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Original Articles

High potential, near free molecular regime Coulombic collisions in aerosols and dusty plasmas

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Pages 933-957 | Received 29 Nov 2018, Accepted 26 Apr 2019, Published online: 17 May 2019

References

  • Adachi, M., Y. Kousaka, and K. Okuyama. 1985. Unipolar and bipolar diffusion charging of ultrafine aerosol-particles. J. Aerosol Sci. 16 (2):109–123. doi: 10.1016/0021-8502(85)90079-5.
  • Adachi, M., K. Okuyama, H. Kozuru, Y. Kousaka, and D. Y. H. Pui. 1989. Bipolar diffusion charging of aerosol particles under high particle/ion concentration ratios. Aerosol Sci. Technol. 11 (2):144–156. doi: 10.1080/02786828908959307.
  • Allen, J. E. 1992. Probe theory—The orbital motion approach. Phys. Scr. 45 (5):497–503. doi: 10.1088/0031-8949/45/5/013.
  • Autricque, A., S. A. Khrapak, L. Couëdel, N. Fedorczak, C. Arnas, J. M. Layet, and C. Grisolia. 2018. Electron collection and thermionic emission from a spherical dust grain in the space-charge limited regime. Phys. Plasmas 25 (6):063701. doi: 10.1063/1.5032153.
  • Bonitz, M., C. Henning, and D. Block. 2010. Complex plasmas: A laboratory for strong correlations. Rep. Prog. Phys. 73 (6):066501. doi: 10.1088/0034-4885/73/6/066501.
  • Bricard, J. 1962. La fixation des petits ions atmosphériques sur les aérosols ultra-fins. Geofisica Pura e Applicata 51 (1):237–242. doi: 10.1007/BF01992666.
  • Bystrenko, O., and A. Zagorodny. 1999. Critical effects in screening of high-z impurities in plasmas. Phys. Lett. A 255 (4–6):325–330. doi: 10.1016/S0375-9601(99)00137-1.
  • Chandrasekhar, S. 1943. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15 (1):1–89. doi: 10.1103/RevModPhys.15.1.
  • Chaudhuri, M., A. V. Ivlev, S. A. Khrapak, H. M. Thomas, and G. E. Morfill. 2011. Complex plasma—The plasma state of soft matter. Soft Matter 7 (4):1287–1298. doi: 10.1039/C0SM00813C.
  • Coles, S. 2001. An introduction to statistical modeling of extreme values. Berlin: Springer.
  • D’Yachkov, L. G., A. G. Khrapak, S. A. Khrapak, and G. Morfill. 2007. Model of grain charging in collisional plasmas accounting for collisionless layer. Phys. Plasmas 14 (4):042102.
  • Dahneke, B. E. 1983. Simple kinetic theory of Brownian diffusion in vapors and aerosols. In Theory of dispersed multiphase flow, ed. R. E. Meyer, New York: Academic Press.
  • Daugherty, J. E., R. K. Porteous, and D. B. Graves. 1993. Electrostatic forces on small particles in low-pressure discharges. J. Appl. Phys. 73 (4):1617–1620. doi: 10.1063/1.353194.
  • Daugherty, J. E., R. K. Porteous, M. D. Kilgore, and D. B. Graves. 1992. Sheath structure around particles in low‐pressure discharges. J. Appl. Phys. 72 (9):3934–3942. doi: 10.1063/1.352245.
  • Ermak, D. L., and H. Buckholz. 1980. Numerical integration of the Langevin equation: Monte Carlo simulation. J. Comput. Phys. 35 (2):169–182. doi: 10.1016/0021-9991(80)90084-4.
  • Filippov, A. V. 1993. Charginf of aerosol in the transition regime. J. Aerosol Sci. 24 (4):423–436. doi: 10.1016/0021-8502(93)90029-9.
  • Fortov, V. E., A. V. Ivlev, S. A. Khrapak, A. G. Khrapak, and G. E. Morfill. 2005. Complex (dusty) plasmas: Current status, open issues, perspectives. Phys. Rep. 421 (1–2):1–103. doi: 10.1016/j.physrep.2005.08.007.
