Analytical Prediction of Particle Detachment from a Flat Surface by Turbulent Air Flows

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1 Chiang Mai J. Sci. 2011; 38(3) 503 Chiang Mai J. Sci. 2011; 38(3) : Short Communication Analytical Prediction of Particle Detachment from a Flat Surface by Turbulent Air Flows Nakorn Tippayawong* and Ittichai Preechawuttipong Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand. *Author for correspondence; nakorn.t@cmu.ac.th Recieved: 22 April 2010 Accepted: 4 June 2011 ABSTRACT Detachment of deposited particles in turbulent air flows has been theoretically investigated, based on a quasi-static, critical moment model. Micrometer and submicrometer particles were considered in this study. Forces, i.e. adhesion, gravitation, aerodynamic lift and drag, and moments of these forces acting on particles deposited to a surface were considered and calculated as a function of particle size, and particle/surface system. Critical velocities of air flows for particle detachment were determined, and compared with experimental results from literature. The analytical prediction and experimental data were found to be in reasonable agreement. Trends between the two were similar. The analytical solutions predicted that the effect of aerodynamic drag played an important role in removal of fine particles from the surface. Critical velocity was found to increase with a decrease in particle size. Keywords: adhesion, deposition, detachment, fine particle, moment balance. 1. INTRODUCTION Detachment of deposited particles due to turbulent fluid flow is important in the interaction between the atmosphere and various surfaces, and in many industrial processes. When the flow velocity is sufficiently high, the deposited particles will detach from the surface and resuspend. This phenomenon influences various unit operations. For example, in hard disk drive industry, micrometer- and submicrometer-sized particles generated during fabrication and assembly can deposit, detach and resuspend in the assembly line and containment. Consequently, these particulate contaminants can lead to fatal flaws in finished devices. Understanding particle adhesion and removal from surfaces is very important in quality control of these products. As feature sizes continue to reduce [1], means to remove these fine particles will be crucial in this industry. There are a number of different models and data for the detachment process of particles adhering to a surface [2-5]. Among them, the moment balance model was often used to analyze the forces acting on the particles. Most previous studies reported on supermicrometer sized particles ( μm). There has been rather limited research on detachment and resuspension of micrometer particles with relative size close to critical dimension in microelectronics industry. The aim of this study is therefore to

2 504 Chiang Mai J. Sci. 2011; 38(3) theoretically investigate the detachment and resuspension mechanism of microparticles deposited on a surface, taking into account forces and moments acting on them. The present study involves applying simple analytical models of particle forces due to turbulent flows from existing literature to resuspension, evaluating the critical velocity and comparing it with experimental data. 2. DETACHMENT MECHANISM AND MODELING Particle behaviour depends on its size range. Equations governing the particle motion are based on the particle position and acceleration, as a result of all forces acting upon it. A number of these forces depend on the nature of flow and particles being investigated. For the present study, the model and the forces acting on the particle are shown in Figure 1. The surface is assumed to be smooth. A spherical particle is assumed to submerge in a viscous sublayer where the shear flow is steady and undisturbed by the presence of the particle. Five forces are shown: (i) the mean aerodynamic drag force,, acting in the forward horizontal direction, (ii) the friction force, F f, in the reverse horizontal direction, (iii) the mean aerodynamic lift force, F l, in the upward vertical direction, (iv) the surface pull-off force, F po, in the downward vertical direction, and (v) the gravitational force, F g, in the downward vertical direction. Detachment refers to the process of breaking the adhesion bond between the particle and the surface. Resuspension occurs when the particle begins to move on the surface. Three modes are possible; (i) lifting off, F l > F po + F g (1) (ii) sliding, > F f (2) (iii) rolling, 0.87D p + 0.5sF l > sf po + 0.5sF g (3) where D p and s are the particle diameter and contact distance, respectively. The contact distance, evaluated from the paper of Johnson et al. [6] is s = in which γ is the surface energy of adhesion. K is the composite Young s modulus given by K = where E p and E s are the values of Young s modulus and ν p and ν s are the values of Poisson s ratio for the particle and the surface, respectively. The adhesion force consists of the van der Waals force, the force arising from surface tension of adsorbed liquid, and electrostatic force. The latter two forces can be neglected when relative humidity and particle charge are low. Thus, the mean adhesion force, F a, is given by Phares et al. [7], for soft contact systems, as (4a) Figure 1. Forces acting on a fine particle attached to a surface in a viscous sublayer. for hard contact systems, as F a = πγd p (4b) The surface pull-off force is estimated from F po = C fa F a (5) where C fa is a contact parameter. Ibrahim et al. [5] derived its values from surface asperity height. Tsai et al. [8] suggested that it can be derived from C fa = 0.5 exp(0.124( 0.01) ) +

