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Brownian coagulation of like-charged aerosol particles

Pijush Patra and Anubhab Roy*

  • Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India

  • *Author to whom correspondence should be addressed: anubhab@iitm.ac.in
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Phys. Rev. Fluids 7, 064308 – Published 29 June, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.064308

Abstract

In this paper, we study the coagulation rate of like-charged Brownian spherical particles dispersed in a gaseous medium. Most previous calculations of the Brownian-induced coagulation rate have considered that the particle pairs interact through continuum hydrodynamics, and at a close approach, van der Waals attraction forces allow the collision and subsequent coagulation. However, the continuum approximation of the hydrodynamic interactions is no longer valid when the gap thickness between the surface is less than the mean free path of the surrounding fluid medium and the noncontinuum lubrication interactions lead to surface-to-surface contact in a finite time. We report the Brownian coagulation rate in the presence of noncontinuum lubrication resistances for a range of pair size ratios. At small separations, like-charged conducting particles almost always attract each other. Thus we also incorporate the attractive electrostatic interactions between like-charged conducting spheres in our calculation and report the effects of van der Waals and electrostatic forces on the coagulation rate of conducting spheres interacting with each other through noncontinuum hydrodynamics for a range of size and charge ratios.

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References (74)

  1. H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and Precipitation: Reprinted 1980 (Springer, Berlin, 2012).
  2. S. K. Friendlander, Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics (Oxford University Press, London, 2000).
  3. R. A. Shaw, Particle-turbulence interactions in atmospheric clouds, Annu. Rev. Fluid Mech. 35, 183 (2003).
  4. W. W. Grabowski and L.-P. Wang, Growth of cloud droplets in a turbulent environment, Annu. Rev. Fluid Mech. 45, 293 (2013).
  5. M. Balthasar, F. Mauss, A. Knobel, and M. Kraft, Detailed modeling of soot formation in a partially stirred plug flow reactor, Combust. Flame 128, 395 (2002).
  6. M. V. Smoluchowski, Versuch einer mathematishen Theorie dar koagulationskinetik kollider Losungen, Z. Phys. Chem. 92U, 129 (1918).
  7. L. A. Spielman, Viscous interactions in Brownian coagulation, J. Colloid Interface Sci. 33, 562 (1970).
  8. I. A. Valioulis and E. J. List, Collision efficiencies of diffusing spherical particles: Hydrodynamic, van der Waals and electrostatic forces, Adv. Colloid Interface Sci. 20, 1 (1984).
  9. S. Kim and C. F. Zukoski, A model of growth by hetero-coagulation in seeded colloidal dispersions, J. Colloid Interface Sci. 139, 198 (1990).
  10. A. Z. Zinchenko and R. H. Davis, Gravity-induced coalescence of drops at arbitrary Péclet numbers, J. Fluid Mech. 280, 119 (1994).
  11. J. Chun and D. L. Koch, Coagulation of monodisperse aerosol particles by isotropic turbulence, Phys. Fluids 17, 027102 (2005).
  12. J. Chun and D. L. Koch, The effects of non-continuum hydrodynamics on the Brownian coagulation of aerosol particles, J. Aerosol Sci. 37, 471 (2006).
  13. N. A. Fuchs, The Mechanics of Aerosols (Perggamon, New York, 1964).
  14. M. Sitarski and J. H. Seinfeld, Brownian coagulation in the transition regime, J. Colloid Interface Sci. 61, 261 (1977).
  15. P. E. Wagner and M. Kerker, Brownian coagulation of aerosols in rarefied gases, J. Chem. Phys. 66, 638 (1977).
  16. S. N. Shon, G. Kasper, and D. T. Shaw, An experimental study of Brownian coagulation in the transition regime, J. Colloid Interface Sci. 73, 233 (1980).
  17. G. Narsimhan and E. Ruckenstein, The Brownian coagulation of aerosols over the entire range of Knudsen numbers: Connection between the sticking probability and the interaction forces, J. Colloid Interface Sci. 104, 344 (1985).
  18. D. S. Kim, S. H. Park, Y. M. Song, D. H. Kim, and K. W. Lee, Brownian coagulation of polydisperse aerosols in the transition regime, J. Aerosol Sci. 34, 859 (2003).
