MOVEMENT OF AEROSOL PARTICLES 677 (c) Compare these values with those given as examples in Tables II, IV, V, VI, VIII, and IX. (d) From these comparisons, judge which [orce has the predomi- nant effect. A rough estimate o[ the efficiency ot• deposition may be made simply by scanning these tables. I[ desired, the efficiency o[ aerosol deposition (or collision) upon the surface in question may be estimated more accurately from the equa- tions given or cited. b (cm) C d•, (cm) D (cm) 5) (cm"/sec) (dyne) (cm/sec •) k z, (cm) Q•, (coulombs) R (cm) Re t (sec) T(øK) • ½m/se•) •o ½m/•e•) • ½m/•) • ½m/•) •o ½m/•) TABLE OF SYMBOLS = spacing between center line of flow and outermost streamline within which all particles collide with obstacle in path --Cunningham factor, correction to Stokes law for small particles = diameter of spherical aerosol particle = characteristic dimension of obstacle in path = diffusion coefficient of particle due to BrownJan motion = drag force upon particle moving relative to air = acceleration due to gravity, 980 cm/sec 2 = dimensionless parameter (general) for gravity deposi- tion = Boltzman's constant = dimensionless parameter for electrostatic attraction = length of duct or tube, also a horizontal dimension = electrostatic charge on an aerosol particle = Peclet number, dimensionless = radial position in a tube = radius of a sphere or cylinder, also vertical dimension = Reynolds number, dimensionless = time = absolute temperature = speed of motion of particle = initial speed of motion of particle in still air = terminal settling velocity of particle = horizontal component of velocity of particle = vertical component of velocity of particle = average velocity of fluid

678 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS v r (cm/sec) = % (cm/sec) •_ (cm/sec) Ax B (cm) x era) (cm) y (cm) •0 • (dyne/cm sec) = = 0p (g/cma) = 0l (g/cma) = ½½c) -- velocity of fluid stream in axial direction, at radial position r horizontal component of velocity of fluid streamline vertical component of velocity of fluid streamline mean displacement of particle by Brownian motion distance traveled horizontally by particle stopping distance of particle in stream distance traveled vertically by particle geometric standard deviation in •/•p dielectric constant of collector pmmittivity of free space collection efficiency of particles by obstacle collection efficiency of particles due to diffusion collection efficiency of particles due to electrostatic force viscosity of fluid inertial impaction parameter, dimensionless density of particle density of fluid relaxation time of particle (Received November 15, 1971 ) REFERENCES (1) Findeisen, W., Arch. Gesamt. Physiol., 286, 467 (1935). (2) Landahl, H., Bull. Math. Biophys., 12, 43 (1950). (3) Hatch, T. F., and Gross, P., Pulmonary D• position and Retention o[ Inhaled Aerosols, Amer. Ind. Hyg. Assn., Academic Press, New York, N.Y., 1964, pp. 67-8. (4) Fuchs, N. A., The Mechanics o[ Aerosols, The Macmillan Co., New York, N.Y., 1964, p. 112. (5) Whitby, K. T., Calculation of the clean fractional efficiency of low media density filters, ASHREA J., 7, 56-65 (Sept. 1965). (6) Fuchs, N. A., The Mechanics o! Aerosols, The Macmillan Co., New York, N.Y.. 1964, p. 165. (7) lb"d., p. 184. (8) Langmuir, I., Theory of Filtration of Smohes, O.S.R.C. Rep. No. 865 (1942). (9) Ranz, W. E., Tech. Rep. No. 8, I11. Univ. Eng. Exp. Sta., Jan. 1, 1953. (10) Lundgren, D. A., and Whitby, K. T., The effect of particle electrostatic charge on filtra- tion by fibrous filters, Ind. Eng. Chem., Process Des. Develop., 4, 345-9 (1965). (11) Fuchs, N, A., The Mechanics of Aerosols, The Macmillan Co., New York, N.Y., 1964, pp. 192-204.