3 Chiang Mai J. Sci. 2011; 38(3) in which =. The gravitational force is (6) where ε is the distance of closest approach between contact bodies, ρ p is the particle density, and g is the gravitational acceleration. The aerodynamic drag on a sphere near a surface in simple shear flow is used, with corrections made for inertial, wall and slip effects [9].Other forces such as buoyancy, virtual mass, and Basset forces are much smaller as the particle density is much larger than air. The mean aerodynamic drag force is given by Stempniewicz et al. [2] as (7) with and where ρ is the air density, μ is the air viscosity, u τ is the friction velocity, C is the Cunningham correction factor, and Kn is the Knudsen number. The mean aerodynamic lift force is given by Stempniewicz et al. [2] as (8) Having evaluated eqs. (1), (2) and (3) for these forces and moments, it was evident that rolling provides the least resistance for inception of detachment, compared to lifting off and sliding. In this work, only rolling is considered as the mechanism of initial detachment and resuspension. When a critical moment is exceeded, the particle will roll to a new position. Because at new equilibrium position, adhesion force is smaller, the particle will continue to roll. With a small but finite vertical force, lifting of the particle from the surface can then occur. This is true for smooth surfaces only. Added complications such as surface roughness and turbulent burst may affect the likelihood of detachment and resuspension, but they are not treated here. Order of magnitude analysis of the moment balance in eq. (3) showed that the aerodynamic lift and gravitational moments are negligible, compared to the aerodynamic drag and adhesion moments. Hence, inception of detachment occurs when the aerodynamic drag moment exceeds adhesion moment. 0.87D p > D p sin θ F po (9) where θ is the contact angle, defined as s/d p. Initial detachment may be characterized in terms of either a free stream velocity, U, or a friction velocity [5] as, u τ = U The moments of the two main forces were analyzed for D p = μm. The range of material properties for particle and surface types required in the calculation are listed in Table 1. Flow conditions are obtained at standard temperature and pressure. 3. RESULTS AND DISCUSSION The calculated moments due to adhesion and drag force are plotted in Figure 2, with different flow velocities between m/s. All moments were found to increase with particle diameter. Nonetheless, the resisting moment due to adhesion and the aerodynamic drag moment intersect each other at a point where they are equal. Beyond this point where the drag moment is greater than the adhesion moment, detachment and resuspension will occur. It was shown that the aerodynamic drag moment was rather small, compared to the adhesion moment at submicrometer particle range. To completely resuspend particles with size of 4 μm or greater, flow velocity of around 50 m/s may be required. This was in similar magnitude to those reported by Theerachaisupakij et al. [10], Soltani and Ahmadi [11], and Yiantsios and Karabelas [12] whose critical flow velocities were 25-35, 40-50, and 60 m/s for 4 μm particles,

4 506 Chiang Mai J. Sci. 2011; 38(3) Table 1. Particle and surface material properties. alumina glass graphite steel polystyrene γ (J/m 2 ) Ε (GPa) ν (-) ρ (kg/m 3 ) respectively. But, it was well below those reported by Harris and Davidson [13]. Figure 3 shows the critical flow velocity when particle detachment from the surface occurs, for a range of particle diameter and composite Young modulus. The composite Young modulus used were between GPa, corresponding to between For a hard particle/surface system, is less than 1.0. The calculated results were also compared against experimental results, obtained from those reported by Tsai et al. [8] and Theerachaisupakij et al. [10]. The analytical prediction and experimental data were found to be in reasonable agreement. Trends between the two were similar. Quantitatively, it was found that the critical flow velocity was more sensitive to particle size than that predicted by the quasi-static model. However, accurate estimate of surface properties is crucial in predicting the critical flow velocity of fine particle from a surface. In general, the critical flow velocity increases with a decrease in particle size. Higher velocities correspond to easier resuspension. A hard particle/surface system can be detached with less difficulty than a soft system. The soft system (K = 0.1 and 1 GPa) appeared to require high velocity to be detached. It should be noted that detachment and resuspension occur suddenly while the quasisteady, critical moment model adopted here only describes detachment when forces are applied infinitely slowly. Dynamics of particle detachment may occur too quickly to maintain equilibrium. A dynamic resuspension model may be required to address the kinetics of particle resuspension. Nonetheless, the current model can provide useful information about the initial state of particle/surface system and demonstrate the importance of aerodynamic drag in removing the deposited particles. Figure 2. Comparison of moments to hold and reentrain the particle, solid line: adhesion moment, broken lines: drag force moment. Figure 3. Critical flow velocity as a function of particle diameter and composite Young modulus for detachment from a surface, lines: calculated results, symbols: experimental data.

