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Effect of particle and fluid properties on the pickup velocity of fine particles
Powder Technology 196 (2009) 237–240
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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / p o w t e c
Short communication
Effect of particle and fluid properties on the pickup velocity of fine particles Devang Dasani, Charay Cyrus, Katherine Scanlon, Rui Du, Kyle Rupp, Kimberly H. Henthorn ⁎ Missouri University of Science and Technology, Rolla, MO, United States
a r t i c l e
i n f o
Article history: Received 6 April 2009 Received in revised form 21 July 2009 Accepted 7 August 2009 Available online 19 August 2009 Keywords: Pickup velocity Entrainment Electrostatic forces Pneumatic conveying Powder technology
a b s t r a c t Systems involving fluid–particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids. In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fluid–particle flows are readily found in a wide range of large-scale industrial applications, but they are also critical in the function of small-scale laboratory and research applications. However, it is often difficult to properly design a particulate system because of the limited availability of applicable equations. A majority of particulate systems operate inefficiently due to the lack of information needed for accurate design, scale-up, and optimization. This is especially true in systems that involve the flow of highly cohesive or non-spherical particles. One critical parameter needed to properly design conveying processes is the minimum fluid velocity required for particle entrainment, also known as pickup velocity. In two-phase conveying systems, fluid velocities below the particle pickup velocity can result in clogged pipelines or channels, and velocities much larger than what is required can lead to particle attrition, excessive pipeline abrasion, and unnecessary energy consumption. Therefore, knowledge of a material's pickup velocity is of great interest to those designing particle conveying processes. However, pickup velocity is a complex function of many variables, including particle properties, such as size, shape, density, and electrostatic behavior, and fluid properties, such as density and viscosity.
⁎ Corresponding author. E-mail address: [email protected] (K.H. Henthorn). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.08.007
Previous work has examined the effect of particle size, shape, and electrostatic behavior on the pickup velocity of particles less than 100 μm in gas-phase pneumatic conveying [1,2]. One major conclusion drawn from this work was that a minimum pickup velocity exists at a particle diameter located in the transition zone between inertiadominated entrainment and entrainment dominated by particle– particle interactions. In other words, at large particle diameters (>50 μm), higher fluid velocities are required due to increased particle mass. At small particle diameters (<20 μm), particle–particle interactions, such as electrostatic and van der Waals forces, become much more significant so that pickup velocity increases with decreasing particle size. Hayden et al. also concluded that electrostatic forces dominate at intermediate particle size ranges (20–50 μm) and that irregular particle shapes result in higher pickup velocities and greater deviation in repeated experimental trials. The previous conclusions are applicable for gas–solid applications; however, many processes, including mixing and slurry flows, involve solids transport in a liquid medium. For these types of systems, the dominant forces acting on the particles are different than those in a gas–solids environment. Particle buoyancy forces become significant due to the increased liquid density relative to that of a gas. In addition, some particle–particle interactions, such as liquid bridging and electrostatic attraction, can be completely dampened in a liquid medium, while other factors, such as zeta potential, must be considered. To better understand the differences between particle entrainment in gas and liquid media, and to ultimately develop a universal expression for pickup velocity in all fluid types, a comparison
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D. Dasani et al. / Powder Technology 196 (2009) 237–240
Fig. 1. Forces acting on a single glass sphere in water at incipient motion.
Fig. 2. Comparison of forces acting on a single glass sphere in water and air at incipient motion.
