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Interactions between fine combustion droplets
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Powder Technology 185 (2008) 267 – 273 www.elsevier.com/locate/powtec
Interactions between fine combustion droplets Changfu You ⁎, Hailiang Zhao, Bin Huang, Haiying Qi, Xuchang Xu Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China Received 15 August 2006; received in revised form 3 September 2007; accepted 27 October 2007 Available online 6 November 2007
Abstract Interactions between fine combustion droplets were directly observed using microscopic flow visualization and high speed photography. The observations revealed “attracting–revolving–repulsing” interactions between the droplets. Force analyses showed that the traditionally considered interparticle forces, including drag, gravitation, the Coulomb force and the van der Waals force, cannot explain these interactions. However, the induced dipoles on the droplets due to the non-uniform distribution of surface charges on the fine droplets have important influence on such interactions. Therefore, the inter-dipole forces must be taken into account in the interaction force analysis as well as the Coulomb force between the net charges. The inter-dipole force includes components in the radial and azimuthal directions and is inversely proportional to r4. This force causes the particles to revolve and repel each other at small distance. The combined effects of the inter-dipole force and the traditionally considered forces give a complete explanation for the particle interactions. © 2007 Elsevier B.V. All rights reserved. Keywords: Fine combustion droplets; Particle interaction; Coagulation; Interparticle force; Inter-dipole force
1. Introduction Inhalable particulate matter has become a much more serious atmospheric pollutant with most coming from combustion processes in power plants, industrial machines and vehicles. The rapid progress in the study of particulate control has led to interest on very fine particles. Particles with sizes less than 2.5 μm (PM2.5) can enter and remain in the human lungs while particles smaller than 1 μm (PM1) can penetrate the deeper alveolar regions, causing chronic lung damage. Unfortunately, the capture efficiencies of these fine particles by cyclones, electrostatic precipitators (ESPs) and filters are all relatively low. The most important way to improve the capturing efficiency is to promote coagulation or aggregation of fine particle into larger particles. Therefore, increasing efforts have been focused on particle interaction or aggregation mechanisms
⁎ Corresponding author. Fax: +86 10 62770209. E-mail address: [email protected] (C. You). 0032-5910/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.10.023
for submicron combustion particles, including solid soot precursors and coagulated droplets produced in combustion process. The interactions and aggregation of fine particles are also important phenomena in many other areas, such as colloid sciences, water treatment, electrophotography, semiconductor processing, and pharmaceuticals. These researches covered solid particles or liquid droplets in air or liquid/water medium. The word particle is used extensively herein including solid particles and liquid droplets. The modelling of the coagulation of fine particles has been studied for many years after the first attempt by Smoluchowski [1], who gave a basic equation for the change rate of the number concentration of aggregates of certain sizes. The equation has formed the core of almost all subsequent research into coagulation modelling, so subsequent developments can be considered as specific modifications of the original equation. Thomas et al. [2] gave a detailed review of recent coagulation modelling work. In Thomas's review, the collision efficiency, α, and the collision frequency, β, were identified as two core parameters in the of coagulation rate model. The collision efficiency and collision frequency are modeled differently for
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C. You et al. / Powder Technology 185 (2008) 267–273
different conditions depending on the interparticle forces, intensity of fluid mixing, particle concentration and size distribution, particle shapes, particle surface chemistry in continuous medium and many other factors. Many simulations have investigated the influence of these various factors on the coagulation rate, along with the investigations of the effect of gravity, convection, interparticle forces, size heterogeneities and so on [2–9]. Experimental studies on the coagulation of fine particles have mostly focused on polystyrene Latex or amorphous silica suspensions in water or other liquid solutions [4,7,8,10,11]. Most of the experimental work have measured changes in the particle concentrations in the solutions using laser techniques and Coulter counters. Only Folkersma et al. [4,11] reported visual observations of perikinetic coagulation in a polystyrene Latex suspension with about 2 μm particles, but they did not analyze the interparticle forces. Calculations and experimental studies of Brownian coagulation resulted in a coagulation zone diagram for a particle diameter of 3 μm, considering various interparticle forces, such as the van der Waals force, electrical forces and hydrodynamics. The coagulation and non-coagulation zones were divided by a graphical plane based on surface potential and ionic strength [6,7]. The results show that for some conditions the coagulation rate is very low as to zero, but is much higher for other conditions. The analysis of particle interactions in aerosols of fine particles mixed with air has also long been of interest in various fields [12–15]. Because of the low viscosity of air, the particle interactions are much more rapid in air than in liquids. Therefore, visual observations of the particle interactions are much more difficult and have not been reported to our knowledge. In air-particle systems, the interparticle forces become more important, while the influences of particle and solution chemistry become negligible. The macroscopic flow and the coagulation are both affected by the interparticle forces. The interaction forces between particles include the long-range forces, such as electrostatic and van der Waals forces, and contact forces, for example the capillary force, solid bridging or mechanical interlocking forces. There have been many studies
Fig. 1. Experimental Setup.
