MOVEMENT OF AEROSOL PAR•IICLES Table II R = 1• cm L = 5 cm v0 = 100 cm/sec 665 Particle Size Removal by Deposition s (dr, t•) G Plug Flow Laminar Flow Turbulent Flow 1 3.47 X 10 10 3.02 X 10 -2 •3% •-•1% •-•2% 50 0.755 •-•75 % •-•41% ,--•38% • Equations for these calculations are given by Fuchs (4). of these cases are related to the same basic parameter G --- (u•L/voR) which might be called the "gravity deposition parameter." To illustrate its effect, consider a set of values: R • « cm, L -- 5 cm, and v0 = 100 cm/sec, for which G = u•/100. Gravity deposition in this case will be as given in Table II. Gravity deposition thus will contribute significantly to the removal of particles larger than 10 g from a flowing stream. In particular, the ex- ample conditions chosen represent very roughly the conditions in a nasal passage, when the flow would be laminar. The data in Tables I and II show that particles of the order of 10 g in diameter may easily be kept suspended for long periods of time by very gentle air currents. Thus a space insecticide, for example, should be dispersed in particles of less than 50 g in diameter for maximum effective- ness. Inertia When a particle is moving with a stream of air, important inertial effects may arise when that stream carries the particle in the neighbor- hood of an obstacle in its path. The stream of air will change its direc- tion in order to flow around the obstacle. But the particle, because of its inertia, may not be able to maintain its position in the streamline of air and thus may be brought into contact with the obstacle. Such collisions are referred to as "inertial impaction." Examples are shown in Fig. 2. Case (a) would represent an obstacle ot• either cylindrical or spherical shape case (b) depicts the situation around either a disk or a flat strip case (c) shows a 90 ø bend in a pipe or tube. The streamlines of the air are represented by the solid lines. The trajectory of a particle, caused by its inertia, is represented by a dashed line. N o effect of gravity is being considered, for the present. Whether a collision occurs depends in part upon the position of the streamline which the particle was following initially. Along lines such

666 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Vo •.ff (b} (o } Figure 2. Collision by inertial impaction as & collision occurs, but along •2 it does not. The possibility of collision also depends in part upon the pattern of the streamline flow: at high velocities the'streamlines diverge suddenly close to the obstacle, while at low velocities the divergence commences more gradually at a greater dis- tance upstream. Collision also depends upon the mass of the particle (e.g., size and density) in addition to the size and shape of the obstacle. Some distance upstream of the obstacle, it may be reasonable to as- sume a uniform air velocity field at v0, and to assume no slip between the particles and the air. However, as soon as the fluid streamlines begin to diverge, they no longer all have the same velocity. As the particle tra- jectory diverts from the initial streamline, it begins to cross fluid stream- lines. Hence, a drag effect comes into play which now must depend upon the vector difference between fluid and particle velocity as mentioned earlier. Careful study, both theoretical and experimental, of this inherently complex phenomenon has revealed that the likelihood of collision de- pends upon two parameters: voDps (a) Reynold's number, Re - (dimensionless) which reflects the patterns of the streamlines and the effect of air speed X s II oT (b) Inertial impaction parameter, • - D - D (dimensionless) (also called Stokes number, Stk), which is the ratio of the stopping dis- tance of the particle, calculated with an initial velocity equal to that of the upstream air velocity, to the appropriate dimension of the obstacle. An "efficiency of collision," or collection efficiency, is defined: cross-sectional area of fluid stream from which particles are removed cross-sectional area represented by dimension D, projected upstream