of relative dominant forces must be made by utilizing pickup velocity data obtained for both types of systems. Hayden et al. [1] developed a simple pickup velocity model based on the vertical force balance of a single particle on a flat surface. The four major forces acting on the particle were the downward gravitational and adhesion forces, and the upward buoyancy and lift forces, the latter of which was derived from Saffman's analysis of a single particle in shear flow [3]. An assessment of the flow profile
showed that all particles in their work were contained in the laminar boundary layer, which is why the existence of a linear velocity profile was assumed. In their expression, it was assumed that van der Waals forces were the dominant adhesive force because liquid bridges and electrostatic effects were minimized in the experimental system. This assumption is also valid for liquid–solid systems, because liquid bridges and electrostatic attractions are eliminated in liquid environments. In the current work, it is also assumed that particle–particle interactions from surface charges (zeta potential) are negligible due to the relatively large size of the particles used. Fig. 1 shows the magnitude of the four major forces acting on a single glass particle at incipient motion in water. For larger particles (>40 μm), it can be seen that gravitational and buoyancy forces dominate the pickup of particles, while adhesion and lift forces are relatively insignificant. The solid lines in Fig. 2 show the same analysis for particles less than 40 μm. For very small particle sizes (<10 μm) adhesion forces dominate pickup, as expected, while lift forces remain the least significant for all particle sizes. The figure also includes values of these forces in air (dotted lines). Gravitational and adhesion forces are only shown once because it is assumed that they are unaffected by the type of fluid used, but the figure shows a significant difference in the relative magnitudes of the buoyancy and lift forces between the two types of fluids. As expected, buoyancy forces are much larger in water than in air, while the lift forces are significantly less. Stevenson et al. [4] proposed that a single model or correlation should exist that incorporates pickup velocity in both gas and liquid media. However, when they compared the experimental liquid-phase data and semi-empirical model developed by Wicks [5] to the experimental gas-phase data reported by Cabrejos and Klinzing [2], they found a significant difference between the two. This large deviation can be partly attributed to the fact that the data were collected in two dissimilar systems so that they cannot be directly compared. In other words, due to differences in pipe dimensions, particle characteristics, and other aspects, it cannot be confidently stated that the large observed deviation is solely due to fluid property effects and not other factors, such as distinct fluid velocity profiles caused by dissimilar system geometries. A significant contribution to the universal pickup velocity literature has stemmed from the work at the Ben-Gurion University of the Negev [6–8]. Kalman et al. [6,7] combined their experimental data collected in a wind tunnel with those of Hayden et al. [1] and Klinzing and Cabrejos [2] to investigate the use of dimensionless parameters to describe pickup for all particle types. They found that when particle Reynolds number (ratio of inertial to viscous forces) is plotted as a function of Archimedes number (ratio of inertial times buoyancy forces to the square of the viscous force), the three sets of data fall onto the same curve, which exists in three distinct zones. The data used for their assessment were mostly from coarse particles in pipes between 1 and 2 in. in size. Rabinovich and Kalman [8] developed a generalized master curve to predict various threshold velocities, including pickup velocity, in a range of fluid types. They again relied
Fig. 3. Schematic of experimental setup.
D. Dasani et al. / Powder Technology 196 (2009) 237–240
239
Table 1 Particles used in pickup velocity experiments. Material
Shape
Density (g/cm3)
Mean diameter
Glass Glass Stainless steel
Spherical Crushed Spherical
2.5 2.5 8.0
12 mean sizes from 7.6 to 438.0 μm 4 mean sizes from 52.5 to 179.4 μm 3 mean sizes from 18.0 to 48.7 μm
on the Reynolds and Archimedes numbers to capture the effect of particle size, particle density, pipe size, and fluid density. Although their data were collected for particles with a wide range of shapes, from spheres to spheroids to cylinders, their master curve assumed the presence of spherical particles only. Although the current literature contains several generalized references to particle entrainment in liquid media [4–12], there is no reported systematic experimental investigation into the effect of individual particle properties on particle pickup in liquid. The current work examines the effect of particle size, density, and shape on the pickup velocity in water. In addition, gas-phase pickup velocity data reported by Hayden et al. [1] were collected using a similar experimental technique to the one used here, allowing for a direct comparison of liquid media pickup velocity data to existing data for particle pickup in gas. 2. Experimental The experimental details for this project are similar to those outlined in Hayden et al. [1], but have been modified slightly to allow for liquid flow. Fig. 3 is a schematic of the experimental setup. Three sections of cylindrical 1-inch diameter transparent acrylic pipe were used to observe particle entrainment and to determine when steady state was reached. The two end sections of pipe were used to minimize end effects and ensure fully-developed flow, and particles were placed in the middle section of pipe at the start of each experiment. Sufficient pipe lengths were verified through one-phase flow simulations in COMSOL Multiphysics®. A particle collection device placed after the acrylic pipe allowed the particles to be separated from the water via gravitational settling. Previous work showed that duning due to compression of the particle pile could be avoided by arranging the particles into an upward slope at the beginning of each experiment. Dry particles were placed in the pipe and distilled water was slowly added to purge all air from the system without disturbing the shape of the pile. The acrylic pipe was positioned below two higher points on either side of the test section so that water could be contained in the pipe during the startup
Fig. 5. Pickup velocity for all particle types in water.
