearance of the phenomenon of slugging. This dg(ppgρ -ρ ) U= (6) same behavior was observed by (Pacek and Nienow, mfc 1650µ 1990). g 2) For higher gas velocity, the formation of cracks and channels at various orientations is observed and where g and g indicate the viscosity and the does not seem to be reproducible. density of the air, respectively. 3) A defluidization is noted in the bottom zone of However, it is important to note that the the bed but, beyond this, a pseudo-fluidization is minimum fluidization velocity (Umfc) is calculated from the physical properties of the primary particles: observed as if the various channels formed acted as 3 gas jets. On top of the jet there is formation of TiO2 (A) (dp=204 nm and p=3900 kg/m ), TiO2 (R1) 3 bubbles (behavior similar to a spouting bed) that (dp=159 nm and p=4200 kg/m ) and TiO2 (R2) 3 maintains this zone in fluidization. The bottom zone (dp=167 nm and p=4200 kg/m ). That is around 5.2 -8 -8 -8 of the bed seems to be reduced with increasing gas 10 m/s, 3.410 m/s and 3.7610 m/s for TiO2 velocity to form a structure made up of (A), TiO2 (R1) and TiO2 (R2), respectively. Finally, 6 agglomerates. the index of fluidization (Umfa/Umfc) is about 3.410 , 6 6 During fluidization of the three types of TiO2 3.210 and 4.610 for TiO2 (A), TiO2 (R1) and powders, only phase 2 and phase 3 were observed for TiO2 (R2), respectively. These results indicate that it gas velocities much higher than the necessary is necessary to inject a gas velocity about 4106 fluidization velocity of the primary particles. This times higher than the velocity (Umfc) necessary to high velocity disintegrates the cohesive structure and fluidize the primary particles for the three powders. eases the fluidization of agglomerates. In addition, the dynamic diameter of the For the TiO2 powders, the preferential passage of agglomerates, dpa, was estimated using equation (6) the gas through the bed of particles seems to be non- according to the minimum gas velocity of the existent; this is due to the initial structure of the TiO2 experimental fluidization or Umfa. Values of dpa=375 powder bed formed by individualized agglomerates µm, dpa=285 µm and dpa=360 µm were obtained, i.e., (self-agglomeration). Figure 12 illustrates all the 1838, 1792 and 2155 times larger than the diameter curves related to the variation of the pressure drop of the primary particles (dp) for the three powders (P) according to the gas velocity (U) for the three TiO2 (A), TiO2 (R1) and TiO2 (R2), respectively. powders (TiO2 (A), TiO2 (R1) and TiO2 (R2)). Supposing that the agglomerates thus formed are Fluidization of cohesive powder highlights the porous, this implies that the density of the suspension of the agglomerates at a very high gas agglomerate (a) is less than that (p) of the primary velocity (above the minimum velocity). Thus, the particles. A simple calculation of a (ap (1-ξ)) cohesive powders are arranged to form a new can be done by estimating the internal porosity () of structure of agglomerates (made up of primary the agglomerates (the mean value bed powder particles). The apparent minimum fluidization porosity between tapped and aerated treatment of the velocity (U ) has been determined approximately mfa bulk powder bed). Thus, values of 0.8, 0.75 and 0.76 from the third zone by the standardized method of were obtained for TiO2 (A), TiO2 (R1) and TiO2 Richardson (Richardson, 1971), that corresponds to (R2)), respectively. The corresponding agglomerate the intersection with the horizontal line (fluidization densities (a) for the three powder of TiO2 are 780 3 3 3 of agglomerates) and the relative curve of the bed kg/m , 1050 kg/m and 1029 kg/m for TiO2 (A), that exhibits the formation of cracks at different TiO2 (R1) and TiO2 (R2), respectively. Taking into orientations. The horizontal line and the relative account the dynamic diameter of the agglomerates curve are estimated with a regression analysis to fit (dpa) and the values of a, this hydrodynamic approximately the corresponding values. As an behavior for the three powders can be classified in example, Figure13 illustrates the determination of group B of Geldart’s classification.