5 Chiang Mai J. Sci. 2011; 38(3) CONCLUSION Investigation of particle detachment from a surface has analytically been studied. The forces and moments acting on fine particles were modeled, taking into account aerodynamic drag, lift, adhesion, friction and gravitation. Factors influencing detachment process such as flow condition, particle size and type were considered. From the study, it was shown that models describing forces and moments on particles can be used as preliminary analytical tools to offer some qualitative insight into detachment and resuspension of deposited particles on a surface. Prediction of critical velocity as a function of particle size was obtained. Results indicated that the present quasi-steady, critical moment model was able to qualitatively predict the detachment of fine particles. However, accurate estimate of surface properties and kinetic model may be required to obtain better quantitative prediction of particle detachment. ACKNOWLEDGEMENTS Financial support of this research project from Industry/University Cooperative Research Center (I/UCRC) in HDD Component, the Faculty of Engineering, Khon Kaen University, and National Electronics and Computer Technology Center, National Science and Technology Development Agency, and Seagate Technology (Thailand) Co., Ltd., under contract no. CPN-R&D EM is gratefully acknowledged. REFERENCES [1] Wood R., Future Hard Disk Drive Systems, Journal of Magnetism and Magnetic Materials, 2009; 321: [2] Stempniewicz M.M., Komen E.M.J. and de With A., Model of Particle Resuspension in Turbulent Flows, Nuclear Engineering and Design, 2008; 238: [3] Ziskind G., Particle Resuspension from Surfaces: Revisited and Re-evaluated, Reviews in Chemical Engineering, 2006; 22: [4] Reeks M.W. and Hall D., Kinetic Models for Particle Resuspension in Turbulent Flows: Theory and Measurement, Journal of Aerosol Science, 2001; 32: [5] Ibrahim A.H., Dunn P.F. and Qazi M.F., Experiments and Validation of a Model for Microparticle Detachment from a Surface by Turbulent Air Flow, Journal of Aerosol Science, 2008; 39: [6] Johnson K.L., Kendall K. and Roberts A.D., Surface Energy and the Contact of Elastic Solids, Proceedings of the Royal Society of London Series A, 1971; 324: [7] Phares D.J., Smedley G.T. and Flagan R.C., Effect of Particle Size and Material Properties on Aerodynamic Resuspension from Surfaces, Journal of Aerosol Science, 2000; 31: [8] Tsai C.J., Pui D.Y.H. and Liu B.Y.H., Particle Detachment from Disk Surfaces of Computer Disk Drives, Journal of Aerosol Science, 1991; 22: [9] Pratsinis S.E. and Kim K.S., Particle Coagulation, Diffusion, and Themophoresis in Laminar Tube Flows, Journal of Aerosol Science, 1989; 20: [10] Theerachaisupakij W., Matsusaka S., Akashi Y. and Masuda H., Reentrainment of Deposited Particles by Drag and Aerosol Collision, Journal of Aerosol Science, 2003; 34: [11] Soltani M. and Ahmadi G., Particle Detachment from Rough Surfaces in Turbulent Flows, Journal of Adhesion, 1995; 51: [12] Yiantsios S.G. and Karabelas A.J., Detachment of Spherical Microparticles Adhering on Flat Surfaces by Hydrodynamic Forces, Journal of Colloid and Interface Science, 1995; 176: [13] Harris A.R. and Davidson C.I., Particle Resuspension in Turbulent Flow: A Stochastic Model for Individual Soil Grains, Aerosol Science and Technology, 2008; 42: