Bubble Behaviors of Large Cohesive Particles in a ... - ACS Publications

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Bubble Behaviors of Large Cohesive Particles in a 2D Fluidized Bed Jiliang Ma, Daoyin Liu,* and Xiaoping Chen Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, P. R. China S Supporting Information *

ABSTRACT: Fluidization hydrodynamics is greatly influenced by interparticle cohesive forces. In this paper, we study the bubbling behaviors of cohesive Geldart B particles in a 2D fluidized bed, using the “polymer coating” approach to introduce cohesive force. The effect of cohesive force on bubbles can be differentiated into two regimes: (i) by increasing the cohesive force within a low level, the bubble number increases, while the bubble fraction and bubble diameter decrease; (ii) when the force is large enough to cause the particles to adhere to the side walls of the bed, the bubble numbers and the bed expansion sharply decrease. With the increasing cohesive force, the bubble shape changes from roughly circular shape, to oblong shape, leading to the “short pass” of fluidizing gas through the bed. Finally, we analyzed the switching frequency and standard deviation of local pixel values to characterize the bubble dynamics.

1. INTRODUCTION Fluidized beds are widely used in industrial processes for their vigorous heat and mass transfer and flexibility in handling particles continuously. In many applications of fluidized reactors, the particles processed are cohesive, (e.g., olefin polymerization, liquid waste combustion, granulation, and drying). The presence of interparticle cohesive force causes different fluidizing dynamics compared to the noncohesive case. Thus, it is attractive to address the underlying mechanisms, based on which, the manipulating process of cohesive particulate system could be optimized. Cohesive force may exist in the fluidized beds with different forms, such as van der Waals force,1−3 electrostatic force,4,5 liquid bridge force,6−8 and particle bridge force.9,10 Basically, the existing studies on fluidized beds with cohesive particles mainly focus on: (i) the transition of fluidization behaviors between different groups according to Geldart classification;11−13 (ii) collapse and expansion behaviors of the bed;14−16 (iii) minimum fluidization, particle motion and bubbling characteristics.17−20 Out of the many characteristics of the fluidization hydrodynamics, the bubble behaviors strongly influence the particle motion and mass transfer21,22 in addition to being affected by the interaction between particles.23−25 A detailed understanding of the bubble behaviors is helpful for improving and optimizing the operation of fluidized beds with cohesive particles. The bubbling characteristics of regular noncohesive particles have been extensively studied. Close to the air distributor, there is an annulus structure where the bubbles concentrate near the wall. The annulus zone converges to the bed center with increasing height.26 With further rising, bubbles grow in size through continuous coalescence. If the bed is sufficiently tall, large bubbles are formed and a slugging bed is observed.27,28 The bubble size increases with the fluidization gas velocity.29,30 The bubble diameters keep increasing with bubble elevation.31,32 The bubble size distribution (BSD) at different elevations exhibits mono- and bimodal shape due to repeated coalescence and breakage of bubbles.33,34 However, regarding © XXXX American Chemical Society

the bubble behaviors for cohesive particles, few detailed studies can be found. Recently, Shabanian et al.35 have presented a novel method to introduce cohesive force by coating inert particles with a polymer layer whose cohesiveness is proportional to the temperature. The cohesive force between particles can be changed over a wide range by controlling the bed within a narrow range of temperatures close to ambient temperature. They found that when the cohesive force increases within a low level, the fluidizing gas tends to pass through the emulsion phase36 and the bubble size decreases.37 Generally, 2D fluidized beds are usually used to study bubble behaviors. It is worth pointing out that the translation of results obtained from 2D bed to 3D system or industrial application has to be done with caution, because the fluid dynamics in 2D and 3D beds are different. However, the use of 2D bed is still valuable for, for example, calibration of some types of measurement equipment and for validation of numerical simulation, etc.38 In the present study, the bubble dynamics of cohesive particles are investigated in a 2D fluidized bed using Digital Image Analysis (DIA). The approach of “polymer coating” presented by Shabanian et al.35 is employed to introduce cohesive force between Geldart B particles. Bubble properties such as spatial distribution of bubbles, bubble fraction, equivalent diameter of bubbles (Db), bubble size distribution (BSD), bubble density, bubble aspect ratio (β) and shape factor (φ) at different static bed heights (Hs), fluidization gas velocities (Ug) and cohesive forces are studied. Finally, the effects of cohesive force on the dynamic properties of bubbles are discussed in terms of frequency and standard deviation of local changes of pixel values. Received: August 3, 2015 Revised: December 27, 2015 Accepted: December 31, 2015

