660 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS If it is desired to deposit an aerosol upon a free surface by impinge- ment, the particles should be less than 50 • in diameter, but larger than about 10 t,, in order to take advantage ot5 inertial effects Deposition upon small surfaces, such as a human hair, will be aided by direct interception if the aerosol particle is of the same order of mag- nitude as the surface dimension There is no advantage to using very fine particles, less than say 1 • in diameter, unless it is desired to have an aerosol penetrate deeply into the respiratory tract for medicinal purposes (see below) 1t5 it is desired to protect against an aerosol entering the respiratory tract, it will help to maintain particle size greater than 10 • in order to utilize the removal mechanisms (inertia, gravity) in the nasal system. These statements apply to a material having a density of 1 g/cm a. If the value of p is much different from this, the statements should be modi- fied accordingly. In all cases where it is desired to minimize gravitational effects and/or to promote inertial effects it will be desirable to use as large an air stream velocity as possible. This should be at least of the order ot5 100 cm/sec. Such a speed will also minimize diffusional effects, even for very small particles. Deposition in the respiratory and nasal system is ot5 special impor- tance and has been the subject ot5 detailed study. Formalized schematic representatations ot5 the respiratory tract have been devised by Findeisen (1) and by Landahl (2). These represent the tract by a series of straight and curved tubes, having branching intersections and finally terminating in small spheres. Typical average length and diameter dimensions are assigned to each different part, as well as a number count ot5 each. Then, from a knowledge ot5 typical breathing rates, air speed velocity may be calculated. Using this scheme, calculations may be made using the theory outlined above to estimate deposition, or penetration, ot5 particles ot5 various sizes by the various mechanisms in the several por- tions of the system. The broad results ot5 such theoretical calculations have been sub- stantiated by experimental tests. General conclusions have been sum- inarized by Hatch and Gross (g), and may be paraphrased as follows: 1. Particles greater than 10 • are essentially all removed in the nasal chamber (inertia, sedimentation) and do not penetrate into the lungs. 2. Particles less than 1 • are essentially not removed at all in the upper respiratory tract.

MOVEMENT OF AEROSOL PARTICLES 661 3. The efficiency of particle removal is essentially 100% in the pul- monary air spaces, for particles down to about 2 v. 4. As particle size decreases from 2 v to about 0.5 v, removal in pul- monary air spaces decreases, but increases again for sizes below 0.5 v due to deposition by diffusion.* 5. Deposition in the upper respiratory tract is increased with faster breathing frequency, due to increased rate of air flow. 6. Deposition deep in the lungs increases with slow, deep breathing, as a large fraction of the tidal air gets in and there is a longer time of transit in and out of the lungs. DETAILED ANALYSIS The list of forces which may act upon an aerosol particle will next be reviewed in detail in order to show how to calculate the important quantities associated with each. This in turn leads to the ability to judge which force (or forces) may be controlling the particle behavior in a given case. Throughout the following it will be assumed that the aerosol par- ticles are spherical in shape having a diameter of less than roughly 100 v, and are moving in dry air at 20øC and 1 atm pressure, viscosity • • 1.81 X 10 -4 poises, density p/: 1.20 X 10 -a g/cm •. Drag Under the conditions assumed, the force of frictional resistance (drag) offered by still air, is given by Stokes law* FD = 3•'d•,u• For horizontal motion in still air in the absence of all other forces, Newton's law leads to the quantity r: pvdv"/18v which is a basic property of the particle-air system called the relaxation time. Eventually, the drag effect reduces the speed of the particle to zero. The distance traveled *• Particles of 0.I v remaining in an alveolar sac of 0.03-cm diameter for 1.2 sec (as assumed by Findeisen) would deposit to the extent of 60%, according to the diffusional equation cited above. Particles of 0.01 t• would be completely deposited. t For very small particles Fv must be corrected by dividing by the Curmingham factor C, which is approximately 1 + 0.16/dr in air at 20øC and 1 a•tm, where dvis in microns. For particles generally larger than 100-t• diameter, Stokes law must be replaced by the use of a drag coefficient relationship to express the drag force, but such larger particles are not of interest here.