Fig. 2. Droplet size distribution.
of the particle interaction forces in the literature [12,13,16–20]. However, direct microscopic observations of the interactions between fine particles are needed to accurately analyze the forces. In this research, microscopic flow visualization and high speed photography were utilized to observe the dynamical interactions between fine combustion droplets in air. The aim is to investigate the mechanisms governing the particle interactions and to analyze the interaction forces acting between fine droplets based on the kinematic observations. 2. Experimental setup and droplet parameters Fig. 1 shows the experimental setup. A rectangular channel made of optical glass was mounted on a microscope platform under the objective, with the fine combustion droplets flowing slowly in air through the channel. A high speed CCD camera was attached to the microscope eyepiece. The aerosol flow was magnified by the microscope and then captured by the high speed camera linked to a computer. The flows were also observed on the monitor. This microscopic high speed PIV/PTV system has been described in detail in a previous paper [21]. The PIV/PTV system was able to measure the velocities and diameters of the fine droplets. For convenience, the fine combustion droplets were from burning cigarettes burning naturally in the tank with the smoke flowing from the tank. The microscopic observation shows that cigarettes burning smoke prevailingly composed by oil-like droplets. A camera speed of 125 fps was used. The observed area is 750 μm × 700 μm. The smoke droplet velocities measured by the microscopic high speed PIV/PTV system were mostly in the range of 50–250 μm/ s. The number concentration of the droplets measured by the imaging method was about 360 /mm3. Folkersma et al. [4,11] used a microscope and a regular speed CCD camera in their observations of particle interactions in water, since the particle interactions in liquids are relatively slow compared to the interactions in air. In addition, the magnifying effects of the microscope made the high speed camera indispensable in the current experiments. Particle diameters and surface charge distributions are the most important parameters controlling the interactions of fine
C. You et al. / Powder Technology 185 (2008) 267–273
Fig. 3. Droplet charge distribution.
particles. There are many techniques for particle sizing, including the Coulter counter, which is frequently used in studying of coagulation in liquids [4,7,11]. For the sizing of fine particles in air, a commercially available electrical lowpressure impactor (ELPI) provides a wide size range and high accuracy. Its performance and applications have been well documented [22–25]. The ELPI applies charges to aerosol particles using a corona, with the charged particles then introduced into a 13-stage impactor. Each impactor stage functions as a Faraday well to detect the level of electrostatic charge of the deposited particles. The detected charge level is then related to the particle size which allows for a particle size distribution to be constructed between the size limits (0.03– 10 μm) of the impactor. In this study, part of the aerosol was drawn into the ELPI after dilution, which gave the number distribution of the droplet diameters shown in Fig. 2. The smoke droplet diameters had a bimodal distribution with peaks at 0.03 μm and 0.2–0.4 μm. Studies of combustion soot have shown that soot particles are formed as aggregates of primary particles with diameters of 0.01–0.03 μm, with the diameters of the aggregated soot particles in the range of 0.1–1.0 μm [26]. The combustion soot
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precursors include coagulated droplets and solid particles. The current ELPI measurements are comparable with previous soot data, with the bimodal distribution indicating the primary and secondary particles. The lower limit of the particle size resolution is usually about 2 μm with microscopic photography systems. Fine particles less than 2 μm most create a blurred spot which cannot indicate the real size [27,28]. The current microscopic visualization system has a resolution limit of 1.5 μm with clear images of particles larger than 1.5 μm and blurred spots for the smaller particles, which were more numerous. Therefore, accurate particle size could not be obtained from the images, but the particles were estimated to vary from near submicron to several microns in size. The particles captured in the video images, which were then analyzed in the experiments, then did not have the same size distribution as measured by the ELPI. Studies of the electrostatic properties of aerosols have progressed slowly mostly due to a lack of suitable instrumentation for measuring the particle charges. Glover and Chan [29] reported a novel technique for measuring particle charges together with sizes using the ELPI. The innate electrostatic charge on the aerosol particles can potentially be measured by disenabling the corona charging mechanism in the ELPI. Actually, the charge measured by the ELPI is the average charge of all the particles deposited on each impactor stage. The operation was described in detail by Glover and Chan [29]. The charge distribution on the smoke droplets was measured as shown in Fig. 3 which showed that droplets of different sizes could have different polarities. The droplet size dependence of the charges was also reported by Glover and Chan [29] for pharmaceutical aerosols. This dependence may be caused by different charge mechanisms in different processes. The measured charges on most smoke droplets had less than 10 elementary units of charge per droplet. Karasev et al. [26] measured similar charges on soot aggregates. 3. Discussion of results Fig. 4 shows two successive droplet images from a video with a time interval of 0.016 s. The dynamic observations of the
Fig. 4. Successive droplet images.
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droplet interactions must be made from the video with just two frames given here for an example. The observations of the droplet motions showed that the droplets tended to form transient doublets. When two droplets approached rather closely, they formed a couple due to the strong interactions them but with only very weak interactions with other droplets. The interactions between the coupled droplets involved attraction, rotational and repulsive phases. Fig. 5 shows successive magnified images of one droplet doublet indicating the typical interaction processes (these 7 images are just to show
Fig. 6. The typical interaction tracks of two coupled droplets.