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DOI: 10.1021/acs.iecr.5b02789 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

maintained to the desired value within an accuracy of ±1 °C. To prevent heat loss, we installed four Perspex walls around the bed, forming an insulation layer filled with compressed N2 whose temperature is maintained the same with the bed materials by another electrical heater. The contrast between the emulsion phase and bubble phase is enhanced by placing a light box behind the bed and covering the setup with a shade cloth, which benefits the identification and analysis of bubbles.31−34,39 The whole bubbling behaviors are recorded by a digital camera whose framing rate equals to 24 frames per second for a full size image (1080 × 1920 pixels). 2.2. Materials. Both uncoated and coated glass beads with a density of 2500 kg/m3, were used as bed materials. The particles were carefully sieved using two sieves with mesh sizes of 550 and 650 μm, respectively, so that the average diameter of bed materials was estimated to 600 μm, corresponding to Geldart group B.40 On the basis of the standard pressure-drop test,41 the minimum fluidization velocity of uncoated particles, Umf, was measured to be 0.325 m/s. A detailed procedure for preparing the coated particles can be found in ref 35. An aqueous dispersion of poly(ethyl acrylate) (PEA) and poly(methyl methacrylate) (PMMA) with a mass ratio of 2 to 1 was employed as coating solution (commercial name Eudragit NE30D). The polymer layer thickness is around 10 μm. To guarantee a good coating quality, the spray process for the present work was divided into four batches during which sufficient time was provided for distribution and solidification of polymer layer. Figure 2 shows the surface morphology of glass beads before and after coating on the basis of SEM analysis. According to Bouffard et al.,42 the range of interparticle forces in the present work can be roughly estimated from 0 to 8 times particle gravity. The equations for estimating cohesive force have been provided in the Supporting Information. 2.3. Experimental Procedure. When the fluidization attains steady status, both electrical heaters were switched on and maintained at the same target values. After the bed temperature reaches the desired value, the backlight and video camera were turned on to record the bubbling behaviors. For each condition, the bubbling behaviors were recorded for 3 min, which provides a total of 4000 frames. The experiments were performed at different bed temperatures, static bed heights Hs, and fluidization gas velocities Ug. The bed

2. EXPERIMENTAL SECTION 2.1. Experimental Setup. Figure 1 shows the schematic of experimental setup. The experiment was undertaken in a

Figure 1. Schematic of 2D fluidized bed system.

pseudo-two-dimensional Perspex fluidized bed with a 300 mm width, 1000 mm height, and 20 mm thickness. A stainless steel porous plate with an open area ratio of 2.13% serves as a gas distributor. The interparticle cohesive force is adjusted by controlling the bed temperature that is monitored through a thermal couple inserted from the bed top. Bed materials are heated by fluidizing air whose temperature is controlled by a 1 kW electrical heater located in the air feeding line. The heating rate of the heater is precisely regulated by connecting it to a silicon controlled rectifier so that the air temperature can be

Figure 2. Surface morphology of glass beads before and after coating: (a) uncoated, (b) coated. B


