Nanofluidization electrostatics

Nanofluidization electrostatics J. M. Valverde,1M. A. S. Quintanilla,1M. J. Espin,1,2 and A. Castellanos1 1Faculty of Physics, University of Seville, Avenida Reina Mercedes s/n, 41012 Seville, Spain 2Department of Applied Physics II. EUAT.University of Seville, Avenida Reina Mercedes 4A, 41012 Seville, Spain 共Received 21 December 2007; published 12 March 2008兲 Electrostatic charging of powders is a relevant phenomenon for a number of industrial applications. The design of new processes and the use of high resistivity materials and ultrafine powders may lead to higher charging rates and to higher levels of charge accumulation that can become a serious problem. In this work we investigate experimentally electrostatic charging in nanofluidization. The behavior of a fluidized bed of silica nanoparticles under the influence of an electrostatic field is studied. The electric field is applied in the horizontal direction and perpendicular to the gas flow. On one hand, we observe the influence of the electric field on the bulk behavior of the fluidized bed, which suffers a collapse when the electric field is turned on. For strong electric fields the stationary state of the fluidized bed reminds one of that of a spouted bed, with a solid layer adhered to the wall and a low density core region of local high gas velocity. On the other hand, and in order to gain additional insight, we look at the trajectories of nanoparticle agglomerates as affected by the electric field. This images analysis reveals that these agglomerates are horizontally deflected towards the wall as a consequence of being charged. From the analysis of agglomerate trajectories the charge per agglomerate is estimated. Using these measurements the electrostatic forces between agglomerates are calculated and compared to van der Waals attractive forces. DOI: 10.1103/PhysRevE.77.031301 PACS number共s兲: 45.70.⫺n, 47.55.Lm, 41.20.Cv I. INTRODUCTION Flowing powders can be quite electrostatically active. During the handling of powders, electrostatic charging usually occurs and it is attributed to the processes of contact and triboelectric charging 关1–4兴. Electrostatic energy stored in large quantities of powders can be large enough to cause sparks to be able to ignite the material. Reports of the occurrence of major dust explosions due to electric sparks and static discharges date back to the 18th century 关3兴. A particularly hazardous process is the pneumatic transport of powder in which, even though the powder is dispersed in air, high charge levels are often generated that give rise to static discharges when the powder settles 关3,4兴. Other nuisance situations related to electrostatics are sticking of powders to containers or the collection of dust by fabrics 关1兴. Electrostatic charge may also affect powder handling operations due to enhanced interparticle attractive forces 关4兴. The opposite problem of particle repulsion also exists, leading to difficulties in powder delivery 关4兴. However, electrostatic forces in powders can be effectively used as well in many industrial applications such as xerographic printers 关5兴, pollution control 关6兴, electrostatic separators 关7,8兴and coating in fluidized beds 关7兴to name a few. The physics of these processes is not completely understood and depends upon many parameters, which are often uncontrolled in industrial situations 关4兴. Recently, the development of new industry processes demanding high charge and specific surface levels has created an interest in the production and charging of nanometric particles with extremely high surface-charge density 关9兴. Fluidization of nanoparticles, providing extremely high fluid-solid contact and reaction efficiency, has become one of the most promising techniques for emerging industrial applications. Fluidization is accomplished by passing gas uniformly through the powder by a porous supporting plate. At a certain gas flow the drag balances the powder weight per unit area and the powder becomes fluidized. Recent reports of uniform fluidization of moderate density nanoparticles 关10–20兴have coined the word “nanofluidization” to denote this type of fluidization of nanometric particles also known as ultrafine particles. Even in the case of some nanoparticles 关11兴full suppression of bubbling has been observed, i.e., the fluidized bed transits directly from the uniform fluidlike regime to elutriation of the nanoparticles at high gas velocities 关14兴. The suppression of gas bubbles in fluidized beds of nanoparticles for gas velocities well above the minimum fluidization velocity is related to the existence of porous light agglomerates. Many works have dealt with the problem of estimating the size of nanoparticle agglomerates 共see Ref. 关21兴for a review兲. Noninvasive laser-based planar imaging has been developed in recent years. In this technique in situ images of the fluidized agglomerates are obtained with the aid of a laser source focused on the fluidized bed surface 关10–12,14,16,18,19兴. Photographs of agglomerates in the splash zone of the fluidized bed show an average size of the order of hundreds of microns and a broad size distribution. Wang et al. 关13兴have recently used particle image velocimetry analysis and laser-based planar imaging to measure the terminal settling velocity and size of single agglomerates. By relating both measurements they have obtained that most of the agglomerates have a fractal dimension close to Da =lnNa/ln ka=2.5, suggesting a predominance of the diffusion limit agglomeration 共DLA兲type. Here Nais the average number of primary nanoparticles in an agglomerate and kais the average ratio of agglomerate size d** to primary nanoparticle size dp. While there is a general consensus on the size of nanoparticle agglomerates in fluidization 关21兴, the research on nanoparticle charging in fluidized beds is still scarce. Kashyap et al. 