period (see Fig. 3). Distilled water at ambient temperature was then flowed over the particle pile at a constant volumetric flow rate. Due to the tapered pile configuration, particles were removed in horizontal layers, gradually increasing the free cross-sectional area of the pipe and decreasing the velocity directly over the pile. Eventually, the fluid velocity was no longer sufficient to entrain additional particles, and a steady-state pile height was reached. From the known fluid volumetric flow rate and the steady-state free cross-sectional area, the velocity over the pile, taken to be the particle pickup velocity, was determined. Table 1 gives the physical properties of the particles used in this work. Particle size distributions were obtained with a Microtrac S3500 Laser Diffraction instrument, and the standard deviation of the particle sizes was within 20% of the mean value reported for each particle type. Fig. 4 shows an SEM image of representative crushed glass particles used here. 3. Results and discussion Fig. 5 shows measured pickup velocities for the particles listed in Table 1. In the figure, the bars represent one standard deviation from the reported mean value. Inspection of the data for glass spheres shows that a minimum pickup velocity exists, which is in agreement with previous results [1,2]. In addition, a comparison of the data for crushed glass with those of glass spheres shown in Fig. 5 indicates that
Fig. 4. SEM images of representative crushed glass particles used in experiments.
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D. Dasani et al. / Powder Technology 196 (2009) 237–240
expected because the downward adhesive forces are less in the liquid environment due to the elimination of liquid bridging and electrostatic attractions, while the decrease in the lift force is partially offset by the increase in the upward buoyancy force. Both curves exhibit a minimum Reynolds number, although it occurs at approximately 40 μm in water and approximately 70 μm in gas. This is likely due to the differences in interparticle forces in the range of particle sizes near the minimum pickup velocity. Hayden et al. found that for intermediate particle sizes (20–50 μm), electrostatic attractions dominate particle pickup. Since these forces are eliminated in liquid environments, gravitational forces become the dominant force at smaller particle sizes. 4. Conclusions
Fig. 6. Reynolds number required for incipient motion of glass spheres in air and water.
pickup velocity is not a strong function of particle shape for the sizes investigated here. However, the larger standard deviation seen with the crushed glass implies more variations in measurements from trial to trial. This is likely a result of inconsistencies in particle packing due to the irregular particle shape. The crushed glass particles are very angular and have a wide range of particle shape (Fig. 4). Not only will this affect the contact area between particles, and hence the interparticle forces, but it will also affect the drag on the particles, which is directly related to the lift force. The effect of particle density is illustrated in Fig. 5 through a comparison of pickup velocities for three sizes of stainless steel and glass spheres approximately 20–50 μm. The density of stainless steel is approximately 3.2 times larger than that of glass, and its pickup velocity is between 1.6 and 1.9 times higher than glass. This result is opposite of what was found by Hayden et al. in their gas system, where the pickup velocity for 25 μm glass spheres (an insulator) was 1.3 times higher than for stainless steel (a conductor). In their system, electrostatic attractions dominated the pickup velocity at intermediate particle sizes, and they concluded that triboelectrification of the insulating glass particles increased the interparticle (electrostatic) forces, while the conducting stainless steel particles were able to dissipate charging, resulting in a smaller interparticle attraction. This difference in material charging resulted in the negligible dependence of material density. However, in the current work, electrostatic interactions are eliminated in the liquid environment, leaving the material density (gravitational force) to dominate the pickup of particles. Fig. 5 also shows the theoretical pickup velocity of a single glass sphere calculated from the force balance described in Section 1. The