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Industrial & Engineering Chemistry Research temperature ranges from 26 to 54 °C, Hs from 30 to 50 cm, and Ug from 2Umf to 3Umf. The first step for processing the recorded images is transferring them into binary ones which only consist of black (emulsion phase) and white (bubble phase) pixels using an appropriate threshold value. Basically, converting the original images into binary ones should follow two rules: (i) a constant threshold value is used throughout the binary conversion process; (ii) the threshold value could well discriminate the bubble phase from the emulsion phase. The latter rule is easily achieved because of the high contrast between bubbles and solids in the images used in the present work. We used the Otsu algorithm to estimate the threshold value. Figure 3 shows a comparison between original and binary

Figure 5. Evolution of solid area with time at the condition of Hs = 50 cm and Ug = 2Umf.

attributed to two aspects: (i) although there is a high contrast between the bubble phase and emulsion phase, the boundary between these two phases is still blurred, namely, the gray level of the boundary varies in the medium range, partly overlapped with the threshold value, which causes inconstancy in the identification of bubble boundary; (ii) some particles exist in the bubbles but are neglected in the binary conversion procedure, leading to solid loss in the binary images. The binary images thus obtained were further processed to filter false voids, that is, the freeboard and the bubbles bursting at the bed surface. Afterward, each bubble present in the image was labeled, and its information such as area, equivalent diameter, centroid coordinates, and aspect ratio, etc. were calculated and stored in a matrix based on the image processing toolbox of Matlab 2013b.

Figure 3. Example of original and binary images with the gray histogram.

images. The case we chose is Hs = 50 cm and Ug = 2Umf, because the fraction of pixels occupied by bubbles and solids are nearly the same, which is very appropriate for the Otsu algorithm.43 As can be seen, two peaks in the gray level histogram correspond to bubble and emulsion phases, respectively, leaving a wide and deep valley in the middle section. Therefore, the binary image thus obtained retains most key features of the bubbles. Although the threshold value calculated by the Otsu algorithm changes from image to image, it only fluctuates slightly around the averaged value of 0.332 as illustrated in Figure 4. Therefore, we applied 0.332 to all the images and found that it can efficiently identify the bubbles and filter the noises. The reliability of the method can also be proven by Figure 5 which provides the time-series amount of pixels occupied by solids in each image (solid area). Generally, the solid area remains nearly constant throughout the images studied. Only some slight scatter can be observed. This is

3. RESULTS AND DISCUSSION Since the cohesive force varies almost linearly with the bed temperature,42 hereafter, for the sake of readability, we describe the increase of bed temperature as the increase of the cohesive force. The “non-cohesive” case represents the fluidization of uncoated particles. 3.1. Bubble Properties. 3.1.1. Spatial Distribution of Bubbles. Figure 6 plots the snapshots of bubbling behaviors under various cohesive forces. The figure clearly shows that for the noncohesive case, small bubbles are introduced into the bed from the gas distributor. The bubbles rise with growing size due to coalescence, finally forming one large bubble with a similar dimension to the bed width at the bed surface. With the presence of a cohesive force, the bubbles tend to be smaller with irregular shapes. When the cohesive force is large enough, the particles adhere to the side walls of the bed. It narrows the flow region of particles, compelling the bubbles to rise along the central line, which in turn strengthens the adhesion of particles onto the walls. As a result, the amount of particles involved in the fluidization continues to reduce and the bed height decreases. Finally, the bed turns to channelling and the fluidization fails. It is worth pointing out that although the front/rear walls have a larger area than side walls, due to the geometry limitation in the thickness direction of the bed, the bubbles will fill the space between the front and rear walls, which sweeps the particles adhered on these walls. Thus, few particles can be observed on the walls even for the highcohesive cases.