关22兴have investigated the effect of a horizontal electric field on a bed of 10 nm silica nanoparticles uni- PHYSICAL REVIEW E 77, 031301 共2008兲 1539-3755/2008/77共3兲/031301共10兲©2008 The American Physical Society031301-1 formly fluidized by air. A main observation reported in this recent work is that the electric field markedly hindered bed expansion. The authors explain the experimental results as due to the addition of a vertical electrical force to the gravity force. By inclusion of this electrostatic force ad hoc in a one-dimensional momentum balance equation, their model further predicted a decrease of the agglomerate size and granular temperature of the nanoparticles as the strength of the electric field is increased. In the present work we report similar experimental observations on the bulk behavior of the fluidized bed as affected by the application of a horizontal electrostatic field. Our relevant contribution consists of the direct visualization of the dynamics of fluidized agglomerates by using high speed video analysis. These experiments allow us to provide a clear explanation to the observed decrease of bed expansion upon application of the electric field. Moreover, these measurements enable us to report an estimation of agglomerate charge, which might be valuable information in order to predict possible hazards in potential applications. In the following subsections we give a brief review on the fundamentals of particle charging in powders. Section III is devoted to a description of the experimental setup. In Sec. IV the experimental results are presented and discussed. Finally, we outline the conclusions of this work in Sec. V. A. Measurements of particle charge in fine powders The electric force acting on a suspended particle of net charge Qis given by F=QE+共p·ⵜ兲E,共1兲 where Qis the net charge on the particle, pis the dipole moment of the particle, and Eis the electric field vector. If the net charge of the particle is close to zero the right-hand side of Eq. 共1兲, known as the dielectrophoretic force, will dominate. In general, dielectrophoresis is an effect requiring quite divergent fields and usually requires sizable differences in the permittivities of the particle and the surrounding medium 关23兴. For charged particles in an electrostatic field the direct attraction of the electric field for a charge 共electrophoretic force兲is dominant, even when relatively small charges are present. The first experiment to measure the charge of blown fine powder particles had occurred to Sachsse in 1932 关24兴by using the Millikan oil drop method. Sachsse obtained that particles acquired charges ranging from 10−17 to 10−15 C, depending on the type of material and method of dust generation. In 1950 Kunkel and Hansen 关25兴described an improved device, inspired in the Hopper and Laby modification of the oil drop experiment, to measure the size and charge of blown powder particles. The horizontal deflection of particles as they settle under the influence of gravity in a horizontal electric field was recorded photographically by dark field illumination periodically interrupted by a rotating shutter. Then, the size and charge of the particles were derived by the application of Stokes’ law. Results from this experiment were presented by Kunkel in a separate paper 关26兴. Particles of diverse materials in sizes ranging from 0.5 to 30 ␮ m were analyzed. The charges measured varied from 0 to 10−14 C depending on the type of material and on the dispersion process employed. Generally, it was observed that all dusts contained charged particles. These included electroneutral homogeneous dusts gently dispersed and with no impact on solid surfaces, for which the charges of opposite sign measured were about the same. Current instruments for measuring the charge of powder particles from measurements of electrical mobility distributions are based on those pioneer works 关27–29兴. In electrostatic elutriators and spectrometers the aerosol flows through a flat channel in which a transversal electric field is applied and particles are removed by deposition onto the wall due to electrophoretic forces. Other methods consist of measuring the electrical potential or current due to collected charged particles by some devices 关27兴. For example, the electrical current in a Faraday cage induced by the charged particles has served to measure the charge of aerosol particles 关29兴. Measurements of the potential of a capacitor connected between ground and a metal filter holder in which the charged blown powder is accumulated have shown that powders such as starch or Cabosil©may have up to 10−3 C of charge per kilogram of powder 关1兴. The charging tendency of dielectric powders measured in industrial operations show little dependence on the materials themselves but are rather dependent on the type of operations and the specific surface area of the powders 关3兴. For instance, it has been observed that sieving can charge the powder in a range between 10−11 C/kg and 10−9 C/kg, and pouring in the range 10−9–10−7 C/kg. On the other hand, operations involving high energy input such as micronizing or pneumatic transfer create charge levels in the range 10−7–10−4 C/kg 关2–4兴. In general, the greater the energy of operation and specific surface area of the powder the greater is the measured charging 关2,3兴. Experimental values for the charge-to-mass ratio Qmr of many powders of different specific Ssurface area obtained using laboratory scale pneumatic transport devices are reviewed in Ref. 