FACTORS CONTROLLING THE ACTION OF HAIR SPRAYS--Ill 547 than 10 •tm. For such large particles the forces aiding capture are mainly gravity, inertia and direct interception. Gravitational settling contributes significantly to the removal of particles in excess of 10 •tm from a flowing stream. However, settling is only of importance when the stream is flowing over a horizontal surface and will contribute little to the capture of particles by fibres. Inertial impaction and direct interception are thus the major mechanisms controlling the capture of hair spray particles by hair fibres, and it is useful to consider these more fully in order to define the dependence on the particle diameter and velocity. First we shall consider inertial impaction. When a particle-laden gas stream approaches an obstacle placed in its path, the gas stream alters its path to flow around the obstacle. Because of its inertia, a particle will not be able to follow completely the flow lines of the gas and may leave these flow lines sufficiently to impact on the obstacle. The probability of collision depends on two parameters (4), the Reynold's number which defines the pattern of the gas streamlines, and its dependence on the stream velocity, and the inertial impaction parameter. The inertial impaction parameter is defined as: d2p V0 ? - (1) 18•D where d is the particle diameter, V0 the gas stream velocity, p the density of the particle, • the gas viscosity and D the obstacle dimension, which for a fibre is the fibre diameter. Light (4) has shown how the efficiency of capture may be calculated from the Reynold's number and the inertial impaction parameter. For a hair fibre of 100 •tm diameter Light gives the capture efficiencies for particles of various sizes approaching at speeds of 10,100 and 1000 cm s -x (Table 5 of ref. 4). The efficiency increases with increasing particle diameter and velocity and reaches 100• for a 10 pm particle at 1000 cm s 4 or a 50 •tm particle at 100 cm s 4. Next we shall consider the contribution of direct interception to the total capture. When the size of the aerosol particles approaches the diameter of the fibres, capture by direct interception becomes significant and increases the capture occurring by inertial impaction. Because of the way in which capture efficiency is defined: cross-sectional area of stream from which particles are removed efficiency = cross-sectional area of fibres projected upstream

548 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS it is possible for the total efficiency to be greater than 100•o. For example, let us assume that the inertia of all the particles is so great that they continue to travel in straight lines when the streamlines diverge around the obstacle. Then all particles whose centres are within the projected area of the fibre will be captured. In addition those particles whose centres are within a distance d/2 of the surface of the fibre will also be captured. The total D+d capture efficiency is then D Inertial interception becomes significant for did 0.1 and increases with increasing diameter of the particles. From the foregoing analysis we can see that the capture of hair spray particles by hair fibres can be predicted to increase with increase in both the diameter and velocity of the particles. Conversely, maximum penetration into an array of fibres requires the use of small, low-velocity particles. EXPERIMENTAL Measurement of particle velocities in aerosol sprays produced by pressurized packs The determination of the velocities of particles in an aerosol spray is difficult since there is a distribution of velocity across the spray cone. Particles at the centre of the spray have the highest velocity while those at the outside have the lowest velocity since here the particle-laden gas stream is in contact with the stagnant air of the surrounding atmosphere. We can thus expect a parabolic velocity distribution similar to that shown by a fluid moving through a pipe under laminar flow conditions. The situation is further complicated by local turbulence which is apparent in the spray, par- ticularly on the outside of the cone. Attempts to measure the particle velocities using a high-speed photo- graphic technique were of limited use, owing to the restricted depth of field, together with the problems outlined above. Instead we eventually chose to measure the velocity of the gas stream carrying the particles rather than the velocity of the particles themselves. The work thus contains the assumption that the particles travel isokinetically with the gas stream. This restriction is probably of little significance when compared with the overall accuracy of the velocity measurements.