Fig. 5. The typical interaction process of a droplet doublet.
the interaction stages, the time intervals between each image are not equal). The continuous and dashed circles indicate the two coupled droplets. As the two droplets approach each other, diffusion and fluid drag cause them to accelerate towards each other in the attraction phase and to revolve around each other with oscillations of the distance between the droplets. When they approach very close to each other, they begin to repel each other and lose contact. These droplet doublets frequently formed and broke apart so they are referred to as transient doublets. A whole interaction process of transient doublets lasted for about 1 s. These interactions in aerosols are much faster than observed in water by Folkersma et al. [4,11] which lasted nearly 50 s, even though there are some similarities in the interaction behavior. These phenomena were observed many times with various humidity levels for various kinds of particles and/or droplets, including soot particles from oil flames and smoke from burning incense. Thus, these attracting, revolving and repulsing interactions are very repeatable. The similar phenomenon was found in the studies for two particles falling process, such as the drafting–kissing–tumbling event [30,31]. In our earlier study [31], the phenomenon refers to nonlinear interactions between two spheres where the trailing sphere is first drawn into the wake of the leading sphere, it touches it, and then overtakes the leading sphere by tumbling around it. Here, the trail vortex following the leading sphere is a dominant reason. As to the current case, the Reynolds number of the combustion droplet is less than 1. The influence of the wake following it is negligible. Brownian motion was also observed in the droplet flows, but due to its small time and space scales, the irregular Brownian motion had little influence on the macroscopic droplet interactions. Analyses of the interactions between pairs of droplet were made on a plane perpendicular to the direction of sight. The two most important parameters were their projected interaction distance (i.e., the projection of the distance between the two droplet centers onto the plane) and projected interaction angle
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Fig. 7. Variation of the projected interaction. Fig. 9. Variation of the droplet approach velocity.
(i.e., the projected angle between the line connecting the two droplet centers and the direction of gravity, on the observation plane). Although errors exist in the projections, these analyses were very useful for understanding the interaction processes. Fig. 6 shows typical interaction tracks in the observation plane of a droplet doublet for a period of one second. The tracks show them experiencing the attraction, rotation and repulsion interaction stages. Fig. 7 shows the variations of the projected interaction distances between the coupled droplets. Fig. 8 shows the variations of the projected interaction angles (the orientation of droplet 2 relative to droplet 1) during this interaction (the reference direction is the horizontal axis with positive rotations being counter-clockwise). Fig. 9 shows the variations of the droplet approach velocity (positive values represent moving apart). These figures show that the coupled droplets initially attract each other and accelerate towards each other until they are very close, at the same time, the droplet motions are accompanied with oscillations and rotations. When the droplets reached the smallest separation distances at t = 0.35 s and 0.6 s, the rotation velocity increase rapidly with the approach velocity
changed direction with the droplets beginning to move away from each other. The oscillations and rotations also occurred as they moved away from each other. The droplet interactions involving attraction, rotation and repulsion represent typical interactions between fine particles. They directly influence the macroscopic flow characteristics of the aerosols, including coagulation, diffusion and sedimentation. Interestingly, droplet contact and coagulation were not frequently observed in the experiments. Also, Folkersma et al. [4,11] did not report particle contact in their visual observations of 2 μm latex particles in water. Combustion particles are known to mostly aggregate into primary 10–30 nm particles with frequent coagulation of these primary nanometer particles. This usually occurs in the flame or near flame regions. However, the coagulation of micron or near submicron particles is controlled by different mechanisms. As pointed out by Han and Lee [7], the occurrence of coagulation depends on a variety of parameters. The smoke droplets observed in this experiment were not the primary particles but micron or submicron particles far from the flame that have already coagulated or aggregated to some extent. Therefore, these interactions may be typical for this kind of particles in air. 4. Interaction force analysis
Fig. 8. Variation of the projected interaction angle.
The observed interactions between fine droplets were used to evaluate the interparticle forces. Since all these interactions occurred without direct contact, contact forces and deformation of droplet surfaces were not considered. Normally, the forces acting on particles considered in the literature include gravity, drag, the van der Waals force and the electrostatic Coulomb force. The average droplet diameter is in the order of micron and the Knudsen number is calculated to be 0.07. In this regime, the flow is still continuum flow and the normal drag force formula can apply [32]. The changes in the magnitudes of these forces with the interparticle distances are compared in Fig. 10 as for the average droplet parameters in this experiment (opposite charges). When the distances are relatively large, both the drag
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Fig. 10. Effect of distance in Interaction forces.
force and the electrostatic Coulomb force are significant while gravity and the van der Waals forces can be neglected. When the distance decreases to less than 7 μm, the electrostatic Coulomb force increases rapidly and exceeds the drag force as the dominant force. For distances less than 2 μm, the van der Waals force begins to increase rapidly and exceeds the drag force, but it is still negligible compared with the electrostatic force. When the droplets are relatively far apart (N 10 μm) the drag force is dominant. According to the Stokes–Einstein analysis of Brownian motion, the drag force causes the net particle diffusion [15]. When two droplets approach due to diffusion, the electrostatic Coulomb force increases to become the dominant force exceeding the diffusion force, and attracts the droplet to each other (droplets with the same polarity will repel while oppositely charged droplets will attract). Oppositely charged droplets then accelerate towards each other with the Coulomb force increasing with decreasing distance. With no other forces, the droplets must collide. However, the experiments showed that droplets did not collide as they were attracted close to each other but were repelled from each other with droplet rotation. Therefore, other forces must act on the droplets to produce the observed interactions. Results in the literature and the current ELPI measurements both support that the fine particles usually acquire only several elementary units of charge (0–10 in this experiment), so the charge distribution on the particle surface must be very nonuniform [33–36]. The surface charge distribution then has an important influence on the particle interactions. Basic electrostatics principles indicate that this non-uniform charge distribution will induce dipoles on the particle surface. As shown in Fig. 11, the non-uniformly distributed charges on a particle
Fig. 12. Interaction forces comparison.