关3兴. It is shown that the rate of increase of Qmr with Sis more or less linear 共Qmr⬃10−7 S, where Qmr is expressed in C/kg and Sis in the range between 1 m2/kg and 103m2/kg兲关3兴. The maximum surface charge that can be attained by a particle usually depends on the breakdown field strength Emax of air. For a charged flat surface in air, the expected breakdown threshold is Emax⬃3⫻106V/m, which corresponds to a surface charge density ␴ ⬃ ⑀ 0Emax ⯝26.5 ␮ C/m2关4,8兴. In the case of a curved surface, and due to the high nonuniformity of the electric field near the surface, higher fields can be sustained. An empirical formula for the maximum field that can be supported in terms of the particle diameter dpof a spherical particle is Emax ⬃106/dp 0.3 V/m共dpin meters兲, which gives a maximum charge per particle Qmax⬃3⫻10−5dp 1.7 C and a charge-to- mass ratio Qmr⬃6⫻10−5/共 ␳ pdp 1.3兲C/kg 关4兴. For example, for 50- ␮ m-sized particles it is obtained Qmax⬃10−12 C and Qmr⬃0.02 C/kg 共using ␳ p=2500 kg/m3兲. It is, however, uncertain whether this equation might apply to smaller particles that are usually aggregated due to the predominance of interparticle attractive forces over particle weight 关30兴. VALVERDE et al. PHYSICAL REVIEW E 77, 031301 共2008兲 031301-2 B. Mechanism of particle charging in fine powders Why powders charge has been the subject of considerable research, yet truly quantitative and repeatable results are difficult to obtain 关1,27兴. Commonly, the mechanism of charging is regarded as a result of collisions between particles and possibly friction of very short duration 共triboelectric charging兲. However, most investigations suggest that the main cause for the charge buildup on powders during industrial handling and processing is contact charging 关3兴. According to this mechanism, the main charge separation occurs at the first mechanical separation of the particles due to the dissimilarity between the work functions of the materials at contact. Generally, electrification is governed by the physics of the contact between the surfaces separated. Nevertheless, shearing forces during friction may change the work functions of the materials, which might affect the charging tendency 关3兴. In his pioneer work Kunkel 关26兴had already suggested that powder charging should occur at mechanical separation of contacting surfaces at the moment of dispersion. Contact charging would explain why the dust cloud was electroneutral as a whole, but with almost all the particles being charged. Kunkel 关26兴pointed out that transfers of electrons on particle separation were easily possible due to imperfections at the contact area. He proposed a theory of random charge transfer by which particle charge was predicted to increase with particle diameter as measured experimentally 关26兴. Loeb 关31兴claimed in accordance that, in most cases, charge transfer required only intimate contact, while for two identical surfaces the frictional charging effect was rare. Currently, it is generally accepted that charges are exchanged whenever any two surfaces come into contact with each other even for cases where the bulk materials are the same due to surface impurities and imperfections 关32兴. If contact is broken, a net charge may subsequently exist on each of the surfaces. Yet, the electrification at interfaces and the charges remaining after the surfaces in contact are separated are completely unpredictable due to the effect of numerous uncontrolled parameters such as surface imperfections and contaminants, ambient humidity, nature of the contact, speed of separation, charge carrier species, and charge back flow across the interface 关3,32,33兴. In general, the work functions are not well defined for most materials, particularly for those which are amorphous 关34兴. II. ROLE OF PARTICLE CHARGING ON POWDER FLOWABILITY In situations in which particles carry a substantial charge level, electrostatic interactions could play a role on the rheological behavior of powders 关35,36兴. Theoretically, the electrostatic force between two charged dielectric spheres of size dpin contact, carrying charges Q1and Q2and immersed in a dielectric surrounding medium of permittivity ⑀ m, can be written in the form 关35兴 fe=Q2 2 4 ␲ ⑀ mdp 2 再 ␣ 冋 冉 Q1 Q2 冊 2 +1 册 − ␤ Q1 Q2 冎 .共2兲 In our case the ambient fluid is a gas, thus ⑀ m⯝ ⑀ 0. The first term on the right side of Eq. 共2兲represents the attraction from the image charge of Q1induced in the sphere 2. The second term describes the net dielectrophoretic force on the sphere 1 induced by the nonhomogeneous electric field due to the charge on sphere 2. The third term is due to the Coulomb force between both spheres. Feng 关35兴has used the Galerkin finite-element method to investigate the dependence of the coefficients ␣ and ␤ on the permittivity ⑀ of the spheres. For instance, one would obtain ␣ ⯝0.25 and ␤ ⯝1.3 for ⑀ =3.8 ⑀ 0, corresponding to amorphous silica 关37兴. Thus, for 50 ␮ m silica spheres charged to the levels measured in pneumatic transfer 共Qmr⬃10−4 C/kg, Q⬃1.6 ⫻10−14 C兲关2兴, the electrostatic force is fe⯝1.7 nN 共attractive兲for charges of different sign and fe⬃−0.8 nN 共repulsive兲for charges of equal sign. These values are comparable to particle weight wp⬃1.6 nN 共using ␳ p=2500 kg/m3兲. It must be noted that the above calculations are made for ideally spherical particles. Hays 关38兴has pointed out that the electrostatic adhesion force for irregularly shaped particles can be larger than that calculated from Eq. 