  • Fortov, V. E., O. F. Petrov, A. D. Usachev, and A. V. Zobnin. 2004. Micron-sized particle-charge measurements in an inductive RF gas-discharge plasma using gravity-driven probe grains. Phys. Rev. E 70:046415.
  • Friedlander, S. K. 2000. Smoke, dust, and haze: Fundamentals of aerosol dynamics. New York: Oxford University Press.
  • Fuchs, N. A. 1963. On the stationary charge distribution on aerosol particles in a bipolar ionic atmosphere. Geofis. Pura Appl. 51:185–193. doi: 10.1007/BF01993343.
  • Fuchs, N. A. 1964. The mechanics of aerosols. New York: Macmillan.
  • Fuchs, N. A., and A. G. Sutugin. 1970. Highly dispersed aerosols. Ann Arbor, MI: Ann Arbor Science Publishers.
  • Gatti, M., and U. Kortshagen. 2008. Analytical model of particle charging in plasmas over a wide range of collisionality. Phys. Rev. E 78:046402. doi: 10.1103/PhysRevE.78.046402.
  • Gelbard, F., Y. Tambour, and J. H. Seinfeld. 1980. Sectional representations for simulating aerosol dynamics. J. Colloid Interface Sci. 76 (2):541–556. doi: 10.1016/0021-9797(80)90394-X.
  • Gnedenko, B. V. 1948. On a local limit theorem of the theory of probability. Usp. Mat. Nauk 3:187–194 (in Russian).
  • Gopalakrishnan, R., and C. J. Hogan. 2011. Determination of the transition regime collision kernel from mean first passage times. Aerosol Sci. Technol. 45 (12):1499–1509. doi: 10.1080/02786826.2011.601775.
  • Gopalakrishnan, R., and C. J. Hogan. 2012. Coulomb-influenced collisions in aerosols and dusty plasmas. Phys. Rev. E 85:026410.
  • Gopalakrishnan, R., P. H. McMurry, and C. J. Hogan. 2015. The bipolar diffusion charging of nanoparticles: A review and development of approaches for non-spherical particles. Aerosol Sci. Technol. 49 (12):1181–1194. doi: 10.1080/02786826.2015.1109053.
  • Gopalakrishnan, R., M. J. Meredith, C. Larriba-Andaluz, and C. J. Hogan, Jr. 2013. Brownian dynamics determination of the bipolar steady state charge distribution on spheres and non-spheres in the transition regime. J. Aerosol Sci. 63:126–145. doi: 10.1016/j.jaerosci.2013.04.007.
  • Gopalakrishnan, R., T. Thajudeen, and C. J. Hogan. 2011. Collision limited reaction rates for arbitrarily shaped particles across the entire diffusive Knudsen number range. J. Chem. Phys. 135 (5):054302. doi: 10.1063/1.3617251.
  • Gopalakrishnan, R., T. Thajudeen, H. Ouyang, and C. J. Hogan, Jr. 2013. The unipolar diffusion charging of arbitrary shaped aerosol particles. J. Aerosol Sci. 64:60–80. doi: 10.1016/j.jaerosci.2013.06.002.
  • Goree, J. 1992. Ion trapping by a charged dust grain in a plasma. Phys. Rev. Lett. 69 (2):277–280. doi: 10.1103/PhysRevLett.69.277.
  • Hagen, D. E., and D. J. Alofs. 1983. Linear inversion method to obtain aerosol size distributions from measurements with a differential mobility analyzer. Aerosol Sci. Technol. 2 (4):465–475. doi: 10.1080/02786828308958650.
  • Han, B., M. Shimada, M. Choi, and K. Okuyama. 2003. Unipolar charging of nanosized aerosol particles using soft X-ray photoionization. Aerosol Sci. Technol. 37 (4):330–341. doi: 10.1080/02786820390125197.
  • Hogan, C. J., L. Li, D. R. Chen, and P. Biswas. 2009. Estimating aerosol particle charging parameters using a Bayesian inversion technique. J. Aerosol Sci. 40 (4):295–306. doi: 10.1016/j.jaerosci.2008.11.008.