can be described by an equivalent combination of the net charge and the induced dipole. Therefore, when two particles approach, the electrostatic forces include not only the Coulomb force between the net charges but also the force between the induced dipoles. According to electrostatics, the forces between two dipoles with dipole moments of p1 and p2 are [37]: The radial component: Fr ¼
3P1 P2 1 3cos2 h r4 4pe0
The azimuthal component: Fh ¼
6P1 P2 sinh cosh r4 4pe0
where θ is the orientation angle of particle 2 relative to the dipole direction of particle 1. The inter-dipole forces on the droplets are compared with the other forces in Fig. 12. The results show that the inter-dipole forces, which are inversely proportional to r 4 , are short-range forces compared with the other forces. When the interparticle distance is small enough, these forces are dominant, exceeding even the Coulomb force. Depending on the polarities of the droplet charges and the relative positions (θ), the radial component of the inter-dipole force can be either attractive or repulsive. The azimuthal component makes the droplets rotate around each other in a direction tangent to the line connecting the two droplets. These forces cause the droplets to rotate and to repel each other at small separation distances. The combined
Fig. 11. Equivalence between non-uniform charge and the combination of a net charge and an induced dipole.
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effects of this force together with the Coulomb and diffusion forces give a complete explanation of the experimentally observed interactions involving attraction, rotation and repulsion. Sine no droplet contact or coagulation was observed and the force analysis was made within the domain of non-contact interaction, the contact forces and the deformation of droplet surface had negligible effect on such procedure. Therefore, the analysis in above can also be made upon the interaction between fine particles of different nature such as solid soot or liquid aerosol. Because the relative orientations of the two droplets vary during the interactions, the magnitudes and directions of the inter-dipole forces also vary.The surface geometries and charge distributions on each droplet in a particle doublet vary widely, so accurate, dynamic descriptions of these forces and the droplet motions caused by these forces will require detailed simulations. Further work to simulate these forces will average geometries and charge distributions to qualitatively explain the droplet interactions. Moreover, the interaction between droplets of diverse parameters and flow conditions need more simulation study to extend this analysis method for other fine particles, such as varying Knudsen number, combustion condition and flow parameters etc. 5. Conclusions Microscopic observations showed that the interactions between fine (micron or submicron) combustion droplets involves attraction, rotation and repulsion of the droplets. The traditional interparticle forces can not explain all of these interactions. Nonuniform surface distributions of the droplet charges must create induced dipoles that result in interparticle forces that must be added to the Coulomb force between the droplets. The combination of the inter-dipole forces, the Coulomb force and the diffusion force give a reasonable explanation of the interactions. Acknowledgement This research was supported by the Special Funds for Major State Basic Research Projects (No. 2002CB211604). References [1] M. Smoluchowski, Z. Phys. Chem. 92 (1917) 129. [2] D.N. Thomas, S.J. Judd, N. Fawcett, Water Res. 33 (1999) 1579. [3] R. Folkersma, H.N. Stein, J. Colloid Interface Sci. 206 (1998) 494.
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[4] R. Folkersma, A.J.G. van Diemen, H.N. Stein, Adv. Colloid Interface Sci. 83 (1999) 71. [5] X.Y. Li, J.J. Zhang, J. Colloid Interface Sci. 262 (2003) 149. [6] M. Han, H. Lee, D.F. Lawler, S. Choi, Water Sci. Technol. 36 (1997) 69. [7] M. Han, H. Lee, Colloids Surf., A Physicochem. Eng. Asp. 202 (2002) 23. [8] Z.W. Sun, R.L. Qiao, J. Colloid Interface Sci. 223 (2000) 126. [9] J.L. Baldwin, B.A. Dempsey, Colloids Surf., A Physicochem. Eng. Asp. 177 (2001) 111. [10] M. Kobayashia, T. Maekitab, Y. Adachic, H. Sasaki, Int. J. Miner. Process. 73 (2004) 177. [11] R. Folkersma, A.J.G. van Diemen, H.N. Stein, J. Colloid Interface Sci. 206 (1998) 482. [12] V. Arunachalam, R.R. Lucchese, W.H. Marlow, Phys. Rev. E. 60 (1999) 2051. [13] K. Kendall, C. Stainton, Powder Technol. 121 (2001) 223. [14] X.M. Zeng, G.P. Martin, C. Marriott, Particulate interactions in dry powder formulations for inhalation, Taylor & Francis, London, 2001, p. 1. [15] W.C. Hinds, Aerosol Technology: properties, behavior, and measurement of airborne particles, John Wiley & Sons, New York, 1999, p. 141. [16] D.S. Rimai, D.J. Quesnel, J. Adhes. 78 (2002) 413. [17] J. Visser, Powder Technol. 58 (1989) 1. [18] S.W. Montgomery, M.A. Franchek, V.W. Goldschmidt, J. Colloid Interface Sci. 227 (2000) 567. [19] V. Arunachalam, W.H. Marlow, J.X. Lu, Phys. Rev. E. 58 (1998) 3451. [20] J.Q. Feng, D.A. Hays, Powder Technol. 135–136 (2003) 65. [21] H.L. Zhao, C.F. You, H.Y. Qi, X.C. Xu, Atmos. Environ. 39 (2005) 3015. [22] J. Keskinen, K. Pietarinen, M. Lehtimaki, J. Aerosol Sci. 23 (1992) 353. [23] J. Keskinen, M. Marjamaki, A. Virtanen, T. Makela, R. Hillama, J. Aerosol Sci. 30 (1998) 111. [24] M.M. Mariq, D.H. Podsiadlik, R.E. Chase, Aerosol Sci. Tech. 33 (2000) 239. [25] M. Marjamaki, J. Keskenin, D.R. Chen, D.Y.H. Pui, J. Aerosol Sci. 31 (2000) 249. [26] V.V. Karasev, N.A. Ivanova, A.R. Sadykova, N. Kukhareva, A.M. Baklanov, A.A. Onischuk, F.D. Kovalev, S.A. Beresnev, J. Aerosol Sci. 35 (2004) 363. [27] Z.J. He, et al., Researching on sensitivity threshold and parameters optimization of measurement, Proc. 1st Int. Symp. of Test and Measurement, Taiyuan, China, 1995, p. 10. [28] Y.C. Guo, C. Gao, J. Chongqing, Vocational & Technical Institute (Comprehensive Ed.), 13, 2004, p. 1, (in Chinese). [29] W. Glover, H.K. Chan, J. Aerosol Sci. 35 (2004) 755. [30] G. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, Int. J. Multiph. Flow, 25 (1999) 755. [31] Y. Qiu, C.F. You, H.Y. Qi, X.C. Xu, J. Chem. Ind. Eng. 57 (2006) (in Chinese). [32] G. Tedeschi, H. Gouin, M. Elena, Exp. Fluids 26 (1999) 288. [33] D.A. Hays, Photogr. Sci. Eng. 22 (1978) 232. [34] D.A. Hays, Electric field detachment of charged particles, in: K.L. Mittal (Ed.), Particle on Surfaces: 1. Detection, Adhesion and Removal, Plenum, New York, 1988, p. 351. [35] D.A. Hays, Electrostatic adhesion of non-uniformly charged dielectric spheres, in: B.C. O'Neill (Ed.), Electrostatics 1991, Institute of Physics Conference Series, 118, Institute of Physics, Bristol, UK, 1991, p. 223. [36] M.H. Lee, J. Ayala, J. Imag. Technol. 11 (1985) 279. [37] C.G. Bao, Principles of electrostatics, Beijing Institute of Technology Press, Beijing, 1993, p. 77, (in Chinese).