model underpredicts the experimental pickup velocity for all particle sizes, and does not capture the existence of a minimum pickup velocity. This is similar to what Hayden et al. found in their analysis. The underprediction is likely due to the simplification in the adhesion force term, which did not include the effects of multiple particles, variations in particle shape, or the existence of additional interparticle forces. Fig. 6 gives a direct comparison of the entrainment behavior for glass spheres in both water and air, with the latter data taken from Hayden et al. [1]. The pickup velocity data have been incorporated into the reported dimensionless Reynolds number, which was calculated for flow directly above the particle pile. Error bars are included, but are too small to be seen in the figure. Both sets of data were collected in nearly identical experimental systems, so differences seen in the figure are assumed to be a function of fluid type. It is clear that for all particle sizes investigated here, the Reynolds number required for particle entrainment is greater in air than it is in water. This is
For particles less than 450 μm entrained in water, a minimum pickup velocity exists due to the dependence of dominant forces on particle size. As was shown previously, small particle entrainment is dominated by interparticle forces, while inertial forces dominate the pickup of larger particles. For the parameters investigated here, particle shape has a negligible effect on the pickup velocity, but nonspherical particles have a broader range of pickup velocity than spherical particles at a given diameter due to more random packing. Comparison of the liquid–solids data to previously reported gas– solids data shows the effect of fluid type on pickup velocity. The effects of electrostatic forces and liquid bridging are eliminated in liquid environments, so the Reynolds number directly above the particles as they are entrained is smaller in water than it is in air. The buoyancy and lift forces are also affected by fluid type, and it was found that the increased buoyancy force in liquid is partially offset by the decrease in lift force. The minimum Reynolds number occurs at smaller particle sizes in liquids because the effects of electrostatic and liquid bridging forces, which dominate in intermediate particle sizes (20–50 μm) in gases, are no longer present in liquids. This means that inertial forces begin to dominate at smaller particle sizes in liquid media. Acknowledgments The authors are grateful to the American Chemical Society — Petroleum Research Fund (#44508-G9), Mo-Sci Corporation (Rolla, MO), and undergraduate research students Debra Terrell, Aaron Hanewinkel, and Shaye Bouckaert. References [1] K. Hayden, K. Park, J. Curtis, Effect of particle characteristics on particle pickup velocity, Powder Technol. 131 (1) (2003) 7–14. [2] F. Cabrejos, G. Klinzing, Incipient motion of solid particles in horizontal pneumatic conveying, Powder Technol. 72 (1992) 51–61. [3] P. Saffman, The lift on a small sphere in a shear flow, J. Fluid Mech. 22 (2) (1965) 385–400. [4] P. Stevenson, F. Cabrejos, R. Thorpe, Incipient motion of particles on a bed of like particle in hydraulic and pneumatic conveying, 4th World Congress of Particle Technology, Sydney, July 21–25, Paper 400, 2002. [5] M. Wicks, Transport of solids at low concentration in horizontal pipes, in: I. Zandi (Ed.), Advances in Solid–Liquid Flow in Pipes and its Application, Pergamon Press, New York, 1971, pp. 101–124. [6] H. Kalman, A. Satran, D. Meir, E. Rabinovich, Pickup (critical) velocity of particles, Powder Technol. 160 (2005) 103–113. [7] E. Rabinovich, H. Kalman, Pickup, critical, and wind threshold velocities of particles, Powder Technol. 176 (2007) 9–17. [8] E. Rabinovich, H. Kalman, Generalized master curve for threshold superficial velocities in particle–fluid systems, Powder Technol. 183 (2008) 304–313. [9] Y. Niño, F. Lopez, M. Garcia, Threshold for particle entrainment into suspension, Sedimentology 50 (2003) 247–263. [10] C. Ling, Criteria for incipient motion of spherical sediment particles, J. Hydraul. Eng. (1995) 472–478. [11] F. Wu, Y. Chou, Rolling and lifting probabilities for sediment entrainment, J. Hydraul. Eng. (2003) 110–119. [12] M. Abdelrhman, J. Paul, W. Davis, Analysis procedure for and application of a device for simulating sediment entrainment, Mar. Geol. (1996) 337–350.