  • Hopkins, M. B., and W. G. Graham. 1986. Langmuir probe technique for plasma parameter measurement in a medium density discharge. Rev. Sci. Instrum. 57 (9):2210–2217. doi: 10.1063/1.1138684.
  • Hoppel, W. A., and G. M. Frick. 1986. Ion-aerosol attachment coefficients and the steady-state charge distribution on aerosols in a bipolar ion environment. Aerosol Sci. Technol. 5 (1):1–21. doi: 10.1080/02786828608959073.
  • Hussin, A., H. G. Scheibel, K. H. Becker, and J. Porstendörfer. 1983. Bipolar diffusion charging of aerosol particles—I: Experimental results within the diameter range 4–30 nm. J. Aerosol Sci. 14 (5):671–677. doi: 10.1016/0021-8502(83)90071-X.
  • Hutchinson, I. H., and L. Patacchini. 2007. Computation of the effect of neutral collisions on ion current to a floating sphere in a stationary plasma. Phys. Plasmas 14 (1):013505. doi: 10.1063/1.2431584.
  • In Jeong, J., and M. Choi. 2001. A sectional method for the analysis of growth of polydisperse non-spherical particles undergoing coagulation and coalescence. J. Aerosol Sci. 32 (5):565–582. doi: 10.1016/S0021-8502(00)00103-8.
  • Iza, F., and J. K. Lee. 2006. Particle-in-cell simulations of planar and cylindrical Langmuir probes: Floating potential and ion saturation current. J. Vacuum Sci. Technol. A: Vacuum Surf. Films 24:1366–1372. doi: 10.1116/1.2187991.
  • Jiang, J. K., C. J. Hogan, D. R. Chen, and P. Biswas. 2007. Aerosol charging and capture in the nanoparticle size range (6–15 nm) by direct photoionization and diffusion mechanisms. J. Appl. Phys. 102 (3):034904. doi: 10.1063/1.2768061.
  • Khrapak, S., and G. Morfill. 2009. Basic processes in complex (dusty) plasmas: Charging, interactions, and ion drag force. Contrib. Plasma Phys. 49 (3):148–168. doi: 10.1002/ctpp.200910018.
  • Khrapak, S. A., and G. E. Morfill. 2008. An interpolation formula for the ion flux to a small particle in collisional plasmas. Phys. Plasmas 15 (11):114503. doi: 10.1063/1.3035913.
  • Khrapak, S. A., S. V. Ratynskaia, A. V. Zobnin, A. D. Usachev, V. V. Yaroshenko, M. H. Thoma, M. Kretschmer, H. Höfner, G. E. Morfill, O. F. Petrov, et al. 2005. Particle charge in the bulk of gas discharges. Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 72 (1 Pt 2):016406. doi: 10.1103/PhysRevE.72.016406.
  • Khrapak, S. A., P. Tolias, S. Ratynskaia, M. Chaudhuri, A. Zobnin, A. Usachev, C. Rau, M. H. Thoma, O. F. Petrov, V. E. Fortov, et al. 2012. Grain charging in an intermediately collisional plasma. Europhys. Lett. 97 (3):35001. doi: 10.1209/0295-5075/97/35001.
  • Lampe, M., R. Goswami, Z. Sternovsky, S. Robertson, V. Gavrishchaka, G. Ganguli, and G. Joyce. 2003. Trapped ion effect on shielding, current flow, and charging of a small object in a plasma. Phys. Plasmas 10 (5):1500–1513. doi: 10.1063/1.1562163.
  • Lampe, M., and G. Joyce. 2015. Grain-grain interaction in stationary dusty plasma. Phys. Plasmas 22 (2):023704. doi: 10.1063/1.4907649.
  • Lieberman, M. A., and A. J. Lichtenberg. 2005. Principles of plasma discharges and materials processing. New York: Wiley.
  • Liu, B. Y. H., and D. Y. H. Pui. 1974. Equilibrium bipolar charge distribution of aerosols. J. Colloid Interface Sci. 49 (2):305–312. doi: 10.1016/0021-9797(74)90366-X.