Powder Technology 185 (2008) 267 – 273 www.elsevier.com/locate/powtec
Interactions between fine combustion droplets Changfu You ⁎, Hailiang Zhao, Bin Huang, Haiying Qi, Xuchang Xu Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China Received 15 August 2006; received in revised form 3 September 2007; accepted 27 October 2007 Available online 6 November 2007
Abstract Interactions between fine combustion droplets were directly observed using microscopic flow visualization and high speed photography. The observations revealed “attracting–revolving–repulsing” interactions between the droplets. Force analyses showed that the traditionally considered interparticle forces, including drag, gravitation, the Coulomb force and the van der Waals force, cannot explain these interactions. However, the induced dipoles on the droplets due to the non-uniform distribution of surface charges on the fine droplets have important influence on such interactions. Therefore, the inter-dipole forces must be taken into account in the interaction force analysis as well as the Coulomb force between the net charges. The inter-dipole force includes components in the radial and azimuthal directions and is inversely proportional to r4. This force causes the particles to revolve and repel each other at small distance. The combined effects of the inter-dipole force and the traditionally considered forces give a complete explanation for the particle interactions. © 2007 Elsevier B.V. All rights reserved. Keywords: Fine combustion droplets; Particle interaction; Coagulation; Interparticle force; Inter-dipole force
1. Introduction Inhalable particulate matter has become a much more serious atmospheric pollutant with most coming from combustion processes in power plants, industrial machines and vehicles. The rapid progress in the study of particulate control has led to interest on very fine particles. Particles with sizes less than 2.5 μm (PM2.5) can enter and remain in the human lungs while particles smaller than 1 μm (PM1) can penetrate the deeper alveolar regions, causing chronic lung damage. Unfortunately, the capture efficiencies of these fine particles by cyclones, electrostatic precipitators (ESPs) and filters are all relatively low. The most important way to improve the capturing efficiency is to promote coagulation or aggregation of fine particle into larger particles. Therefore, increasing efforts have been focused on particle interaction or aggregation mechanisms
⁎ Corresponding author. Fax: +86 10 62770209. E-mail address: [email protected] (C. You). 0032-5910/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.10.023
for submicron combustion particles, including solid soot precursors and coagulated droplets produced in combustion process. The interactions and aggregation of fine particles are also important phenomena in many other areas, such as colloid sciences, water treatment, electrophotography, semiconductor processing, and pharmaceuticals. These researches covered solid particles or liquid droplets in air or liquid/water medium. The word particle is used extensively herein including solid particles and liquid droplets. The modelling of the coagulation of fine particles has been studied for many years after the first attempt by Smoluchowski [1], who gave a basic equation for the change rate of the number concentration of aggregates of certain sizes. The equation has formed the core of almost all subsequent research into coagulation modelling, so subsequent developments can be considered as specific modifications of the original equation. Thomas et al. [2] gave a detailed review of recent coagulation modelling work. In Thomas's review, the collision efficiency, α, and the collision frequency, β, were identified as two core parameters in the of coagulation rate model. The collision efficiency and collision frequency are modeled differently for
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C. You et al. / Powder Technology 185 (2008) 267–273
different conditions depending on the interparticle forces, intensity of fluid mixing, particle concentration and size distribution, particle shapes, particle surface chemistry in continuous medium and many other factors. Many simulations have investigated the influence of these various factors on the coagulation rate, along with the investigations of the effect of gravity, convection, interparticle forces, size heterogeneities and so on [2–9]. Experimental studies on the coagulation of fine particles have mostly focused on polystyrene Latex or amorphous silica suspensions in water or other liquid solutions [4,7,8,10,11]. Most of the experimental work have measured changes in the particle concentrations in the solutions using laser techniques and Coulter counters. Only Folkersma et al. [4,11] reported visual observations of perikinetic coagulation in a polystyrene Latex suspension with about 2 μm particles, but they did not analyze the interparticle forces. Calculations and experimental studies of Brownian coagulation resulted in a coagulation zone diagram for a particle diameter of 3 μm, considering various interparticle forces, such as the van der Waals force, electrical forces and hydrodynamics. The coagulation and non-coagulation zones were divided by a graphical plane based on surface potential and ionic strength [6,7]. The results show that for some conditions the coagulation rate is very low as to zero, but is much higher for other conditions. The analysis of particle interactions in aerosols of fine particles mixed with air has also long been of interest in various fields [12–15]. Because of the low viscosity of air, the particle interactions are much more rapid in air than in liquids. Therefore, visual observations of the particle interactions are much more difficult and have not been reported to our knowledge. In air-particle systems, the interparticle forces become more important, while the influences of particle and solution chemistry become negligible. The macroscopic flow and the coagulation are both affected by the interparticle forces. The interaction forces between particles include the long-range forces, such as electrostatic and van der Waals forces, and contact forces, for example the capillary force, solid bridging or mechanical interlocking forces. There have been many studies
