MOVEMENT OF AEROSOL PARTICLES 673 tnoved from suspension. It is only a significant factor for particles of size less than about 1 v. : The mean displacement of a particle in a given direction by Brownfan diffusion in still air may be calculated by Einstein's theory as AxB = i•:Dt (12) where f) is called the diffusion coefficient of the particle and is given by C = (13) where k: Boltzman's constant, and T = absolute temperature. Fuchs (7_) has prepared a table of sample values of •xx, for t = 1 sec, and com- phred them with us. Excerpts are quoted in Table VII. For particle sizes which are much smaller than the mean free path of the gas mole- cules, another method of estimating values of .• is available from Lang- muir (8). Table VII Brownfan Diffusion in Still Air Air at23øC, 1 atm p• = 1 g/cma t = 1 sec Particle Size •D, cm• __ (d v, la) sec AxB, sec u,, cm/sec 10 2.38 X 10 -8 1.74 X 10 -4 3.02 X 10 -2 1 2.74 X 10 -7 5.90 X 10 -4 3.47 X 10 -a 0.1 6.82 X 10 -6 2.95 X 10 -a 8.64 X 10-a 0.01 5.24 X 10 -4 2.58 X 10 -• 6.63 X 10 -6 It is clear from Table VII that for particles smaller than about 0.5 p, the Brownfan motion exceeds that of settling. This provides a rough guideline for identifying what is meant by a "small" particle in terms of the importance of diffusion. When the particles are suspended in a moving air stream flowing over a surface, the contribution which Brownfan diffusion makes toward deposition on that surface will be lessened as the velocity is increased. The effect is judged by the magnitude of the Peclet number, defined as voD (14) Again, D is a characteristic dimension of the surface as was used in the case of inertial impaction and listed in Table III. The smaller the Peclet number, the greater the role played by diffusion.

674 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS A number of studies have been done on the important case of deposi- tion by diffusion on to the surface of a large cylinder, from a gas flowing perpendicular to the axis of the cylinder. The pattern of streamlines is involved just as it was in considering inertia and direct interception. A collection efficiency, by diffusion, is also defined in the same manner. As an example of these studies, the results of Ranz (9) may be quoted: 1 0.55•rRe 1/6 Note that the second term allows for the effect of the changing pattern of streamlines with the Reynolds number. Table VIII gives some effi- ciencies calculated •rom this equation, as applied to a human hair. When these collection efficiencies are compared with those for iner- tial impaction (Table V), it is seen that diffusion contributes practically nothing to the collection unless the particles are very small. But as the particle size decreases, collection by diffusion increases while that due to inertia decreases. At some intermediate particle size there is a mini- mum collection where neither diffusion nor inertia is effective. Table VIII Diffusion onto Human Hair Pv -- 1.0g/cm3 D = 100/z v0 = 10cm/sec Re = 0.662 d v, tz Pe •D •z• (%) • (% Table V) 10 4.2 X 106 0.63 X 10 -4 --•0 ,'-•5% 1 3.65 X 105 0.32 X 10 -3 •0 -,•0 0.1 1.47 X 104 0.28 X 10 -2 •0.3 ,--•0 0.01 1.85 X 102 0.065 •6.5 ,'--'0 Electrostatic Attraction Aerosol particles seem to acquire electrostatic charges rather easily during generation or during flow through air. As they approach an uncharged surface, an image force is set up, which attracts the charged particles to the surface and becomes still another mechanism of deposi- tion or removal. For example, the case of a spherical charged particle flowing near a cylindrical surface has been studied by Lundgren and Whitby (10). They found that the "efficiency of collection" could be calculated from an electrostatic parameter K• by •/• = 1.5K•1/• (16)