  • Lopez-Yglesias, X., and R. C. Flagan. 2013. Ion-aerosol flux coefficients and the steady-state charge distribution of aerosols in a bipolar ion environment. Aerosol Sci. Technol. 47:688–704. doi: 10.1080/02786826.2013.783684.
  • Loyalka, S. K. 1976. Brownian coagulation of aerosols. J. Colloid Interface Sci. 57 (3):578–579. doi: 10.1016/0021-9797(76)90237-X.
  • Loyalka, S. K. 1982. Condensation on a spherical droplet, II. J. Colloid Interface Sci. 87 (1):216. doi: 10.1016/0021-9797(82)90384-8.
  • Lushnikov, A. A., and M. Kulmala. 2004. Flux-matching theory of particle charging. Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 70 (4 Pt 2):046413. doi: 10.1103/PhysRevE.70.046413.
  • Maißer, A., J. M. Thomas, C. Larriba-Andaluz, S. He, and C. J. Hogan. 2015. The mass–mobility distributions of ions produced by a Po-210 source in air. J. Aerosol Sci. 90:36–50. doi: 10.1016/j.jaerosci.2015.08.004.
  • Mann, I., A. Pellinen-Wannberg, E. Murad, O. Popova, N. Meyer-Vernet, M. Rosenberg, T. Mukai, A. Czechowski, S. Mukai, J. Safrankova, et al. 2011. Dusty plasma effects in near earth space and interplanetary medium. Space Sci. Rev. 161 (1–4):1–47. doi: 10.1007/s11214-011-9762-3.
  • Marlow, W. H. 1980. Derivation of aerosol collision rates for singular attractive contact potentials. J. Chem. Phys. 73 (12):6284–6287. doi: 10.1063/1.440126.
  • Mayya, Y. S., and B. K. Sapra. 2002. Image forces on a collection of charged particles near conducting surfaces. J. Aerosol Sci. 33 (5):817–828. doi: 10.1016/S0021-8502(02)00038-1.
  • Mazur, P., and I. Oppenheim. 1970. Molecular theory of Brownian motion. Physica 50 (2):241. doi: 10.1016/0031-8914(70)90005-4.
  • McMurry, P. H. 2000. A review of atmospheric aerosol measurements. Atmos. Environ. 34 (12–14):1959–1999. doi: 10.1016/S1352-2310(99)00455-0.
  • Melzer, A., M. Himpel, H. Krüger, M. Mulsow, and S. Schütt. 2018. Optical diagnostics of dusty plasmas. Plasma Phys. Control. Fusion. 61 (1).
  • Merlino, R. L. 2007. Understanding Langmuir probe current-voltage characteristics. Am. J. Phys. 75 (12):1078–1085. doi: 10.1119/1.2772282.
  • Molotkov, V. I., H. M. Thomas, A. M. Lipaev, V. N. Naumkin, A. V. Ivlev, and S. A. Khrapak. 2015. Complex (dusty) plasma research under microgravity conditions: Pk-3 plus laboratory on the international space station. Int. J. Microgravity Sci. Appl. 35 (3): 320302. doi: 10.15011/jasma.32.320302.
  • Morfill, G. E., and A. V. Ivlev. 2009. Complex plasmas: An interdisciplinary research field. Rev. Mod. Phys. 81 (4):1353–1404. doi: 10.1103/RevModPhys.81.1353.
  • Mott-Smith, H. M., and I. Langmuir. 1926. The theory of collectors in gaseous discharges. Phys. Rev. 28 (4):727–763. doi: 10.1103/PhysRev.28.727.
  • Narsimhan, G., and E. Ruckenstein. 1985. 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 (2):344–369. doi: 10.1016/0021-9797(85)90044-X.
  • Nefedov, A. P., G. E. Morfill, V. E. Fortov, H. M. Thomas, H. Rothermel, T. Hagl, A. V. Ivlev, M. Zuzic, B. A. Klumov, A. M. Lipaev, et al. 2003. PKE-Nefedov*: Plasma crystal experiments on the international space station. New J. Phys. 5:33. doi: 10.1088/1367-2630/5/1/333.