Fig. 1. Experimental Setup.
Fig. 2. Droplet size distribution.
of the particle interaction forces in the literature [12,13,16–20]. However, direct microscopic observations of the interactions between fine particles are needed to accurately analyze the forces. In this research, microscopic flow visualization and high speed photography were utilized to observe the dynamical interactions between fine combustion droplets in air. The aim is to investigate the mechanisms governing the particle interactions and to analyze the interaction forces acting between fine droplets based on the kinematic observations. 2. Experimental setup and droplet parameters Fig. 1 shows the experimental setup. A rectangular channel made of optical glass was mounted on a microscope platform under the objective, with the fine combustion droplets flowing slowly in air through the channel. A high speed CCD camera was attached to the microscope eyepiece. The aerosol flow was magnified by the microscope and then captured by the high speed camera linked to a computer. The flows were also observed on the monitor. This microscopic high speed PIV/PTV system has been described in detail in a previous paper [21]. The PIV/PTV system was able to measure the velocities and diameters of the fine droplets. For convenience, the fine combustion droplets were from burning cigarettes burning naturally in the tank with the smoke flowing from the tank. The microscopic observation shows that cigarettes burning smoke prevailingly composed by oil-like droplets. A camera speed of 125 fps was used. The observed area is 750 μm × 700 μm. The smoke droplet velocities measured by the microscopic high speed PIV/PTV system were mostly in the range of 50–250 μm/ s. The number concentration of the droplets measured by the imaging method was about 360 /mm3. Folkersma et al. [4,11] used a microscope and a regular speed CCD camera in their observations of particle interactions in water, since the particle interactions in liquids are relatively slow compared to the interactions in air. In addition, the magnifying effects of the microscope made the high speed camera indispensable in the current experiments. Particle diameters and surface charge distributions are the most important parameters controlling the interactions of fine
C. You et al. / Powder Technology 185 (2008) 267–273
Fig. 3. Droplet charge distribution.
particles. There are many techniques for particle sizing, including the Coulter counter, which is frequently used in studying of coagulation in liquids [4,7,11]. For the sizing of fine particles in air, a commercially available electrical lowpressure impactor (ELPI) provides a wide size range and high accuracy. Its performance and applications have been well documented [22–25]. The ELPI applies charges to aerosol particles using a corona, with the charged particles then introduced into a 13-stage impactor. Each impactor stage functions as a Faraday well to detect the level of electrostatic charge of the deposited particles. The detected charge level is then related to the particle size which allows for a particle size distribution to be constructed between the size limits (0.03– 10 μm) of the impactor. In this study, part of the aerosol was drawn into the ELPI after dilution, which gave the number distribution of the droplet diameters shown in Fig. 2. The smoke droplet diameters had a bimodal distribution with peaks at 0.03 μm and 0.2–0.4 μm. Studies of combustion soot have shown that soot particles are formed as aggregates of primary particles with diameters of 0.01–0.03 μm, with the diameters of the aggregated soot particles in the range of 0.1–1.0 μm [26]. The combustion soot
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precursors include coagulated droplets and solid particles. The current ELPI measurements are comparable with previous soot data, with the bimodal distribution indicating the primary and secondary particles. The lower limit of the particle size resolution is usually about 2 μm with microscopic photography systems. Fine particles less than 2 μm most create a blurred spot which cannot indicate the real size [27,28]. The current microscopic visualization system has a resolution limit of 1.5 μm with clear images of particles larger than 1.5 μm and blurred spots for the smaller particles, which were more numerous. Therefore, accurate particle size could not be obtained from the images, but the particles were estimated to vary from near submicron to several microns in size. The particles captured in the video images, which were then analyzed in the experiments, then did not have the same size distribution as measured by the ELPI. Studies of the electrostatic properties of aerosols have progressed slowly mostly due to a lack of suitable instrumentation for measuring the particle charges. Glover and Chan [29] reported a novel technique for measuring particle charges together with sizes using the ELPI. The innate electrostatic charge on the aerosol particles can potentially be measured by disenabling the corona charging mechanism in the ELPI. Actually, the charge measured by the ELPI is the average charge of all the particles deposited on each impactor stage. The operation was described in detail by Glover and Chan [29]. The charge distribution on the smoke droplets was measured as shown in Fig. 3 which showed that droplets of different sizes could have different polarities. The droplet size dependence of the charges was also reported by Glover and Chan [29] for pharmaceutical aerosols. This dependence may be caused by different charge mechanisms in different processes. The measured charges on most smoke droplets had less than 10 elementary units of charge per droplet. Karasev et al. [26] measured similar charges on soot aggregates. 3. Discussion of results Fig. 4 shows two successive droplet images from a video with a time interval of 0.016 s. The dynamic observations of the
Fig. 4. Successive droplet images.