  19. W. B. Russel, D. Saville, and W. R. Schowalter, Colloidal Dispersions, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, UK, 1989).
  20. L. M. Hocking, The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres, J. Eng. Math. 7, 207 (1973).
  21. R. H. Davis, The rate of coagulation of a dilute polydisperse system of sedimenting spheres, J. Fluid Mech. 145, 179 (1984).
  22. R. R. Sundararajakumar and D. L. Koch, Non-continuum lubrication flows between particles colliding in a gas, J. Fluid Mech. 313, 283 (1996).
  23. J. Dhanasekaran, A. Roy, and D. L. Koch, Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow, J. Fluid Mech. 910, A10 (2021).
  24. S. E. Devir, On the coagulation of aerosols (part I), J. Colloid Sci. 18, 744 (1963).
  25. S. E. Devir, On the coagulation of aerosols III. Effect of weak electric charges on rate, J. Colloid Interface Sci. 23, 80 (1967).
  26. N. Gavish and K. Promislow, Dependence of the dielectric constant of electrolyte solutions on ionic concentration: A microfield approach, Phys. Rev. E 94, 012611 (2016).
  27. E. B. Lindgren, H.-K. Chan, A. J. Stace, and E. Besley, Progress in the theory of electrostatic interactions between charged particles, Phys. Chem. Chem. Phys. 18, 5883 (2016).
  28. T. B. Jones, Electromechanics of Particles (Cambridge University Press, Cambridge, UK, 2005).
  29. M. H. Davis, Two charged spherical conductors in a uniform electric field: Forces and field strength, Q. J. Mech. Appl. Math. 17, 499 (1964).
  30. A. Russell, The coefficients of capacity and the mutual attractions or repulsions of two electrified spherical conductors when close together, Proc. R. Soc. London, Ser. A 82, 524 (1909).
  31. J. Lekner, Electrostatics of two charged conducting spheres, Proc. R. Soc. A 468, 2829 (2012).
  32. J. Lekner, Regions of attraction between like-charged conducting spheres, Am. J. Phys. 84, 474 (2016).
  33. J. C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 1 (Clarendon Press, Oxford, UK, 1873).
  34. L. D. Landau and E. Lifshitz, Electrodynamics of Continuous Media, Vol. 8 (Elsevier, Amsterdam, 2013).
  35. A. S. Khair, Electrostatic forces on two almost touching nonspherical charged conductors, J. Appl. Phys. 114, 134906 (2013).
  36. S. Banerjee, T. Peters, N. Brown, and Y. Song, Exact closed-form and asymptotic expressions for the electrostatic force between two conducting spheres, Proc. R. Soc. A 477, 20200866 (2021).
  37. V. Munirov and A. Filippov, Interaction of two dielectric macroparticles, J. Exp. Theor. Phys. 117, 809 (2013).
  38. A. V. Khachatourian and A. O. Wistrom, Size effects in aerosol electrostatic interactions, J. Colloid Interface Sci. 242, 52 (2001).
  39. D. D. Huang, J. H. Seinfeld, and K. Okuyama, Image potential between a charged particle and an uncharged particle in aerosol coagulation—enhancement in all size regimes and interplay with van der Waals forces, J. Colloid Interface Sci. 141, 191 (1991).
  40. J. Lu, H. Nordsiek, E. W. Saw, and R. A. Shaw, Clustering of Charged Inertial Particles in Turbulence, Phys. Rev. Lett. 104, 184505 (2010).
  41. Y. Yao and J. Capecelatro, Competition between drag and coulomb interactions in turbulent particle-laden flows using a coupled-fluid–Ewald-summation based approach, Phys. Rev. Fluids 3, 034301 (2018).
  42. W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, Hoboken, NJ, 1999).
  43. Y. Kousaka, K. Okuyama, M. Adachi, and K. Ebie, Measurement of electric charge of aerosol particles generated by various methods, J. Chem. Eng. Jpn. 14, 54 (1981).
  44. C.-J. Tsai, J.-S. Lin, C. G. Deshpande, and L.-C. Liu, Electrostatic charge measurement and charge neutralization of fine aerosol particles during the generation process, Part. Part. Syst. Charact. 22, 293 (2005).
  45. K. Ghosh, S. N. Tripathi, M. Joshi, Y. S. Mayya, A. Khan, and B. K. Sapra, Modeling studies on coagulation of charged particles and comparison with experiments, J. Aerosol Sci. 105, 35 (2017).
  46. A. A. Onischuk, S. di Stasio, V. V. Karasev, A. M. Baklanov, G. A. Makhov, A. L. Vlasenko, A. R. Sadykova, A. V. Shipovalov, and V. N. Panfilov, Evolution of structure and charge of soot aggregates during and after formation in a propane/air diffusion flame, J. Aerosol Sci. 34, 383 (2003).
  47. M. M. Maricq, The dynamics of electrically charged soot particles in a premixed ethylene flame, Combust. Flame 141, 406 (2005).