Figure 4. Time-series threshold values calculated by the Otsu algorithm at the condition of Hs = 50 cm and Ug = 2Umf. C


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The regions near the side walls show the lowest probability, especially at half bed height. It is caused by the preferable rising path of bubbles: the bubbles will move laterally toward the bed center while rising along the bed height. On one hand, it facilitates the bubble coalescence in the bed center, thus generating high-probability regions; on the other hand, it generates low-probability regions along the side walls due to rarely passing by bubbles. This trend is more apparent for the lower static bed heights (Figure 7a). As the cohesive force increases, the low-probability region near the side walls extends to the bed center, indicating an increasing trend for bubbles moving laterally. The high-probability regions (the regions marked by arrows and lines in Figure 7a) are compressed near the bed surface as the cohesive force increases within a low level. When the cohesive force is large enough to cause the adhesion of particles onto the sidewalls as well as the reduction of bed height, the high-probability regions in turn extend downward to the distributor. 3.1.2. Bubble Fraction. Figure 8 plots the overall bubble fraction as a function of cohesive force under various Figure 6. Bubbling behaviors under different cohesive forces at Hs = 50 cm and Ug = 2Umf.

Figure 7 shows the probability for each pixel occupied by bubbles. It reveals the spatial distribution of bubbles and the region where bubbles go through frequently. The region where bubbles present with high probability (the probability larger than 0.5) has been marked with arrows and lines. The distribution of bubbles near the distributor shows a “concave” shape: the probability in the bed corners is apparently higher than that of center, indicating that the bubbles preferentially form near the walls. This phenomenon has been widely reported. Werther and Morelus26 proposed that the altered packing geometry of particles near the bed wall leads to an increased flow through this region. Additionally, the different friction within the fluidized particles and between particles and walls might favor bubble formation in the vicinity of the wall.

Figure 8. Effects of cohesive force on the bubble fraction under different fluidization gas velocities at Hs = 50 cm.

Figure 7. Time-averaged distribution of bubbles under different cohesive forces at Ug = 3Umf: (a) Hs = 30 cm; (b) Hs = 50 cm. D


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Industrial & Engineering Chemistry Research fluidization gas velocities. Bubble fraction is defined as the proportion of the instantaneous bed area occupied by bubbles. The bed area is the sum of bubble and solid areas during fluidization. The bubble fraction is found to increase with the fluidization gas velocity and decrease with the cohesive force. This finding is similar to Shabanian and Chaouki.37 They ascribed the decline of bubble fraction to the fact that increasing the level of cohesive force makes the emulsion phase have a higher capacity for holding the fluidizing gas inside its structure and increases the tendency of gas flowing in the emulsion phase. Rowe and Yates,44 and Yates and Newton45 also claimed the positive effects of increasing the van der Waals force between particles in the decline of bubble fraction. Nevertheless, this explanation is not complete for the present work. From Figure 6 and Figure 7, we observe that the particles will adhere to the sidewalls to form stable agglomerates under high cohesive force. At these conditions, apparently, the gases are not prone to flow through the emulsion phase anymore. Instead, the bubbles are compelled to move inward to the bed center and coalesce strongly. Because of the limitation in the lateral direction, the bubbles can only extend vertically, which will accelerate the breakup of bubbles at the bed surface and cause a sharp drop of bubble fraction. Therefore, the effect of cohesive force on bubbles can be distinguished into two regimes. Increasing the cohesive force within a low level will facilitate the gas passing through the emulsion phase. When the force is large enough, stable agglomerates will form, which leads to the “short pass” of fluidizing gas and the failure of fluidization finally. 3.1.3. Shape Factor and Aspect Ratio. Another property investigated is the bubble shape. It has been found to greatly influence the fluidization dynamics.46 For the present work, bubble shape is characterized by aspect ratio (β) and shape factor (φ) whose definitions are as follows: y β = max xmax (1) φ=

πD b Pb

Figure 9. Distributions of aspect ratio and shape factor under different cohesive forces at Hs = 50 cm and Ug = 3Umf: (a) aspect ratio, (b) shape factor.