共2兲due to nonuniform charge distribution, albeit quantitative predictions are difficult due to the unpredictability of the charged areas really in contact. According to Hays 关38兴, the electrostatic adhesion between an irregularly shaped particle and a flat conducting substrate can be approximated by fH=Qf ␴ 2 ⑀ 0 ,共3兲 where ␴ =Q/Atis the surface-charge density, Atis the total area of the charge patches of the particle, and f=Ac/Atis the ratio of the sum of the charged areas in contact with the conducting surface Acto At. In the cascade development process, widely used in commercial systems for copying documents 关34兴,⬃10 ␮ m toner particles are charged when mixed with ⬃500 ␮ m carrier particles of different material. Measurements on standard carrier-toner combinations give a particle charge between 10−12 and 10−14 C for carrier beads, and between 10−14 and 10−16 C for toner particles 关34,38兴.Inorder to illustrate his theory, Hays 关38兴used as typical values for tribo-charged xerographic toner particles f=0.2, Q =10−14 C, and ␴ =10−3 C/m2, and estimated an electrostatic force of adhesion fH=100 nN, which is one order of magnitude higher than that expected for perfectly spherical particles. Besides the electrostatic force we must consider the ubiquitous van der Waals attractive force produced by the interaction of fluctuating molecular dipole fields 关39兴. Assuming that retardation effects are negligible and that the interaction between molecules is pairwise, Hamaker 关40兴summed up all these interactions between two spherical and rigid particles at contact. The van der Waals attractive force between two spherical particles of same size dpat contact could be approximated by fvdW ⯝Adp 24z0 2,共4兲 where Ais the Hamaker constant 共for most solids A ⯝10−19 J关41兴兲, and z0⯝3–4 Å is the minimum intermolecular distance 关42兴. Because of the short range of the mo- NANOFLUIDIZATION ELECTROSTATICS PHYSICAL REVIEW E 77, 031301 共2008兲 031301-3 lecular interaction, the van der Waals force is actually determined by the local radius of curvature of the surface asperities at contact. Therefore, for micrometric and larger particles, the typical size of the surface asperities damust be used in Eq. 共4兲instead of the particle diameters. A typical value reported for the size of surface asperities of powder particles is da⯝0.2 ␮ m关42–45兴. Thus, we can estimate fvdW⬃10 nN 共attractive兲, independently of particle size. Figure 1serves as an illustration of the relative importance of electrostatic and van der Waals forces on powder flowability depending on particle size. In this figure the ratios fe/wpand fvdW/wpare plotted as a function of particle size dp. The ratio of interparticle force to particle weight is usually defined as the granular Bond number 共Bo兲and is a measure of powder cohesiveness. For Boⱗ1 the material shows a free-flowing behavior whereas for Boⲏ1 the particles have a tendency to aggregate that inhibits powder flow 关46兴. In the calculations we have used typical values for silica 共 ⑀ =3.8 ⑀ 0, ␣ ⯝0.25, ␤ ⯝1.3, ␳ p=2500 kg/m3兲. Figure 1共a兲shows that the electrostatic force estimated from the charge level typically measured in a low energy process such as pouring 共Qmr⬃10−7 C/kg兲does not play a role practically in the whole range of particle sizes. On the other hand, it is seen in Fig. 1共b兲that, if we use the charge level typically measured in a high energy process such as pneumatic transfer 共Qmr⬃10−4 C/kg兲, the hindrance of granular flow due to the attractive electrostatic force can be relevant for dp ⲏ200 ␮ m. Thus, high charge levels of coarse grains could indeed inhibit the flow of otherwise free-flowing materials. If we assume, according to Hays 关38兴, that the irregular morphology of the particle surface produces an increase of one order of magnitude of the electrostatic force over the entire range of particle sizes, the relevance of this force on flow hindrance would be shifted to smaller sizes. By inspection of Fig. 1it can be estimated that, in the case of high charge levels, the electrostatic force would become significant for dpⲏ50 ␮ m for silica particles. In any case, it is clear from these figures that the van der Waals force is the dominant interaction between blown fine powder particles. III. EXPERIMENTAL SETUP AND PROCEDURE The fluidized bed setup used in the present work consists of a vertical 2.54 cm internal diameter polycarbonate vessel, 16.2 cm in height, which is fitted at the bottom with a sintered stainless steel plate having a pore size of 5 ␮ m that acts as gas distributor. The fluidization cell is fixed with a teflon holder and is placed between two parallel square electrodes of 14 cm of side length. The typical distance between the electrodes is d=7.6 cm. One of the electrodes is grounded and high voltage V共up to 30 KV兲is applied to the opposite electrode using a high voltage dc supply 共Spellman model HRH 40PN120/OVP/FG with a range of 0–40 KV兲. Ideally, the electric field strength is pretended to be uniform within the fluidized bed. However, and due to the presence of the metallic gas distributor, the electric field could be distorted near the base of the cell. Other possible sources of field heterogeneity are the finite size of the electrodes and the presence of the dielectric walls of the fluidization cell. To evaluate the spatial extension of these perturbations we have carried out 2D and 3D FEM calculations of the electric field between the electrodes using the software CONSOL. The electric field and equipotential lines calculated showed that these perturbations are not significant within the bed. According to these calculations the electric field strength within the bed can be taken as approximately constant 共E⯝V/d兲. The material used in the experiments was silica Aerosil©R974 from Degussa Company 共particle size 12 nm, particle density 2250 kg/cm3兲. The powder was presieved 共using a sieve opening of 500 ␮ m兲in order to remove previously existing very large agglomerates. In order to correct for elutriation, the presieved powder was weighed before and after each fluidization run. The mass of the sample to be fluidized mwas in the range between 0.20 and 0.45 g. Previous reports 关10–12,14兴show that when subjected to a gas flow, silica nanopowder exhibits agglomerate particulate fluidization 共APF兲behavior, characterized by a large bed expansion and apparent smooth fluidization. Typical values of agglomerate size for this powder in the fluidized bed measured by several authors using noninvasive techniques are of the order of hundreds of microns 共see Ref. 