  48. B. A. Tinsley, R. P. Rohrbaugh, M. Hei, and K. V. Beard, Effects of image charges on the scavenging of aerosol particles by cloud droplets and on droplet charging and possible ice nucleation processes, J. Atmos. Sci. 57, 2118 (2000).
  49. B. Ellasson, W. Egli, J. R. Ferguson, and H. Jodeit, Coagulation of bipolarly charged aerosols in a stack coagulator, J. Aerosol Sci. 18, 869 (1987).
  50. S. Dhanorkar and A. K. Kamra, Effect of coagulation on the particle charge distribution and air conductivity, J. Geophys. Res.: Atmos. 106, 12055 (2001).
  51. M. P. Simones and S. K. Loyalka, Measurements of charged aerosol coagulation, Nucl. Technol. 189, 45 (2015).
  52. M. P. Simones, S. K. Loyalka, C. Duffy, R. MacLoughlin, A. Tatham, and P. Power, Measurement of the size and charge distribution of sodium chloride particles generated by an Aeroneb Pro® pharmaceutical nebulizer, Eur. J. Nanomed. 6, 29 (2014).
  53. X. Zhang and R. H. Davis, The rate of collisions due to Brownian or gravitational motion of small drops, J. Fluid Mech. 230, 479 (1991).
  54. H. Wang, A. Z. Zinchenko, and R. H. Davis, The collision rate of small drops in linear flow fields, J. Fluid Mech. 265, 161 (1994).
  55. G. K. Batchelor, Brownian diffusion of particles with hydrodynamic interaction, J. Fluid Mech. 74, 1 (1976).
  56. J. Dhanasekaran, A. Roy, and D. L. Koch, Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow, J. Fluid Mech. 912, A5 (2021).
  57. R. H. Davis, J. A. Schonberg, and J. M. Rallison, The lubrication force between two viscous drops, Phys. Fluids 1, 77 (1989).
  58. A. Z. Zinchenko and R. H. Davis, Collision rates of spherical drops or particles in a shear flow at arbitrary Peclet numbers, Phys. Fluids 7, 2310 (1995).
  59. J. Mahanty and B. W. Ninham, Dispersion Forces, Vol. 1 (Academic, Cambridge, MA, 1976).
  60. Y. Yao and J. Capecelatro, Deagglomeration of cohesive particles by turbulence, J. Fluid Mech. 911, A10 (2021).
  61. E. Y. Santiago, J. Peréz-Rodríguez, and R. Esquivel-Sirvent, Dispersive properties of mesoporous gold: van der Waals and near-field radiative heat interactions, J. Phys. Chem. C 121, 12392 (2017).
  62. C. Shen, S. A. Bradford, M. Flury, Y. Huang, Z. Wang, and B. Li, DLVO interaction energies for hollow particles: The filling matters, Langmuir 34, 12764 (2018).
  63. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory (Springer, Berlin, 2013).
  64. E. Bichoutskaia, A. L. Boatwright, A. Khachatourian, and A. J. Stace, Electrostatic analysis of the interactions between charged particles of dielectric materials, J. Chem. Phys. 133, 024105 (2010).
  65. A. Khachatourian, H.-K. Chan, A. J. Stace, and E. Bichoutskaia, Electrostatic force between a charged sphere and a planar surface: A general solution for dielectric materials, J. Chem. Phys. 140, 074107 (2014).
  66. A. Khain, V. Arkhipov, M. Pinsky, Y. Feldman, and Y. Ryabov, Rain enhancement and fog elimination by seeding with charged droplets. Part I: Theory and numerical simulations, J. Appl. Meteorol. 43, 1513 (2004).
  67. J. Wen and G. K. Batchelor, The rate of coagulation in a dilute suspension of small particles, Sci. China, Ser. A: Math., Phys., Astron. Technol. Sci. 28, 172 (1985).
  68. H. Hamaker, The London–van der Waals attraction between spherical particles, Physica 4, 1058 (1937).
  69. B. Pailthorpe and W. Russel, The retarded van der Waals interaction between spheres, J. Colloid Interface Sci. 89, 563 (1982).
  70. D. Langbein, Theory of van der Waals Attraction, Springer Tracts in Modern Physics Vol. 72 (Springer, Berlin, 1974), pp. 1–139.
  71. M. Vanni and G. Baldi, Coagulation efficiency of colloidal particles in shear flow, Adv. Colloid Interface Sci. 97, 151 (2002).
  72. S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Scattering theory approach to electrodynamic Casimir forces, Phys. Rev. D 80, 085021 (2009).
  73. B. Spreng, P. A. Maia Neto, and G.-L. Ingold, Plane-wave approach to the exact van der Waals interaction between colloid particles, J. Chem. Phys. 153, 024115 (2020).
  74. J. Lekner, Capacitance coefficients of two spheres, J. Electrost. 69, 11 (2011).

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Phys. Rev. Fluids 7, 064308– Published 29 June, 2022
  • Received 17 January 2022
  • Accepted 6 June 2022
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