(2)

where ymax and xmax are the maximum values of bubble dimension in the vertical and horizontal directions, respectively. Db is the equivalent diameter of bubbles, and Pb is the perimeter. Figure 9 shows the effects of cohesive force on the distribution of (a) aspect ratio and (b) shape factor. A positively skewed monomodal distribution of β for a noncohesive case is observed. The peak aspect ratio appears around 1 (Figure 9a). With the increasing of cohesive force, the peak β decreases and the distribution of β shifts to the right-hand side, which implies that the bubbles become oblong shape. As discussed in section 3.1.1, the cohesive force compels the bubbles to move laterally, thus accelerating the consecutive coalescence of bubbles in the bed center. Moreover, the squeezing effects from the narrowing rising path at high cohesive case (channeling) also contributes to the elongation of bubbles, thereby leading to the positive skewing of the distribution curve. Figure 10 provides typical examples of “consecutive coalescence” and “channeling”. The distribution of the shape factor (Figure 9b) is negatively skewed for all the cases studied, which is consistent with the results of Lim et al.30 For the noncohesive case, φ tends to concentrate around 0.8, implying bubbles roughly closer to

Figure 10. Typical images for “consecutive coalescence” and “channeling” behaviors observed at the condition of Hs = 50 cm, Ug = 3Umf, and bed temperature = 40 °C.

circular shape. As the cohesive force increases, the distribution curve is progressively shifted toward the left-hand side, indicating the multitudes of irregular-shape bubbles in the bed. The trend described above can also be proven by Figure 11 which plots the correlation between β and φ with the variation of cohesive forces. Figure 11 panels d−f are their projections over the XY plane. For the noncohesive case, there is a close relationship between β and φ where φ concentrates around 0.8−0.85 and β between 0.75 and 1.25. This implies that the E


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Glicksman et al.48 demonstrated that the coalescence rate of bubbles is proportional to the bubble fraction. As discussed in Figure 8, with increasing cohesive force, the bubble fraction progressively decreases, which thus decreases the coalescence rate. The absence of frequent coalescence means that the bubbles will present with smaller size and large numbers in the bed. Therefore, the bubble numbers increase first with cohesive force in the initial stage. When the cohesive particles begin to adhere to the side walls, the bubbles are compelled to concentrate in the bed center and coalesce without full development because their rising paths narrow with the side walls being occupied by particles (see the inset). Moreover, the reduction of the bed height with the adhesion of particles also reduces the possibility for bubble splitting that usually contributes to the bubble numbers. Consequently, the combination of the above two aspects causes a decline of bubble numbers at a high cohesive case. Bubble number density at different bed heights can be used to reveal the region where bubble numbsers are sensitive to the cohesive force and the coalescence rate of bubbles. It is calculated by dividing the bed into small slices along the height and calculating the number of bubbles whose centroids fall into each slice.31,49 The coalescence rate is usually estimated by the decay rate of the semilogarithm plot of bubble number density. Figure 13 compares the bubble number density at different bed Figure 11. Correlation between aspect ratio and shape factor at the condition of Hs = 50 cm and Ug = 3Umf: (a−c) noncohesive, 36 °C, 50 °C; (d−f) projections over XY plane.

bubble shape is close to a circle, which agrees well with the observation of Caicedo et al.47 With respect to the cohesive cases, both β and φ scatter over a wide range, reflecting in the decline of peak value and more flat distribution (Figure 11a−c). As the cohesive force increases, the scatter in β and φ increases. This also proves that the bubbles become irregular with the presence of cohesive force. 3.1.4. Bubble Number Density. Figure 12 reports the bubble numbers per frame under different cohesive forces. The Figure 13. Effects of cohesive force on the evolution of bubble number density with the distance from distributor at the condition of Hs = 40 cm and Ug = 3Umf.

heights under different cohesive forces at the conditions with Hs = 40 cm and Ug = 3Umf. Three different stages can be observed clearly. In the formation stage, large amounts of small bubbles are introduced into the bed. The bubble density and its decay rate are not influenced by the presence of cohesive force, indicating a constant coalescence rate in this stage. In the coalescence stage, the bubble density increases while the corresponding decay rate decreases with the cohesive force. The trend is more obvious at 44 °C. This is attributed to the fact that the coalescence between bubbles is inhibited by the presence of cohesive force. On the other hand, it may also be related to the presence of agglomerates in the bed which forces the bubbles to split into more smaller ones. With further rising, the bubbles keep growing in size and break up at the bed surface. The bubble density of the noncohesive case in the eruption stage is nearly constant due to less coalescence of large bubbles. With respect to the cohesive case, the data shows an increasing trend. This occurrence indicates that besides