关21兴for a review兲. FIG. 1. Ratio of interparticle attractive force to particle weight as a function of particle size. As indicated interparticle forces are calculated according to the van der Waals interaction 共solid lines兲 and electrostatic interaction 共dashed lines兲. Results are shown for silicon dioxide 共 ⑀ =3.8 ⑀ 0, ␣ ⯝0.25, ␤ ⯝1.3, ␳ p=2500 kg/m3兲.In共a兲 the electrostatic force is calculated from the typical charge-to-mass ratio measured in pouring processes. In 共b兲the electrostatic force is calculated from the typical charge-to-mass ratio measured in pneumatic transfer processes. Only the attractive electrostatic force is calculated. There will be also a repulsive electrostatic force of the same order of magnitude between charges of the same sign. VALVERDE et al. PHYSICAL REVIEW E 77, 031301 共2008兲 031301-4 In the present work we have concentrated on the effect of application of an electric field on the expansion of the uniformly fluidized bed. Once the sample was presieved, weighed, and placed in the cell, it was initialized by applying a sufficiently high gas flow. The bed height was measured when it reached a stationary state, starting from a gas flow rate of 1000 cm3/min, and subsequently decreasing the gas flow rate in decrements of 100 cm3/min. In a second step, the sample was initialized again and the electric field was applied after the fluidized bed had reached the stationary state. Then the fluidized bed height, with the electric field turned on, was again measured as the gas flow rate was slowly decreased. This procedure was followed for several values of the electric field strength. The flow of gas 共dry nitrogen兲to the column was controlled by means of a MKS flow controller 共model 1179A兲with a full range from 0 to 2000 cm3/min. The height of the fluidized bed was measured using a ruler taped to the side of the bed 共marks in mm兲. Additionally, local observations were performed that allowed us to gain insight into the agglomerate dynamics upon application of the electric field. Images of the fluidized bed were acquired at 462 frames per second using a CMOS highspeed camera VDS Vosskühler HCC-1000 mounting a Cosmicar/Pentax optics with 16 mm focal length and F1.4 aperture, and a 1 mm extension tube to increase the magnification of the optics. The camera was separated about 4 cm from the gap between the electrodes to avoid interaction with the electric field. Illumination was provided by a 90 W halogen light source Intralux 4000-1 共Volpi AG兲. The external diameter of the fluidization cell 共3.18 cm兲was used for spatial calibration of the images. The image size was 1024 ⫻512 pixels grayscale 共256 levels兲, with the larger dimension of the image aligned with the axis of the fluidization cell, thus yielding a maximum resolution of 49.6 ␮ m per pixel. In order to observe the effect of the electric field, the acquisition of each sequence of images was started before the electric field was turned on. IV. EXPERIMENTAL RESULTS AND DISCUSSION Figure 2shows experimental data on the particle volume fraction ␾ of the fluidized bed as a function of the superficial gas velocity vg. The particle volume fraction ␾ is calculated from the measured height hof the bed 关 ␾ =m/共 ␳ pAh兲, where A=5 cm2is the bed cross-sectional area兴. In order to look for data reproducibility, each point of these curves represents the average and standard deviation over 36 independent runs 共for zero electric field兲and 12 independent runs 共for each value of the strength of the electric field兲. As can be seen in this figure, the main effect of the application of the electric field is an apparent increase of the particle volume fraction of the fluidized bed. This observation agrees qualitatively with the results recently reported by Kashyap et al. using a similar setup 关22兴. In our experiments we observed that the effect of the electric field on bed expansion was not reversible: when the electric field was turned off, the height of the bed did not return to its original value in the absence of field 共see Fig. 3兲. This observation suggests that the electric field must have a relevant influence on bed dynamics, possibly consisting of irreversible solid compaction of the powder due to electrical forces on the agglomerates. Clearly, direct visualization of the bed dynamics at a local scale would be of great importance in order to gain physical insight into the mechanisms by which the electric field influences fluidization. A. Effect of the electric field on agglomeration When the nanoparticle bed is fluidized, preexisting simple agglomerates build up the complex agglomerates in a dynamic process 关15,16兴. In this self-rearranging process of simple agglomerates, a stationary state is reached which is characterized by an average size d** of the complex agglomerates. Most of the simple agglomerates observed by Yao et al. have a size d*between 1 and 100 ␮ m. The work of Nam et al. 关10兴suggests d*⬇30 ␮ m关30兴. The size of the complex agglomerates has been predicted from the balance between the drag force on a simple agglomerate attached to the FIG. 2. Average particle volume fraction of the fluidized bed ␾ as a function of the superficial gas velocity vgfor different strengths of the electric field applied. FIG. 3. Series of photographs showing the irreversibility of the effect of the electric field on fluidized bed expansion. The superficial gas velocity is 2.6 cm/s. The strength of the electric field Eis slowly increased from 共a兲to 共c兲.共a兲E=0 V/m. 共b兲E=0.66 ⫻105V/m. 