Contents lists available at ScienceDirect
Powder Technology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / p o w t e c
Short communication
Effect of particle and fluid properties on the pickup velocity of fine particles Devang Dasani, Charay Cyrus, Katherine Scanlon, Rui Du, Kyle Rupp, Kimberly H. Henthorn ⁎ Missouri University of Science and Technology, Rolla, MO, United States
a r t i c l e
i n f o
Article history: Received 6 April 2009 Received in revised form 21 July 2009 Accepted 7 August 2009 Available online 19 August 2009 Keywords: Pickup velocity Entrainment Electrostatic forces Pneumatic conveying Powder technology
a b s t r a c t Systems involving fluid–particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids. In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fluid–particle flows are readily found in a wide range of large-scale industrial applications, but they are also critical in the function of small-scale laboratory and research applications. However, it is often difficult to properly design a particulate system because of the limited availability of applicable equations. A majority of particulate systems operate inefficiently due to the lack of information needed for accurate design, scale-up, and optimization. This is especially true in systems that involve the flow of highly cohesive or non-spherical particles. One critical parameter needed to properly design conveying processes is the minimum fluid velocity required for particle entrainment, also known as pickup velocity. In two-phase conveying systems, fluid velocities below the particle pickup velocity can result in clogged pipelines or channels, and velocities much larger than what is required can lead to particle attrition, excessive pipeline abrasion, and unnecessary energy consumption. Therefore, knowledge of a material's pickup velocity is of great interest to those designing particle conveying processes. However, pickup velocity is a complex function of many variables, including particle properties, such as size, shape, density, and electrostatic behavior, and fluid properties, such as density and viscosity.
⁎ Corresponding author. E-mail address: [email protected] (K.H. Henthorn). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.08.007
Previous work has examined the effect of particle size, shape, and electrostatic behavior on the pickup velocity of particles less than 100 μm in gas-phase pneumatic conveying [1,2]. One major conclusion drawn from this work was that a minimum pickup velocity exists at a particle diameter located in the transition zone between inertiadominated entrainment and entrainment dominated by particle– particle interactions. In other words, at large particle diameters (>50 μm), higher fluid velocities are required due to increased particle mass. At small particle diameters (<20 μm), particle–particle interactions, such as electrostatic and van der Waals forces, become much more significant so that pickup velocity increases with decreasing particle size. Hayden et al. also concluded that electrostatic forces dominate at intermediate particle size ranges (20–50 μm) and that irregular particle shapes result in higher pickup velocities and greater deviation in repeated experimental trials. The previous conclusions are applicable for gas–solid applications; however, many processes, including mixing and slurry flows, involve solids transport in a liquid medium. For these types of systems, the dominant forces acting on the particles are different than those in a gas–solids environment. Particle buoyancy forces become significant due to the increased liquid density relative to that of a gas. In addition, some particle–particle interactions, such as liquid bridging and electrostatic attraction, can be completely dampened in a liquid medium, while other factors, such as zeta potential, must be considered. To better understand the differences between particle entrainment in gas and liquid media, and to ultimately develop a universal expression for pickup velocity in all fluid types, a comparison
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D. Dasani et al. / Powder Technology 196 (2009) 237–240
Fig. 1. Forces acting on a single glass sphere in water at incipient motion.
Fig. 2. Comparison of forces acting on a single glass sphere in water and air at incipient motion.