Figure 12. Bubble numbers as a function of cohesive force at different fluidization gas velocities.

fluidization gas velocity ranges from 2Umf to 3Umf and the static bed height Hs = 40 cm. As the cohesive force increases, the bubble numbers first increase to a peak value then decrease. It also shows that the bubble numbers increase with the fluidization gas velocity as physically expected. F


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The average values of Db within various ROIs with and without cohesive force are plotted in Figure 16 where both

coalescence, the large bubbles would also split into smaller ones, which increases the bubble numbers in this stage. 3.1.5. Equivalent Diameter of Bubbles. Figure 14 plots the effects of cohesive force on Db along the bed height. The

Figure 14. Effects of cohesive force on the average values of equivalent diameter of bubbles in the bed under different fluidization gas velocities.

fluidization gas velocity ranges between 2Umf and 3Umf. Db increases with the fluidization gas velocity, while decreases with cohesive force. This is consistent with the results of Shabanian and Chaouki.37 As elucidated in the sections 3.1.2 and 3.1.4, the coalescence rate of bubbles decreases with the cohesive force. As a main driving force for the growth of bubble size, less coalescence results in a decline of mean values of Db. Moreover, increasing the cohesive force facilitates the splitting of bubbles into smaller ones (it will be discussed in the following). Therefore, the combined effects of less coalescence and more splitting of bubbles cause the decline of Db. To further understand how the cohesive force affects the bubble evolution, we divide the bed into several regions of interest (ROI) as shown in Figure 15. The bubbles whose centroids fall into certain ROI are identified to belong to this region. Each region has a height of 100 mm and the same width to the bed. The number of ROIs investigated depends on the static bed heights. We focus on ROI I−IV for the case of Hs = 30 cm, ROI I−V for Hs = 40 cm, and ROI I−VI for Hs = 50 cm.

Figure 16. Effects of cohesive force on the equivalent diameter of bubbles within regions of interest (ROIs): (a) Hs = 40 cm. (b) Hs = 50 cm.

histogram and trend lines are provided. Regarding noncohesive case at Hs = 40 cm, Db monotonically increases with bubble elevation and slightly decreases in ROI V. The slight decline of Db is likely related to the breakup of bubbles at bed surface. Large bubbles would disappear when their boundaries reach the bed surface, thus only the information on small bubbles is collected, which would underestimate the average bubble size in this region. In the present work, the underestimation is largely reduced by processing more than 3000 images, therefore only slight declines were observed. As the cohesive force increases, Db reaches a peak value within ROI IV and then decreases significantly. This nonlinear evolution of Db becomes more pronounced for Hs = 50 cm, where the maximum Db appears in ROI IV, the region far away from bed surface. It is not only related to the missing of large bubbles but also caused by the presence of cohesive force. It is worth noting that the average bubble sizes at the bed bottom under different cohesive forces are nearly the same. Only the bubbles in the upper part of the bed are influenced by cohesive force. Combining the above observation and the fact that the bubble numbers near the distributor are independent of cohesive force (Figure 13), we can draw a conclusion that the cohesive force has little effects on the formation of bubbles. Having known that the reduction of bubble size mainly occurs in the upper part of the bed, the further step forward is to identify the cause of bubble shrinkage. The bubble size