共c兲E=1.32⫻105V/m. In 共d兲the field is turned off. The arrows indicate the evolution of the free surface. In 共d兲the free surface cannot be neatly distinguished. NANOFLUIDIZATION ELECTROSTATICS PHYSICAL REVIEW E 77, 031301 共2008兲 031301-5 complex agglomerate and the adhesion force f*between simple agglomerates 关21兴. In the absence of humidity the main contribution to f*is the van der Waals force 共fvdW * ⬃10 nN兲, which enables us to obtain a value of d** of the order of hundreds of microns, in agreement with experimental observations 关21兴. Although it is likely that these agglomerates are charged, it is reasonable from our previous analysis to neglect the electrostatic force as compared to van der Waals force. On the other hand, these agglomerates can be polarized when the electric field is applied, giving rise to an additional force that still needs to be discussed. This force between induced dipoles might lead to chainlike structures as seen in many kinds of electrorheological fluids containing dielectric particles 关47,48兴. It is well known from fundamental electrostatics that the dipole moment induced by the electric field on a spherical dielectric particle of permittivity ⑀ in a surrounding medium of permittivity ⑀ 0can be calculated from 关49兴 p=1 6 ␲ dp 33 ⑀ 0 ⑀ − ⑀ 0 ⑀ +2 ⑀ 0 E.共5兲 The force between these interacting dipoles at contact is given by fd=3p2 2 ␲ ⑀ 0dp 4.共6兲 Using as typical values in our experiment dp=12 nm, ⑀ 0 =8.854⫻10−12 F/m, ⑀ =3.8 ⑀ 0, and E=4⫻105V/m, it is obtained fd⬃10−27 N for the force between the polarized primary nanoparticles. This negligible value as compared to the interparticle van der Waals force 关fvdW ⯝Adp/共24z2兲 ⯝0.5 nN兴indicates that the electric field cannot modify directly the internal structure of the agglomerates. The force between simple agglomerates fd *due to their polarization by the electric field can be estimated using the above equations if these aggregates are considered as effective dielectric spheres of size d*. According to effective medium theories for aggregates and numerical analysis on random dielectric materials 关50兴, the effective permittivity ⑀ *of an agglomerate of dielectric spherical particles of permittivity ⑀ located in a homogeneous environment of permittivity ⑀ 0can be calculated from the Bruggeman mixing rule 共1− ␾ int兲 ⑀ 0− ⑀ * ⑀ 0+2 ⑀ *+ ␾ int ⑀ − ⑀ * ⑀ +2 ⑀ *=0, 共7兲 where ␾ int is the particle volume fraction within the agglomerate 关 ␾ int=共d*/dp兲Da−3兴. Using as typical values d* =30 ␮ m and Da=2.5, it is obtained ⑀ *⯝1.03 ⑀ 0and, from the modified versions of Eqs. 共5兲and 共6兲,fd *⬃6⫻10−24 N, which denies any effect of polarization on the dynamics of aggregation between simple agglomerates. Finally, if complex agglomerates are considered as effective spherical particles of size d**⯝200 ␮ m, the force between complex agglomerates due to the dipole moment induced by the electric field can be estimated as fd **⬃4⫻10−23 N共 ⑀ **⯝1.01 ⑀ 0兲. Thus, it must be concluded that the polarization induced by the electric field does not affect essentially the attractive forces between agglomerates in the fluidized bed and, therefore, has no direct effect on agglomeration. B. Effect of the electric field on the flow dynamics To obtain insight into the physics of the fluidized bed as affected by the external field, direct visualization of the agglomerate flow dynamics has been carried out using a fast camera as detailed in the description of the experimental setup. Figure 4shows snapshots of the fluidized bed near the splash zone that illustrate the main qualitative features of the flow dynamics evolution after application of the external field. The arrows indicate the preferential lines of the flow of agglomerates in each situation. In the absence of the external electric field 关Fig. 4共a兲兴the agglomerates are seen to display xx x x FIG. 4. Snapshots of the fluidized bed near the free surface showing the main qualitative features of the effect of the electric field on the flow field at different times since it was applied. In 共a兲 there is no applied field. From 共b兲to 共g兲the strength of the applied horizontal field is E=2.5 ⫻105V/m. The arrows show the main agglomerate flow lines. Video of the experiment is available on request. VALVERDE et al. PHYSICAL REVIEW E 77, 031301 共2008兲 031301-6 a pseudoturbulent random motion with the smaller agglomerates being elutriated off the bed. As schematized in Fig. 4共b兲, a relevant phenomenon, just when the horizontal electric field is turned on, is a preferential flow of agglomerates in the direction of the field and towards the walls. The analysis of the trajectories of the agglomerates as deflected by the electric field will serve us in the next section to have an estimation of the charge of the agglomerates. The deposition of agglomerates in the wall becomes more noticeable near the free surface. This is probably due to stratification, with the smallest agglomerates, of higher mobility, preponderant at the very top. After t⯝200 ms of application of the electric field 关Fig. 4共c兲兴the accumulation of agglomerates on the internal walls of the cell near the splash zone is already significative. Consequently, the intensity of the horizontal flow of agglomerates diminishes in this region. Figure 5shows in detail the evolution of an agglomerate in the splash zone between t=117 ms and t=311 ms. It is seen how this agglomerate is deflected horizontally until it becomes compacted against the layer of agglomerates already adhered at the wall. After t⯝300 ms of application of the electric field 关Fig. 4共d兲兴, the layer of agglomerates adhered to the walls becomes appreciable. This region of powder remains in a solidlike state and is neatly distinguishable from the rest of the bed that still remains in a fluidlike state. As the solid layer becomes