Brazilian Journal of Chemical Engineering
Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 707
1600 P (Pa) 1200
800 ●TiO2 (A)
▲TiO2 (R1) 400 ■TiO2 (R2) U (m/s) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Figure 12: Pressure drop variation versus superficial gas velocity for the three TiO2 powders
1200 P=3219.7U+415.3
1000 P=982.5 800
TO (A) Powder 600 i 2 P(Pa) 400 U 200 mfa 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 U (m/s)
Figure 13: The determination of the apparent minimum fluidization velocity (Umfa) of TiO2 (A)
A model is developed to estimate the agglomerate depends on the Reynolds number (Re). Significant size in a fluidized bed, taking into account the various research has been done on flow past fixed and forces that control the formation of agglomerates in fluidized beds and it is possible to calculate drag this bed of Geldart’s group C powders, and assuming forces over agglomerates in the bulk of a uniform that cohesiveness is principally due to van der Waals suspension of agglomerates with reasonable forces rather than the other interaction forces accuracy. The corresponding drag force according to (capillary and electrostatic forces). (Khan and Richardson, 1990) is given by: The forces acting on an agglomerate in a fluidized bed are determined by the force balance F =0.055πρ dU22-4.8ε (8) (Zhou and Li, 1999): ygaf
Drag force(Fy)+Collision force(Fco) = Gravitational - where (da) is the agglomerate diameter and ε is the Buoyancy force(F )+Cohesive force (F ). f g va fluidized bed voidage. The drag force exerted by a fluid with density The collision force between two agglomerates ‘1’
ρg and a superficial gas velocity (U) flowing past an and ‘2’ vertically aligned in a fluidized bed that collide isolated agglomerate of diameter (d ) is given by: inelastically with a relative velocity (q) is according to a (Timoshenko and Goodier, 1970), given by:
1 2 F=ydg C zρ U (7) 3 2 2 F=ncoα d (9) π.d2 where z= a is the projected area of the sphere 4 where αd is the displacement of the maximum and Cd is the drag coefficient; this coefficient compression and is given by:
Brazilian Journal of Chemical Engineering Vol. 25, No. 04, pp. 697 - 711, October - December, 2008 708 D. Turki and N. Fatah
0.4 2 630.2 5q π q ρa 2 αd = (10) Fco =0.1662 d a (15) 4 n n1 k
The difference in gravitational and buoyancy forces The parameters n and n1 are expressed by: acting on one agglomerate can be expressed by:
8 dda1 a2 n= (11) π 3 2 F= - dg (16) 2 d+d gagaρ ρ 9 π k+k12 a1 a2 6 and The cohesive force is controlled mainly by the van der Waals force, given by (Derjaguin, 1934) as:
m+m12 n=1 (11a) A dd m m a1 a2 12 F=va 2 (17) 12δ d+da1 a2 where m1 and m2 are the masses and da1 and da2 are the diameters of agglomerates ‘1’ and ‘2’ where δ is the distance between the agglomerates’ respectively, k is a function of Poisson’s ratio and surfaces and A is the Hamaker constant. According Young’s modulus. Since the two agglomerates are to (Israelachvili, 1985), this constant can be assumed to have the same properties, then m1=m2=m evaluated when the medium is a vacuum from: and k1=k2=k and therefore: 2 2 2 0.4 3 ε -1 3 h ν N-11 22 3 3 A= B T 1 + c (18) 5q π k ρaa1a2d d d+d a1a2 2 1.5 α = (12) 4 ε1 +1 16 2 N+1 d 33 1 8(da1 +d a2 ) 2 d a1 d a2 where h is Plank’s constant, B is Boltzmann’s where a is the density of agglomerate estimated by constant, T is the absolute temperature, N is the measuring the internal porosity of the agglomerate 1 index of refraction of the particles and is the UV (mean value powder bed porosity between tapped νc and aerated powder). The factor k is given by adsorption frequency. (Timoshenko and Goodier, 1970). Taking da1=da2 =da and substituting these equations into the force balance equation we have: 1-υ2 k= (13) 0.2 63 π E 22-4.8π q ρa ρag-ρ g d a - 0.33ρ g U ε f+0.3172 d+ a k2 where is the Poisson’s ratio and E is the Young’s (19) modulus. A =0 Substituting equations (12) and (11) into equation 2 (9) we obtain: 4 πδ
3 It has been observed that the significant 2 parameters that disturb the solution of equation (19) F=nco α d =0.2516 are: the density of the agglomerates and the fluid, the (14) relative collision velocity and the distance between 3 0.2 the agglomerate surfaces. The solution of equation 63 3 3 π q ρadd a1a2 2 dd a1a2 (19) depends on the exact estimation of the 233 kd+dd+da1 a2 a1 a2 parameters, so some parameters have been experimentally obtained from different powders of