Figure 15. Definition of regions of interest. G


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splitting of bubbles, thus causing the reduction of bubble size in the upper bed as observed in Figure 16. 3.2. Dynamic Properties of Bubbles. In this section, the fluctuations of bubble properties with time are investigated to evaluate bubble dynamics. We introduce the local frequency ( f local), local standard deviation (σlocal), and overall standard deviation (σoverall) to evaluate bubble dynamics. f local is defined as the number of occurrences for each pixel value switching from “0” to “1” or “1” to “0” per second (“1” represents the pixel occupied by bubbles and “0” by particles). σlocal is the standard deviation of the pixel values. σoverall is the standard deviation of bubble fractions of the bed over more than 3000 images. 3.2.1. Local Frequency. Figure 18 plots f local under different cohesive forces at the conditions of Hs = 50 cm and Ug = 2.5Umf. The corners and central region of the bed exhibit large f local due to rapid introduction and coalescence of bubbles. Because the bubbles seldom pass by the bed sides, the local frequency there is thus much lower. A similar low-frequency region can also be found in the upper part of the bed due to less switching of local state caused by large bubbles. As the cohesive force increases within a low level (lowcohesive regime), the coalescence region (the region with the largest f local in the bed center) narrows and moves downward to the distributor. This is caused by the formation of oblong-shape bubbles as discussed in the section 3.1.3. In the high-cohesive regime, the sectional area of the bed reduces with the adhesion of particles onto the side walls, which increases the local gas velocity as well as the bubble velocity, thus leading to the frequent switching of pixel values. Therefore, f local is much larger than that of noncohesive and low-cohesive regimes. Moreover, similar to the low-cohesive regime, the coalescence region in the high-cohesive regime shifts toward the distributor with increasing cohesive force due to the reduction of bed height. 3.2.2. Local Standard Deviation. Figure 19 plots σlocal under different cohesive forces, at the condition of Hs = 50 cm and Ug = 2.5Umf. For all the cases studied, the upper part of the bed exhibits the largest σlocal, even larger than the bed corners. For the noncohesive case, as physically expected, the isolines distribute uniformly over the bed and the regions near the side walls exhibit low σlocal. According to the equation of σlocal (see the Supporting Information), there are two possibilities: this region is occupied by few bubbles or by most of the bubbles. Apparently, the former one is more reasonable. Thus, we infer

distribution (BSD) within ROI V and VI as a function of cohesive force is plotted in Figure 17. BSD is computed by

Figure 17. Bubble size distributions within (a) ROI V and (b) ROI VI relevant to a static bed height of 50 cm and a fluidization gas velocity of 2.5Umf.

calculating the relative amount of bubbles whose diameters fall into each size range. As can be seen, the distribution of bubble size presents a bimodal shape, in which two peaks are observed for small and large bubbles, respectively. The primary peak (small bubbles) is related to the bubble splitting. As the cohesive force increases, the proportion of small bubbles rises sharply, while the proportion of large bubbles decreases slightly. This indicates that the presence of cohesive force facilitates the

Figure 18. Contour plots of local frequency under various cohesive forces. Hs = 50 cm, Ug = 2.5Umf. H


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Figure 19. Local standard deviation under different cohesive forces. Hs = 50 cm, Ug = 2.5Umf.

Figure 21 plots the effects of cohesive force on σoverall under different fluidization gas velocities and static bed heights. As can

that these two regions might be the first to defluidize as the cohesive force increases gradually. As the cohesive force increases within the low-cohesive regime, the large-σlocal region in the upper part of the bed gradually narrows due to the shrinkage of bubble size, as introduced in section 3.1.5. Moreover, the oblong-shape bubbles generated at higher level of cohesive force also contributes to the reduction of the horizontal dimension of bubbles, thus leading to the narrowing of the large-σlocal region. Regarding the high-cohesive regime, the isolines of σlocal are forced to move inward with the adhesion of particles onto the side walls, confirming the previous speculation that the side walls are among the first to become defluidized. The increased gas velocity in the central bed prevents the low-σlocal region from moving inward further and thus compresses them in a narrow region. It then leads to further adhesion of particles, ultimately resulting in channelling and failure of fluidization. 3.3.3. Overall Standard Deviation. Figure 20 plots the fluctuations of bubble fraction for a period of 60 s obtained at