thicker, some big chunks in the outer region of this layer cannot be supported by the gas flow and fall down in avalanches. At this stage the compaction of powder against the walls starts to produce an appreciable collapse of the free surface of the fluidized region. At the same time, and due to the migration of agglomerates towards the walls, the density of agglomerates in the core region begins to decrease. This creates a less resistance path for the upwards flowing gas. Thus, the local gas velocity increases in the core, which gives rise to an upward flow of agglomerates across this channel. Figure 4共e兲shows the situation after t⯝500 ms of application of the electric field. At this stage, the solid layer adhered to the walls across the whole bed is significant. A marked upward flow of agglomerates in the core region is observed. When these agglomerates arrive at the free surface, the local gas velocity and therefore the vertical drag force decrease. Then, these aggregates are pushed toward the wall by the horizontal electric field. Downwards avalanches of big aggregates that become detached from the solid layer and cannot be sustained by the gas flow are frequent and the decrease of the fluidized bed height is quite significative. After t⯝700 ms 关Fig. 4共f兲兴there are two regions clearly identifiable: the low density core, with an upward flow of agglomerates, and the solid layer adhered to the wall. Both regions are separated by a convective flow of agglomerates, pushed towards the walls by the electric field and falling under the action of gravity when they move to a region of small local gas velocity and become attached to the solid layer to form bigger agglomerates. At this stage the bed height has decreased considerably and the free surface becomes rather diffuse. Finally, Fig. 4共g兲illustrates the stationary state, which is reached after t⯝1 s. The main agglomerate flows are in the vertical direction. Only a small fraction of agglomerates are flowing up across the almost void central channel while a thick solid layer is adhered to the wall, with some agglomerates avalanching down across the interphase between these two regions. The stationary fluidized state is highly heterogeneous and reminds one of the behavior of a spouted bed. C. Estimation of electrical charge on the agglomerates Since the electric field is almost homogeneous and the effective permittivity of the agglomerates is very small 共 ⑀ **⯝1.01 ⑀ 0兲, the physical mechanism behind the deflection of the agglomerates by the electric field must be the action of the electrophoretic force 共Fe⯝Q**E兲due to the presence of an electrostatic charge Q** on the agglomerates even though the powder as a whole is electroneutral. Using the Stokes’ law for an isolated agglomerate, its charge can be estimated as Q** =3 ␲ ␮ d**vh ** E,共8兲 where vh ** is the terminal velocity of the aggregate in the horizontal direction 关the time for the agglomerate to reach the terminal velocity is ␶ ⬃m**/共3 ␲ ␮ d**兲⬃1 ms, where m**=共1/6兲 ␳ pdp 3共d**/dp兲Dais the mass of the agglomerate兴. In this preliminary investigation we are just concerned with an estimation of the order of magnitude of the charge acquired by the agglomerates in the fluidized state. Uncertainties due to irregular shapes of the aggregates and long range interactions, and the consequent deviations from Stokes’ law, are disregarded. We have analyzed the trajectories of some agglomerates at the initial stage of application of the electric field in the FIG. 5. Snapshots of the fluidized bed near the free surface showing the deflection of an agglomerate towards the wall. The time elapsed since application of the electric field is indicated. The strength of the applied horizontal field is E=2.5⫻105V/m. Video of the experiment is available on request. NANOFLUIDIZATION ELECTROSTATICS PHYSICAL REVIEW E 77, 031301 共2008兲 031301-7 splash zone, where the density of agglomerates is smaller and flow perturbations are less relevant. The size d** of each agglomerate has been directly measured as the diameter of the circle with the same area as the agglomerate. Figure 6 shows some snapshots illustrating an example of an almost horizontal trajectory followed by an agglomerate. Between consecutive snapshots there are ten frames, which has allowed us to follow individual trajectories. An additional inconvenient to estimate agglomerate charge stems from the proper agglomeration dynamics of simple agglomerates in the fluidized bed. As seen in Fig. 6, a complex agglomerate may change dynamically and, therefore, its size and shape may be altered during its trajectory towards the wall. Thus, the size and velocity of the agglomerates have been checked in each step of their trajectory. The motion and size of nanoparticle agglomerates was investigated by manual tracking of the agglomerates. The selection of agglomerates for tracking was based on judgment by the naked eye, avoiding the smaller aggregates in order to minimize the error on size measurement. Since the agglomerate charge should not depend on the strength electric field applied we chose a fixed value of the field strength for the measurements 共E=2.5⫻105V/m兲. Results from this preliminary study are summarized in Table I. The agglomerate charge Q** of the agglomerates manually tracked was found on the order of 10−14 C, which gives a charge-to-mass ratio Qmr in the range 10−5–10−4 C/kg. This value is similar to the values typically measured for common micrometric or larger particles in high energy operations such as pneumatic transfer 关2,3兴. In our case, this high value of Qmr can be rationalized from the very high specific surface area of the nanopowder 共it is obtained SB.E.T.