of relative dominant forces must be made by utilizing pickup velocity data obtained for both types of systems. Hayden et al. [1] developed a simple pickup velocity model based on the vertical force balance of a single particle on a flat surface. The four major forces acting on the particle were the downward gravitational and adhesion forces, and the upward buoyancy and lift forces, the latter of which was derived from Saffman's analysis of a single particle in shear flow [3]. An assessment of the flow profile
showed that all particles in their work were contained in the laminar boundary layer, which is why the existence of a linear velocity profile was assumed. In their expression, it was assumed that van der Waals forces were the dominant adhesive force because liquid bridges and electrostatic effects were minimized in the experimental system. This assumption is also valid for liquid–solid systems, because liquid bridges and electrostatic attractions are eliminated in liquid environments. In the current work, it is also assumed that particle–particle interactions from surface charges (zeta potential) are negligible due to the relatively large size of the particles used. Fig. 1 shows the magnitude of the four major forces acting on a single glass particle at incipient motion in water. For larger particles (>40 μm), it can be seen that gravitational and buoyancy forces dominate the pickup of particles, while adhesion and lift forces are relatively insignificant. The solid lines in Fig. 2 show the same analysis for particles less than 40 μm. For very small particle sizes (<10 μm) adhesion forces dominate pickup, as expected, while lift forces remain the least significant for all particle sizes. The figure also includes values of these forces in air (dotted lines). Gravitational and adhesion forces are only shown once because it is assumed that they are unaffected by the type of fluid used, but the figure shows a significant difference in the relative magnitudes of the buoyancy and lift forces between the two types of fluids. As expected, buoyancy forces are much larger in water than in air, while the lift forces are significantly less. Stevenson et al. [4] proposed that a single model or correlation should exist that incorporates pickup velocity in both gas and liquid media. However, when they compared the experimental liquid-phase data and semi-empirical model developed by Wicks [5] to the experimental gas-phase data reported by Cabrejos and Klinzing [2], they found a significant difference between the two. This large deviation can be partly attributed to the fact that the data were collected in two dissimilar systems so that they cannot be directly compared. In other words, due to differences in pipe dimensions, particle characteristics, and other aspects, it cannot be confidently stated that the large observed deviation is solely due to fluid property effects and not other factors, such as distinct fluid velocity profiles caused by dissimilar system geometries. A significant contribution to the universal pickup velocity literature has stemmed from the work at the Ben-Gurion University of the Negev [6–8]. Kalman et al. [6,7] combined their experimental data collected in a wind tunnel with those of Hayden et al. [1] and Klinzing and Cabrejos [2] to investigate the use of dimensionless parameters to describe pickup for all particle types. They found that when particle Reynolds number (ratio of inertial to viscous forces) is plotted as a function of Archimedes number (ratio of inertial times buoyancy forces to the square of the viscous force), the three sets of data fall onto the same curve, which exists in three distinct zones. The data used for their assessment were mostly from coarse particles in pipes between 1 and 2 in. in size. Rabinovich and Kalman [8] developed a generalized master curve to predict various threshold velocities, including pickup velocity, in a range of fluid types. They again relied
Fig. 3. Schematic of experimental setup.
D. Dasani et al. / Powder Technology 196 (2009) 237–240
239
Table 1 Particles used in pickup velocity experiments. Material
Shape
Density (g/cm3)
Mean diameter
Glass Glass Stainless steel
Spherical Crushed Spherical
2.5 2.5 8.0
12 mean sizes from 7.6 to 438.0 μm 4 mean sizes from 52.5 to 179.4 μm 3 mean sizes from 18.0 to 48.7 μm
on the Reynolds and Archimedes numbers to capture the effect of particle size, particle density, pipe size, and fluid density. Although their data were collected for particles with a wide range of shapes, from spheres to spheroids to cylinders, their master curve assumed the presence of spherical particles only. Although the current literature contains several generalized references to particle entrainment in liquid media [4–12], there is no reported systematic experimental investigation into the effect of individual particle properties on particle pickup in liquid. The current work examines the effect of particle size, density, and shape on the pickup velocity in water. In addition, gas-phase pickup velocity data reported by Hayden et al. [1] were collected using a similar experimental technique to the one used here, allowing for a direct comparison of liquid media pickup velocity data to existing data for particle pickup in gas. 2. Experimental The experimental details for this project are similar to those outlined in Hayden et al. [1], but have been modified slightly to allow for liquid flow. Fig. 3 is a schematic of the experimental setup. Three sections of cylindrical 1-inch diameter transparent acrylic pipe were used to observe particle entrainment and to determine when steady state was reached. The two end sections of pipe were used to minimize end effects and ensure fully-developed flow, and particles were placed in the middle section of pipe at the start of each experiment. Sufficient pipe lengths were verified through one-phase flow simulations in COMSOL Multiphysics®. A particle collection device placed after the acrylic pipe allowed the particles to be separated from the water via gravitational settling. Previous work showed that duning due to compression of the particle pile could be avoided by arranging the particles into an upward slope at the beginning of each experiment. Dry particles were placed in the pipe and distilled water was slowly added to purge all air from the system without disturbing the shape of the pile. The acrylic pipe was positioned below two higher points on either side of the test section so that water could be contained in the pipe during the startup
Fig. 5. Pickup velocity for all particle types in water.