TiO2: ε (fluidized bed porosities), a (densities of If d=d=d then f a1 a2 a agglomerates), U (superficial gas velocities, as explained above). For TiO2 powders, the parameters:
Brazilian Journal of Chemical Engineering
Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 709 properties of the powders is an interesting way of N1, 1, νc , B and h are obtained from (Perry and Green, 1984; Israelachvili, 1985), where h is Plank’s describing the hydrodynamic behavior of these very constant h=6.626×10-34 J.s and B Boltzmann’s cohesive powders. constant B=1.381×10-23J/K. The index of refraction This work constitutes a fundamental step in comprehending the behavior of cohesive powders in (N ) and the dielectric constant ( ) of TiO particles 1 1 2 a fixed or fluidized bed. Indeed, these effects present are 2.493 and 40-60, respectively. The UV a challenge due to the complexity of the microscopic adsorption frequency is =3×1015 s-1. With an νc processes such as the formation of agglomerates and absolute ambient temperature, the Hamaker (A) the trajectory of gas within the solid structure. constant calculated from equation (18) is The flow properties of the powders could not be A=3.97×10-19 J. The distance between agglomerate predicted by only one indicator or inherent parameter surfaces ( δ ) is taken as 4×10-10 m (Krupp, 1967). describing the powders properties. The parameter k calculated with Poisson’s ratio and The connections of two or several flow tests are Young’s modulus is k=3.0×10-06 Pa-1 (Krupp, 1967). enough to predict the flow of powders: free flow,
For an estimated porosity = aerated ( = aerated = 1- non-free flow or intermediate flow. However, in ρae / ρp) of 0.85, 0.82 and 0.81 and an experimental some categories of powders such as TiO2 superficial gas velocity (U) of 0.5, 0.21 and 0.39 m/s (nanometric powder) it is suitable to link all tests for for TiO2 (A), TiO2 (R1) and TiO2 (R2), respectively, different requests. Indeed, the cohesive character is the corresponding velocities (q) (Horio and Iwadate, established only under high external pressures. The 1996) are 0.24 m/s, 0.188 m/s, and 0.218 m/s, distinction between the behavior of micronic and respectively. nanometric powders is an interesting area that needs A successive approximation method was applied to to be further investigated. solve equation (19). Diameters of da=310 m, da=352 m and da=298 m were found for the three different NOMENCLATURE powders (TiO2 (A), TiO2 (R1) and TiO2 (R2)), respectively. The numerical prediction of the A Hamaker constant J agglomerate size (da) is a factor of 1520, 2213 and 2 1784 higher than the diameter of the primary particles C Cohesion of powder N/m (d ) for the three powders TiO (A), TiO (R1) and Cd Drag coefficient (-) p 2 2 C Index of uniformity (-) TiO (R2), respectively. These results are in accord u 2 B Boltzmann’s constant J/K with the agglomerates diameters (d ) estimated from pa d Average diameter in class i m equation (6), with a variation of 17 to 20%. i dp Mean particule diameter m dpa Dynamic diameter of m agglomerate ( calculated by CONCLUSION equation 6) da Calculated particle diameter m The disintegration of the cohesive structure in a of agglomerate (numerical fluidized bed was performed under a high gas 6 approach) velocity up to 4×10 times the velocity necessary for E Young’s modulus Pa fluidizing the primary particles. F Force N In the fluidized state, the experiments show that 2 Fc Compressive resistance N/m the exchange is carried out particularly between gas Fco Collision forces N and the agglomerates formed from primary particles FFc Parameter to characterize (-) of different size and shape. There is a close the flow properties correlation between the hydrodynamics and the local Fg Gravitational force N structure, controlled primarily by the van der Waals Fva Cohesive force N forces. The fluidized bed of agglomerates constitutes Fy Drag force N a new structure characterized by new physical g Gravitational acceleration m.s-2 properties of the agglomerates (a, ξ, da). Indeed, this HR Hausner’s index (-) new hydrodynamic behavior can be classified in h Planck’s constant J.s group B of Geldart’s classification. K Function of Poisson’s ratio Pa-1 The integration of the flowability and the physical and Young’s modulus
Brazilian Journal of Chemical Engineering Vol. 25, No. 04, pp. 697 - 711, October - December, 2008 710 D. Turki and N. Fatah