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droplet interactions must be made from the video with just two frames given here for an example. The observations of the droplet motions showed that the droplets tended to form transient doublets. When two droplets approached rather closely, they formed a couple due to the strong interactions them but with only very weak interactions with other droplets. The interactions between the coupled droplets involved attraction, rotational and repulsive phases. Fig. 5 shows successive magnified images of one droplet doublet indicating the typical interaction processes (these 7 images are just to show
Fig. 6. The typical interaction tracks of two coupled droplets.
Fig. 5. The typical interaction process of a droplet doublet.
the interaction stages, the time intervals between each image are not equal). The continuous and dashed circles indicate the two coupled droplets. As the two droplets approach each other, diffusion and fluid drag cause them to accelerate towards each other in the attraction phase and to revolve around each other with oscillations of the distance between the droplets. When they approach very close to each other, they begin to repel each other and lose contact. These droplet doublets frequently formed and broke apart so they are referred to as transient doublets. A whole interaction process of transient doublets lasted for about 1 s. These interactions in aerosols are much faster than observed in water by Folkersma et al. [4,11] which lasted nearly 50 s, even though there are some similarities in the interaction behavior. These phenomena were observed many times with various humidity levels for various kinds of particles and/or droplets, including soot particles from oil flames and smoke from burning incense. Thus, these attracting, revolving and repulsing interactions are very repeatable. The similar phenomenon was found in the studies for two particles falling process, such as the drafting–kissing–tumbling event [30,31]. In our earlier study [31], the phenomenon refers to nonlinear interactions between two spheres where the trailing sphere is first drawn into the wake of the leading sphere, it touches it, and then overtakes the leading sphere by tumbling around it. Here, the trail vortex following the leading sphere is a dominant reason. As to the current case, the Reynolds number of the combustion droplet is less than 1. The influence of the wake following it is negligible. Brownian motion was also observed in the droplet flows, but due to its small time and space scales, the irregular Brownian motion had little influence on the macroscopic droplet interactions. Analyses of the interactions between pairs of droplet were made on a plane perpendicular to the direction of sight. The two most important parameters were their projected interaction distance (i.e., the projection of the distance between the two droplet centers onto the plane) and projected interaction angle
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Fig. 7. Variation of the projected interaction. Fig. 9. Variation of the droplet approach velocity.
(i.e., the projected angle between the line connecting the two droplet centers and the direction of gravity, on the observation plane). Although errors exist in the projections, these analyses were very useful for understanding the interaction processes. Fig. 6 shows typical interaction tracks in the observation plane of a droplet doublet for a period of one second. The tracks show them experiencing the attraction, rotation and repulsion interaction stages. Fig. 7 shows the variations of the projected interaction distances between the coupled droplets. Fig. 8 shows the variations of the projected interaction angles (the orientation of droplet 2 relative to droplet 1) during this interaction (the reference direction is the horizontal axis with positive rotations being counter-clockwise). Fig. 9 shows the variations of the droplet approach velocity (positive values represent moving apart). These figures show that the coupled droplets initially attract each other and accelerate towards each other until they are very close, at the same time, the droplet motions are accompanied with oscillations and rotations. When the droplets reached the smallest separation distances at t = 0.35 s and 0.6 s, the rotation velocity increase rapidly with the approach velocity
changed direction with the droplets beginning to move away from each other. The oscillations and rotations also occurred as they moved away from each other. The droplet interactions involving attraction, rotation and repulsion represent typical interactions between fine particles. They directly influence the macroscopic flow characteristics of the aerosols, including coagulation, diffusion and sedimentation. Interestingly, droplet contact and coagulation were not frequently observed in the experiments. Also, Folkersma et al. [4,11] did not report particle contact in their visual observations of 2 μm latex particles in water. Combustion particles are known to mostly aggregate into primary 10–30 nm particles with frequent coagulation of these primary nanometer particles. This usually occurs in the flame or near flame regions. However, the coagulation of micron or near submicron particles is controlled by different mechanisms. As pointed out by Han and Lee [7], the occurrence of coagulation depends on a variety of parameters. The smoke droplets observed in this experiment were not the primary particles but micron or submicron particles far from the flame that have already coagulated or aggregated to some extent. Therefore, these interactions may be typical for this kind of particles in air. 4. Interaction force analysis
Fig. 8. Variation of the projected interaction angle.