period (see Fig. 3). Distilled water at ambient temperature was then flowed over the particle pile at a constant volumetric flow rate. Due to the tapered pile configuration, particles were removed in horizontal layers, gradually increasing the free cross-sectional area of the pipe and decreasing the velocity directly over the pile. Eventually, the fluid velocity was no longer sufficient to entrain additional particles, and a steady-state pile height was reached. From the known fluid volumetric flow rate and the steady-state free cross-sectional area, the velocity over the pile, taken to be the particle pickup velocity, was determined. Table 1 gives the physical properties of the particles used in this work. Particle size distributions were obtained with a Microtrac S3500 Laser Diffraction instrument, and the standard deviation of the particle sizes was within 20% of the mean value reported for each particle type. Fig. 4 shows an SEM image of representative crushed glass particles used here. 3. Results and discussion Fig. 5 shows measured pickup velocities for the particles listed in Table 1. In the figure, the bars represent one standard deviation from the reported mean value. Inspection of the data for glass spheres shows that a minimum pickup velocity exists, which is in agreement with previous results [1,2]. In addition, a comparison of the data for crushed glass with those of glass spheres shown in Fig. 5 indicates that
Fig. 4. SEM images of representative crushed glass particles used in experiments.
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D. Dasani et al. / Powder Technology 196 (2009) 237–240
expected because the downward adhesive forces are less in the liquid environment due to the elimination of liquid bridging and electrostatic attractions, while the decrease in the lift force is partially offset by the increase in the upward buoyancy force. Both curves exhibit a minimum Reynolds number, although it occurs at approximately 40 μm in water and approximately 70 μm in gas. This is likely due to the differences in interparticle forces in the range of particle sizes near the minimum pickup velocity. Hayden et al. found that for intermediate particle sizes (20–50 μm), electrostatic attractions dominate particle pickup. Since these forces are eliminated in liquid environments, gravitational forces become the dominant force at smaller particle sizes. 4. Conclusions
Fig. 6. Reynolds number required for incipient motion of glass spheres in air and water.
pickup velocity is not a strong function of particle shape for the sizes investigated here. However, the larger standard deviation seen with the crushed glass implies more variations in measurements from trial to trial. This is likely a result of inconsistencies in particle packing due to the irregular particle shape. The crushed glass particles are very angular and have a wide range of particle shape (Fig. 4). Not only will this affect the contact area between particles, and hence the interparticle forces, but it will also affect the drag on the particles, which is directly related to the lift force. The effect of particle density is illustrated in Fig. 5 through a comparison of pickup velocities for three sizes of stainless steel and glass spheres approximately 20–50 μm. The density of stainless steel is approximately 3.2 times larger than that of glass, and its pickup velocity is between 1.6 and 1.9 times higher than glass. This result is opposite of what was found by Hayden et al. in their gas system, where the pickup velocity for 25 μm glass spheres (an insulator) was 1.3 times higher than for stainless steel (a conductor). In their system, electrostatic attractions dominated the pickup velocity at intermediate particle sizes, and they concluded that triboelectrification of the insulating glass particles increased the interparticle (electrostatic) forces, while the conducting stainless steel particles were able to dissipate charging, resulting in a smaller interparticle attraction. This difference in material charging resulted in the negligible dependence of material density. However, in the current work, electrostatic interactions are eliminated in the liquid environment, leaving the material density (gravitational force) to dominate the pickup of particles. Fig. 5 also shows the theoretical pickup velocity of a single glass sphere calculated from the force balance described in Section 1. The