⯝1.7⫻105m2/kg by using the so-called B.E.T. method 关11兴兲, which is about 3000 times the specific surface area of powders of ⬃50 ␮ m particles. In fact, if the empirical correlation Qmr⬃10−7 Sfor powder charging in pneumatic transfer were extrapolated to nanopowders, one would obtain Qmr⬃10−2 C/kg, which is comparable to the maximum value that 50 ␮ m powder particles may acquire at the limit of air breakdown. Our measurements indicate therefore that a low energy operation such as fluidization may charge nanopowders up to quite high levels of Qmr just because of their extremely high specific surface area. This result can be of relevance in the assessment of hazards associated with nanopowder charging 关3兴. We are currently developing a specific software that will allow us, by means of particle image velocimetry, to obtain robust statistics for deeper insight such as investigating the correlation between agglomerate size and charge. Assuming that agglomerates can be considered as effective spherical particles, Eq. 共2兲can be modified to estimate the electrostatic force between agglomerates with charge Q**, fe ** ⬃共Q**兲2 4 ␲ ⑀ 0共d**兲2,共9兲 where it has been used ␣ ⯝0 and ␤ ⯝1 since the agglomerate effective permittivity is close to ⑀ 0关35兴.IfweuseQ** =10−14 C and d**=200 ␮ m, it is estimated fe **⬃0.01 nN, which is negligible as compared to the van der Waals force 共fvdW⬃10 nN兲. If it is assumed that the charge Q** is equidistributed among the simple agglomerates that build up the complex agglomerates, the charge per simple agglomerate would be Q*=Q**/共d**/d*兲Da⬃10−16 C, where d* ⬃30 ␮ m and Da⯝2.5. This charge value gives also a neg- FIG. 6. Snapshots of the fluidized bed near the free surface showing the individual trajectories of two complex agglomerates 共squared and circled, respectively兲. The time elapsed since application of the electric field is indicated. The strength of the applied horizontal field is E=2.5⫻105V/m. Video of the experiment is available on request. VALVERDE et al. PHYSICAL REVIEW E 77, 031301 共2008兲 031301-8 ligible electrostatic force between simple agglomerates 共fe * ⬃10−4 nN兲. From these estimations, it can be concluded that in the absence of an external electric field, the electrostatic forces do not play a role in the agglomeration of nanoparticles in the fluidized bed. The agglomerates charged with the same sign are compacted against the wall with a force fc⬃Q**E⬃1−10 nN, which is larger than their own weight 关w**=wp共d**/dp兲Da ⬃1nN兴, and is similar to the van der Waals attractive force in the absence of compaction. It is well known that van der Waals attractive forces between agglomerates of fine particles are enhanced by compaction 关51兴while as we have seen the electrostatic forces, either attractive or repulsive, are negligible. Thus, it is explainable that the cohesiveness of the layer of agglomerates is increased by compaction and it remains adhered to the wall even when the field is turned off as seen experimentally. V. CONCLUSIONS We have analyzed the effect of an electrostatic field horizontally applied on the behavior of a fluidized bed of nanopowders. A main result from this analysis is that nanoparticle agglomerates carry an electrostatic charge in the fluidized bed of a value of the order of 10−14 C, which is comparable to the typical charge measured in pneumatic conveying of micron sized and larger particles. This high charge level acquired in fluidization is attributable to the large specific surface area of nanopowders. This work provides for the first time an estimation of the agglomerate charge in fluidization that can be useful in the assessment of potential hazards in industry operations. The electrostatic forces between agglomerates due to the estimated charge are negligible as compared to the attractive van der Waals force. Thus, the charge of nanoparticles in the fluidized bed does not have an influence on the agglomeration dynamics. When a strong electric field is applied, neither the forces between induced dipoles are significant to affect the agglomerate size or structure. Instead, the action of the field is to push the agglomerates towards the lateral walls of the bed. The appearance of the bed after application of the electric field in the stationary state is reminiscent of a spouted bed, with a solidlike layer of powder adhered to the walls and a central low density channel through which most of the gas bypasses the powder. As a consequence, bed expansion is hindered and the uniform fluidization state turns to a highly heterogeneous fluidization state when the electrostatic field is applied. ACKNOWLEDGMENTS We acknowledge Spanish Government Agency Ministerio de Ciencia y Tecnologia 共Contract No. FIS2006-03645兲and Junta de Andalucia 共Contract No. FQM 421兲. We thank Daniel Lepek, from the New Jersey Institute of Technology, who helped us in performing the bed expansion experiments during his stay at the University of Seville. TABLE I. Estimation of agglomerate charges using the Stokes’ law and measurements of agglomerate size and horizontal terminal velocity during time intervals after application of the electric field. Time interval 共ms兲 Agglomerate size 共 ␮ m兲 ⫾50 Traveled distance 共mm兲 ⫾0.3 Average velocity 共cm/s兲 ⫾0.2 Field strength 共kV/cm兲 ⫾0.1 Electric charge 共10−14 C兲 ⫾0.3 0–9.5 560 2.41 12.4 2.5 4.6 19.5–41.2 600 2.27 10.5 2.5 4.3 41.2–62.8 390 1.85 8.6 2.5 2.3 19.5–41.2 300 2.27 10.5 2.5 2.1 41.2–62.8 370 2.56 11.9 2.5 2.9 62.8–84.5 370 3.98 18.3 2.5 4.5 84.5–106.1 250 2.41 11.2 2.5 1.9 117.0–138.6 490 1.07 4.6 2.5 1.5 138.6–160.3 480 1.14 5.3 2.5 1.7 160.3–181.9 450 1.14 5.3 2.5 1.6 181.9–203.6 450 1.70 7.8 2.5 2.4 203.6–225.3 530 1.56 7.2 2.5 2.6 225.3–246.9 580 1.42 6.6 2.5 2.6 246.9–268.6 520 1.56 7.2 2.5 2.5 268.6–290.2 530 1.42 6.6 2.5 2.4 290.2–311.9 530 0.99 4.6 2.5 1.6 NANOFLUIDIZATION ELECTROSTATICS PHYSICAL REVIEW E 77, 031301 共2008兲 031301-9