  • Ouyang, H., R. Gopalakrishnan, and C. J. Hogan. 2012. Nanoparticle collisions in the gas phase in the presence of singular contact potentials. J. Chem. Phys. 137 (6):064316. doi: 10.1063/1.4742064.
  • Porstendörfer, J., A. Hussin, H. G. Scheibel, and K. H. Becker. 1984. Bipolar diffusion charging of aerosol particles—II. Influence of the concentration ratio of positive and negative ions on the charge distribution. J. Aerosol Sci. 15 (1):47–56. doi: 10.1016/0021-8502(84)90055-7.
  • Pui, D. Y. H., S. Fruin, and P. H. McMurry. 1988. Unipolar diffusion charging of ultrafine aerosols. Aerosol Sci. Technol. 8 (2):173–187. doi: 10.1080/02786828808959180.
  • Pustylnik, M. Y., M. A. Fink, V. Nosenko, T. Antonova, T. Hagl, H. M. Thomas, A. V. Zobnin, A. M. Lipaev, A. D. Usachev, V. I. Molotkov, et al. 2016. Plasmakristall-4: New complex (dusty) plasma laboratory on board the international space station. Rev. Sci. Instrum. 87 (9):093505. doi: 10.1063/1.4962696.
  • Ratynskaia, S., S. Khrapak, A. Zobnin, M. H. Thoma, M. Kretschmer, A. Usachev, V. Yaroshenko, R. A. Quinn, G. E. Morfill, O. Petrov, et al. 2004. Experimental determination of dust-particle charge in a discharge plasma at elevated pressures. Phys. Rev. Lett. 93:085001.
  • Reischl, G. P., J. M. Mäkelä, R. Karch, and J. Necid. 1996. Bipolar charging of ultrafine particles in the size range below 10 nm. J. Aerosol Sci. 27 (6):931–949. doi: 10.1016/0021-8502(96)00026-2.
  • Reischl, G. P., H. G. Scheibel, and J. Porstendörfer. 1983. The bipolar charging of aerosols: Experimental results in the size range below 20-nm particle diameter. J. Colloid Interface Sci. 91 (1):272–275. doi: 10.1016/0021-9797(83)90332-6.
  • Rogak, S. N., and R. C. Flagan. 1992. Coagulation of aerosol agglomerates in the transition regime. J. Colloid Interface Sci. 151 (1):203–224. doi: 10.1016/0021-9797(92)90252-H.
  • Semenov, I. L., S. A. Khrapak, and H. M. Thomas. 2015. Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma. Phys. Plasmas 22 (5):053704. doi: 10.1063/1.4921249.
  • Shukla, P. K., and B. Eliasson. 2009. Colloquium: Fundamentals of dust-plasma interactions. Rev. Mod. Phys. 81 (1):25–44. doi: 10.1103/RevModPhys.81.25.
  • Stober, J., B. Schleicher, and H. Burtscher. 1991. Bipolar diffusion charging of particles in noble gases. Aerosol Sci. Technol. 14 (1):66–73. doi: 10.1080/02786829108959471.
  • Stolzenburg, M. R., and P. H. McMurry. 1991. An ultrafine aerosol condensation nucleus counter. Aerosol Sci. Technol. 14 (1):48–65. doi: 10.1080/02786829108959470.
  • Taccogna, F., S. Longo, and M. Capitelli. 2003. A particle-in-cell/Monte Carlo model of the Ar+ ion collection in He gas by a cylindrical Langmuir probe in the transition regime. Eur. Phys. J. Appl. Phys. 22 (1):29–39. doi: 10.1051/epjap:2003015.
  • Tarasov, V. I., and M. S. Veshchunov. 2018. On the theory of bipolar charging of large aerosol particles. Aerosol Sci. Technol. 52 (7):740–747. doi: 10.1080/02786826.2018.1455964.