The observed interactions between fine droplets were used to evaluate the interparticle forces. Since all these interactions occurred without direct contact, contact forces and deformation of droplet surfaces were not considered. Normally, the forces acting on particles considered in the literature include gravity, drag, the van der Waals force and the electrostatic Coulomb force. The average droplet diameter is in the order of micron and the Knudsen number is calculated to be 0.07. In this regime, the flow is still continuum flow and the normal drag force formula can apply [32]. The changes in the magnitudes of these forces with the interparticle distances are compared in Fig. 10 as for the average droplet parameters in this experiment (opposite charges). When the distances are relatively large, both the drag
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Fig. 10. Effect of distance in Interaction forces.
force and the electrostatic Coulomb force are significant while gravity and the van der Waals forces can be neglected. When the distance decreases to less than 7 μm, the electrostatic Coulomb force increases rapidly and exceeds the drag force as the dominant force. For distances less than 2 μm, the van der Waals force begins to increase rapidly and exceeds the drag force, but it is still negligible compared with the electrostatic force. When the droplets are relatively far apart (N 10 μm) the drag force is dominant. According to the Stokes–Einstein analysis of Brownian motion, the drag force causes the net particle diffusion [15]. When two droplets approach due to diffusion, the electrostatic Coulomb force increases to become the dominant force exceeding the diffusion force, and attracts the droplet to each other (droplets with the same polarity will repel while oppositely charged droplets will attract). Oppositely charged droplets then accelerate towards each other with the Coulomb force increasing with decreasing distance. With no other forces, the droplets must collide. However, the experiments showed that droplets did not collide as they were attracted close to each other but were repelled from each other with droplet rotation. Therefore, other forces must act on the droplets to produce the observed interactions. Results in the literature and the current ELPI measurements both support that the fine particles usually acquire only several elementary units of charge (0–10 in this experiment), so the charge distribution on the particle surface must be very nonuniform [33–36]. The surface charge distribution then has an important influence on the particle interactions. Basic electrostatics principles indicate that this non-uniform charge distribution will induce dipoles on the particle surface. As shown in Fig. 11, the non-uniformly distributed charges on a particle
Fig. 12. Interaction forces comparison.
can be described by an equivalent combination of the net charge and the induced dipole. Therefore, when two particles approach, the electrostatic forces include not only the Coulomb force between the net charges but also the force between the induced dipoles. According to electrostatics, the forces between two dipoles with dipole moments of p1 and p2 are [37]: The radial component: Fr ¼
3P1 P2 1 3cos2 h r4 4pe0
The azimuthal component: Fh ¼
6P1 P2 sinh cosh r4 4pe0
where θ is the orientation angle of particle 2 relative to the dipole direction of particle 1. The inter-dipole forces on the droplets are compared with the other forces in Fig. 12. The results show that the inter-dipole forces, which are inversely proportional to r 4 , are short-range forces compared with the other forces. When the interparticle distance is small enough, these forces are dominant, exceeding even the Coulomb force. Depending on the polarities of the droplet charges and the relative positions (θ), the radial component of the inter-dipole force can be either attractive or repulsive. The azimuthal component makes the droplets rotate around each other in a direction tangent to the line connecting the two droplets. These forces cause the droplets to rotate and to repel each other at small separation distances. The combined
Fig. 11. Equivalence between non-uniform charge and the combination of a net charge and an induced dipole.
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effects of this force together with the Coulomb and diffusion forces give a complete explanation of the experimentally observed interactions involving attraction, rotation and repulsion. Sine no droplet contact or coagulation was observed and the force analysis was made within the domain of non-contact interaction, the contact forces and the deformation of droplet surface had negligible effect on such procedure. Therefore, the analysis in above can also be made upon the interaction between fine particles of different nature such as solid soot or liquid aerosol. Because the relative orientations of the two droplets vary during the interactions, the magnitudes and directions of the inter-dipole forces also vary.The surface geometries and charge distributions on each droplet in a particle doublet vary widely, so accurate, dynamic descriptions of these forces and the droplet motions caused by these forces will require detailed simulations. Further work to simulate these forces will average geometries and charge distributions to qualitatively explain the droplet interactions. Moreover, the interaction between droplets of diverse parameters and flow conditions need more simulation study to extend this analysis method for other fine particles, such as varying Knudsen number, combustion condition and flow parameters etc. 5. Conclusions Microscopic observations showed that the interactions between fine (micron or submicron) combustion droplets involves attraction, rotation and repulsion of the droplets. The traditional interparticle forces can not explain all of these interactions. Nonuniform surface distributions of the droplet charges must create induced dipoles that result in interparticle forces that must be added to the Coulomb force between the droplets. The combination of the inter-dipole forces, the Coulomb force and the diffusion force give a reasonable explanation of the interactions. Acknowledgement This research was supported by the Special Funds for Major State Basic Research Projects (No. 2002CB211604). References [1] M. Smoluchowski, Z. Phys. Chem. 92 (1917) 129. [2] D.N. Thomas, S.J. Judd, N. Fawcett, Water Res. 33 (1999) 1579. [3] R. Folkersma, H.N. Stein, J. Colloid Interface Sci. 206 (1998) 494.
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