M Mass of the packed bed of kg σsf Normal stress (stationary Pa particles flow) mi Mass of agglomerate i (i = 1, kg σ1 Principal stress Pa 2) Shear stress Pa n Function defined by (-) sf Shear stress (stationary Pa equation 11 flow) -1 n1 Function defined by (-) c UV absorption frequency s equation 11a ξ Internal porosity (-) Ni Number of particles in class (-) Poisson’s ratio (-) i N1 Index of refraction of (-) particles REFERENCES P Total pressure drop in Pa fluidized bed Chirone, R., Massimilla, L. and S. Russo, Bubble- q Relative velocity of m/s free fluidization of cohesive powder in an agglomerate acoustic field, Chemical Engineering Science 48, S Cross-sectional area of the m2 p. 41-51 (1993). glass piston Derjaguin, B., Untersuchungen über die Reibung und 2 Ss Specific surface area m /g Adhäsion. Kolloid. Zeits., 69, p. 155 (1934). T Temperature K Fatah, N. and Cavrois, V., Measurement of U Superficial gas velocity m/s fluidization properties of fine particles and Umfa Minimum apparent m/s interaction with rheological parameters. fluidization velocity Fluidisation IX, Engineering Foundation, Ed., Umfc Minimum fluidization m/s Fan, L.S. and Knowlton, T., p. 277- 284, New velocity calculated by York (1998). equation (6) Fatah, N., Pietrzyk, S. and Cavrois, V., Mesures de 3 Vt Total volume of the packed m paramètres rhéologiques des poudres cohésives, bed of particles 2ème Colloque Science et Technologie des z Projected area of a sphere m2 Poudres, 3-5 mars Lyon, p. 283-290 (1998). Fatah, N., Sanchez-Calvo, L., Effet de la pression Greek Letters acoustique sur la fluidisation des poudres cohèsives, 4ème colloque, Science et Technologie Angle of repose (°) des Poudres, Récent progrès en Génie des d Maximum compression m Procédés 91 (2004). displacement Geldart, D., Types of gas fluidisation, Powder Angle of slide (°) Technology 7, p. 285-292 (1973). Distance between m Horio, M. and Iwadate, Y., The prediction of sizes of agglomerates or particles agglomerates formed in Fluidized beds, Proc. of Bed voidage (-) the 5th World Congress of Chem. Engineering, 2nd 1 Dielectric constant of Intl. Particle Technology Forum V, p. 571 (1996). particles Israelachvili, J. N., Intermolecular and Surface
aerated Aerated porosity of the bed (-) forces, Academic press, London (1985). of particles Jenike, A.W., Better design for bulk handling, Chem. εf Fluidized bed voidage (-) Eng 175 (1954). -1 -1 g Gas viscosity kg.m .s Khan, A. R. and Richardson, J. F., Pressure gradient -3 a Agglomerate density kg.m and friction factor for sedimentation and -3 fluidisation of uniform spheres in liquids, Chem. ae Aerated powder bed density kg.m -3 Eng. Sci. 45 (1), p. 255 (1990). g Gas density kg.m -3 Krupp, H., Particle adhesion. Theory and p Particle density kg.m -3 experiment, Adv. Coll. Interf. Sci., 1, p. 111-239 Tapped density kg.m t (1967). σ Normal stress Pa
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Behavior and Fluidization of the Cohesive Powders: Agglomerates Sizes Approach 711 Leu, L. and Huang, C. T, Fluidization of cohesive particles, Powder Technology 82, p. 219-230 powders in a sound waves vibrated fluidized bed, (1995). AIChE Sym. Ser. 90, p. 124-141 (1994). Schlosser, F., Eléments de mécanique des sols, Lifshitz, E. M., The theory of molecular attractive Presses de l’école National des Ponts et forces between solids, Soviet Phys. JETP (Engl. Chaussées 26 (1988). Transl.) 2, p. 73-83 (1956). Schulze, D., Appropriate devices for the measurement Nezzal, A., Etude de la fluidisation agitée des of flow properties for silo design and quality poudres fines, Thèse UTC (1996). control, 3rd Euro. Symp. Storage and flow of Pacek, W. and Nienow, A. W., Fluidization of fine particulate solids, PARTEC, Nuremberg/ and very dense hardmetal powders, Powder Germany 21-23, p. 45-56 (1995). Technology 60, p. 145-158 (1990). Timoshenko, S. P. and Goodier, J. N., Theory of Perry, R. H. and Green, D., Perry’s Chemical elasticity Mc Graw-Hill (1970). Engineers’ Handbook 6th ed. McGraw Hill Wen, C. Y. and Yu, Y. H., A generalized method for (1984). predicting the minimum fluidization velocity. Richardson, J. F. Incipient Fluidization and A.I.Ch.E.Journal. 12, p. 610 (1966). Particulate Systems. In: Davidson, J. F. and Wen, C. Y. and Yu, Y. H., Mechanics of Harrison, D., Eds., Academic Press London fluidization., Chem. Prog. Symp. Ser. 62, p. 100- (1971). 111 (1966). Russo, P., Chirone, R., Massimilla, L. and Russo, S., Zhou, T. and Li, H., Estimation of agglomerate size The influence of the frequency of acoustic waves for cohesive particles during fluidization, Powder on sound assisted fluidization of beds of fine Technology 101, p. 57-62 (1999).
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