  • Thajudeen, T., R. Gopalakrishnan, and C. J. Hogan. 2012. The collision rate of non-spherical particles and aggregates for all diffusive knudsen numbers. Aerosol Sci. Technol. 46 (11):1174–1186. doi: 10.1080/02786826.2012.701353.
  • Trunec, D., M. Holík, P. Kudrna, O. Bilyk, A. Marek, R. Hippler, and M. Tichý. 2004. Monte Carlo simulations of the electron currents collected by electrostatic probes. Contrib. Plasma Phys. 44 (7–8):577–581. doi: 10.1002/ctpp.200410084.
  • Varney, R. N. 1971. Mean free paths, ion drift velocities, and the Poisson distribution. Am. J. Phys. 39 (5):534–538. doi: 10.1119/1.1986207.
  • Vaulina, O. S., A. Y. Repin, and O. F. Petrov. 2006. Empirical approximation for the ion current to the surface of a dust grain in a weakly ionized gas-discharge plasma. Plasma Phys. Rep. 32 (6):485–488. doi: 10.1134/S1063780X06060055.
  • Veshchunov, M. S. 2010. A new approach to the brownian coagulation theory. J. Aerosol Sci. 41 (10):895–910. doi: 10.1016/j.jaerosci.2010.07.001.
  • Veshchunov, M. S. 2011. A new approach to diffusion-limited reaction rate theory. J. Eng. Thermophys. 20 (3):260–271. doi: 10.1134/S1810232811030040.
  • Veshchunov, M. S. 2012. Development of the new approach to the diffusion-limited reaction rate theory. J. Exp. Theor. Phys. 114 (4):631–644. doi: 10.1134/S1063776112020148.
  • Veshchunov, M. S., and I. B. Azarov. 2012. Next approximation of the random walk theory for Brownian coagulation. J. Aerosol Sci. 47:70–77. doi: 10.1016/j.jaerosci.2011.12.009.
  • Wiedensohler, A. 1988. An approximation of the bipolar charge-distribution for particles in the sub-micron size range. J. Aerosol Sci. 19 (3):387–389. doi. doi: 10.1016/0021-8502(88)90278-9.
  • Wiedensohler, A., and H. J. Fissan. 1988. Aerosol charging in high-purity gases. J. Aerosol Sci. 19:867–870. doi: 10.1016/0021-8502(88)90054-7.
  • Wiedensohler, A., E. Lutkemeier, M. Feldpausch, and C. Helsper. 1986. Investigation of the bipolar charge-distribution at various gas conditions. J. Aerosol Sci. 17 (3):413–416. doi: 10.1016/0021-8502(86)90118-7.
  • Wu, J. J., and R. C. Flagan. 1988. A discrete-sectional solution to the aerosol dynamic equation. J. Colloid Interface Sci. 123:339–352.
  • Yaroshenko, V. V., B. M. Annaratone, S. A. Khrapak, H. M. Thomas, G. E. Morfill, V. E. Fortov, A. M. Lipaev, V. I. Molotkov, O. F. Petrov, A. I. Ivanov, et al. 2004. Electrostatic modes in collisional complex plasmas under microgravity conditions. Phys. Rev. E 69:066401. doi: 10.1103/PhysRevE.69.066401.
  • Yun, K. M., S. Y. Lee, F. Iskandar, K. Okuyama, and N. Tajima. 2009. Effect of X-ray energy and ionization time on the charging performance and nanoparticle formation of a soft X-ray photoionization charger. Adv. Powder Technol. 20 (6):529–536. doi: 10.1016/j.apt.2009.07.002.
  • Zobnin, A. V., A. P. Nefedov, V. A. Sinel’shchikov, and V. E. Fortov. 2000. On the charge of dust particles in a low-pressure gas discharge plasma. J. Exp. Theor. Phys. 91 (3):483–487. doi: 10.1134/1.1320081.
  • Zobnin, A. V., A. D. Usachev, O. F. Petrov, and V. E. Fortov. 2008. Ion current on a small spherical attractive probe in a weakly ionized plasma with ion-neutral collisions (kinetic approach). Phys. Plasmas 15 (4):043705. doi: 10.1063/1.2903052.

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