Figure 20. Time series of bubble fraction at the condition of Hs = 50 cm and Ug = 2Umf. Figure 21. Standard deviation of bubble fraction versus cohesive force under different fluidization gas velocities: (a) Hs = 30 cm; (b) Hs = 50 cm.

the condition of Hs = 50 cm and Ug = 2.5Umf. The average bubble fraction is 0.24. Because of the introduction of small bubbles from the distributor and the rupture of large bubbles at the bed surface, the bubble fraction fluctuates widely. Generally, the peak values correspond to the uniform distribution of bubbles in the bed and approach of large bubbles to the bed surface. During a periodic time scale, the large bubbles rupture and leave the bed, causing a significant drop of bubble fraction.27,50 Basically, the evolution of bubble behaviors can be quantified by the standard deviation of bubble fraction, σoverall.

be seen, the increase of fluidization gas velocity enhances σoverall, because the growth of bubbles as well as their rising and rupture process are accelerated by increasing fluidization gas velocity. As the cohesive force increases, σoverall decreases progressively and the discrepancy in σoverall caused by fluidization gas velocity also reduces. This could deteriorate I



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the particle motion and mixing in the bed. The comparison between Figure 21 panels a and b also reveals that the bed with smaller Hs exhibits larger σoverall. It is consistent with the results of Ozawa et al.50 that the fluctuation of bubble fraction is a decreasing function of bed height. Therefore, the smooth operation of a fluidized bed with cohesive particles would benefit from controlling the bed with a smaller static height.

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NOMENCLATURE

Acronyms

BSD = bubble size distribution DIA = digital image analysis PEA = poly(ethyl acrylate) PMMA = poly(methyl methacrylate) Symbols

4. CONCLUSIONS Bubbling behaviors of large cohesive particles in a 2D fluidized bed are studied experimentally using digital image analysis. The effects of interparticle cohesive force, static bed height, and fluidization gas velocity on the bubble properties are analyzed, including both the time averaged properties, for example, the bubble spatial distribution, bubble size, bubble shape, and bubble fraction, and dynamic properties, such as the frequency and standard deviation of local changes, and the overall standard deviation of bubble fraction. The main conclusions are drawn as follows: (1) The effect of cohesive force on bubbles can be differentiated into two regimes. By increasing the cohesive force within a low level, the bubble number increases, while the bubble fraction and bubble diameter decrease. When the force is large enough to cause the particles to adhere to the side walls of the bed, the bubble numbers and the bed expansion sharply decreases. (2) The bubble shape is evaluated by the aspect ratio and shape factor. With the increase of cohesive force, the bubble shape changes from roughly circular shape to oblong shape, and the correlation between the aspect ratio and shape factor decreases. (3) The variations of bubble number and bubble size distribution along the bed height indicate that the cohesive force can decrease the bubble coalescence and increase the bubble splitting, while it has limited effect on the bubble formation. (4) The local frequency is significant in the corners near the distributor and the bubble coalescence region in the bed center. The local standard deviation is significant in the upper part of the bed.

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Db = equivalent diameter of bubbles (mm) f local = local frequency (Hz) Hs = static bed height (cm) Pb = bubble perimeter (mm) Ug = fluidization gas velocity (m/s) Umf = minimum fluidization velocity (m/s) xmax = maximum value of bubble dimension in the horizontal direction (mm) ymax = maximum value of bubble dimension in the vertical direction (mm) Greek letters

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02789. Calculation of local standard deviation of pixel values, σlocal; estimation of interparticle cohesive force under different temperatures (PDF)

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β = aspect ratio (−) φ = shape factor (−) σlocal = local standard deviation (−) σoverall = overall standard deviation (−)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to acknowledge the financial supports for this study by the National Nature Science Foundation of China (51306035 and 51276036) and Scientific Research Foundation of Graduate School of Southeast University. J


Article

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