model underpredicts the experimental pickup velocity for all particle sizes, and does not capture the existence of a minimum pickup velocity. This is similar to what Hayden et al. found in their analysis. The underprediction is likely due to the simplification in the adhesion force term, which did not include the effects of multiple particles, variations in particle shape, or the existence of additional interparticle forces. Fig. 6 gives a direct comparison of the entrainment behavior for glass spheres in both water and air, with the latter data taken from Hayden et al. [1]. The pickup velocity data have been incorporated into the reported dimensionless Reynolds number, which was calculated for flow directly above the particle pile. Error bars are included, but are too small to be seen in the figure. Both sets of data were collected in nearly identical experimental systems, so differences seen in the figure are assumed to be a function of fluid type. It is clear that for all particle sizes investigated here, the Reynolds number required for particle entrainment is greater in air than it is in water. This is
For particles less than 450 μm entrained in water, a minimum pickup velocity exists due to the dependence of dominant forces on particle size. As was shown previously, small particle entrainment is dominated by interparticle forces, while inertial forces dominate the pickup of larger particles. For the parameters investigated here, particle shape has a negligible effect on the pickup velocity, but nonspherical particles have a broader range of pickup velocity than spherical particles at a given diameter due to more random packing. Comparison of the liquid–solids data to previously reported gas– solids data shows the effect of fluid type on pickup velocity. The effects of electrostatic forces and liquid bridging are eliminated in liquid environments, so the Reynolds number directly above the particles as they are entrained is smaller in water than it is in air. The buoyancy and lift forces are also affected by fluid type, and it was found that the increased buoyancy force in liquid is partially offset by the decrease in lift force. The minimum Reynolds number occurs at smaller particle sizes in liquids because the effects of electrostatic and liquid bridging forces, which dominate in intermediate particle sizes (20–50 μm) in gases, are no longer present in liquids. This means that inertial forces begin to dominate at smaller particle sizes in liquid media. Acknowledgments The authors are grateful to the American Chemical Society — Petroleum Research Fund (#44508-G9), Mo-Sci Corporation (Rolla, MO), and undergraduate research students Debra Terrell, Aaron Hanewinkel, and Shaye Bouckaert. References [1] K. Hayden, K. Park, J. Curtis, Effect of particle characteristics on particle pickup velocity, Powder Technol. 131 (1) (2003) 7–14. [2] F. Cabrejos, G. Klinzing, Incipient motion of solid particles in horizontal pneumatic conveying, Powder Technol. 72 (1992) 51–61. [3] P. Saffman, The lift on a small sphere in a shear flow, J. Fluid Mech. 22 (2) (1965) 385–400. [4] P. Stevenson, F. Cabrejos, R. Thorpe, Incipient motion of particles on a bed of like particle in hydraulic and pneumatic conveying, 4th World Congress of Particle Technology, Sydney, July 21–25, Paper 400, 2002. [5] M. Wicks, Transport of solids at low concentration in horizontal pipes, in: I. Zandi (Ed.), Advances in Solid–Liquid Flow in Pipes and its Application, Pergamon Press, New York, 1971, pp. 101–124. [6] H. Kalman, A. Satran, D. Meir, E. Rabinovich, Pickup (critical) velocity of particles, Powder Technol. 160 (2005) 103–113. [7] E. Rabinovich, H. Kalman, Pickup, critical, and wind threshold velocities of particles, Powder Technol. 176 (2007) 9–17. [8] E. Rabinovich, H. Kalman, Generalized master curve for threshold superficial velocities in particle–fluid systems, Powder Technol. 183 (2008) 304–313. [9] Y. Niño, F. Lopez, M. Garcia, Threshold for particle entrainment into suspension, Sedimentology 50 (2003) 247–263. [10] C. Ling, Criteria for incipient motion of spherical sediment particles, J. Hydraul. Eng. (1995) 472–478. [11] F. Wu, Y. Chou, Rolling and lifting probabilities for sediment entrainment, J. Hydraul. Eng. (2003) 110–119. [12] M. Abdelrhman, J. Paul, W. Davis, Analysis procedure for and application of a device for simulating sediment entrainment, Mar. Geol. (1996) 337–350.