192 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS One method of particle size measurement which I have not mentioned so far is the electron microscope. This, of course, has widened greatly the scope for examination of extremely fine powders. It goes beyond the magnifying power of the optical microscope to give resolution of particles of 0-01 micron and less. At the same time the amount of sample examined is proportionately lower. Its great scope would seem to lie in revealing fine particle structure which will help to explain some of the anomalies observed in the more statistical methods. ANDREASEN METHOD Having described some Of the methods of particle size determination together with their attendant advantages and shortcomings you might expect me to tell you which is ihe best. This is impossible, of course, because much depends on the purpose for which the information is needed. For this industry I would say that possibly the Andreasen pipette supported by a good microscope is the most versatile instrument. It is simple to use, and cheap. It can be used over a wide range of materiMs and many suspending fluids may be used. A determination may be completed in a day and will occupy only two hours of an operator's time. The sample examined is 7-15 gm. In view of this I would like to give a little more detail of the sedimentation method. The flow of a particle in a liquid has been very extensively studied. The type of flow has been described as streamline gradually changing to turbulent as the speed of the particle increases. For streamline flow the speed of fall is proportional to the square of the diameter of the particle. As the speed of. the particle increases eddies begin to develop around the particle and to impede its flow. In fully turbulent conditions the speed of fall becomes proportional to the square root of the diameter. In sedimenta- tion work care should be taken to keep the motion in the streamline range. The form of flow can be calculated from the known properties of the suspen- sion by the magnitude of the Reynolds Number Velocity of particle x diameter Kinematic viscosity of the liquid For values of this expression up to 0.2 the motion is streamline. For fully turbulent conditions the value is over 700. For most materials up to 60 microns and density up to 4 the movement is essentially streamline in water, and the Stokes equation involving d • may be used. The interaction between the particles themselves is always a problem. In the sub-sieve range for a 1 per cent suspension by voltune the average distance apart is of the order of four or five diameters. Andreasen con- sidered this sufficient clearance to allow the particles to fall freely. Some other authorities consider that the free space around the particle should be

FINE PARTICLES IN THE COSMETIC INDUSTRY 193 about fifteen diameters. There is no doubt that from this point of view the more dilute the suspension the better. However, 1 per cent concentration, whilst not ideal, does not give rise to errors approaching the overall error inherent in the method. The 1 per cent concentration is about the minimum to allow of reasonable accuracy in the weighing of the sampled fractions. The overall error in determinations of particle size by the Andreasen method has been estimated as =k 0.5 per cent. This may be true for an expe•t operator. The error may vary somewhat with the nature of the material. I would put the figure for a good operator as :• 1.5 per cent. One important feature of the Andreasen method which must be stressed is the necessity for close temperature control during the determination. Slight changes of temperature at the outside wall of a column will set up convection currents which will completely invalidate the method for the finer particles. Andreasen points out that convection hazards are less troublesome with more concentrated suspensions and considers this another point in fayour of using a suspension of initial concentration as high as 1 per cent. It has been considered that the zone of suction around the immersed tip of the pipette is far too widespread. It should, of course, be kept to a minimum by very careful steady suction at the time of sampling the suspen- sion. Even so, the withdrawal of the sample should not take longer than 15 seconds for water, and a little longer for more viscous fluids. Two other small points, but important ones' the column should be vertical and the determination carried out in a place free from vibrations. PARTICLE SIZE Having said so much of the measurement of particle size we come to the problem of what is the size of a particle ? As far as the microscope is concerned a particle on a slide will tend to rest with its smallest dimension in the vertical plane. The particle is normally viewed in silhouette so that one sees the projected area. The usual method is to match this area to a sphere of the same area or to a circumscribing rectangle, and the particle size is described in terms of such references. Where many particles have to be measured the dimension termed a statistical diameter is sometimes used. This is the length of the line bisecting the projected area of t,•he particle as it lies on the slide, and read off in the same direction for all particles measured. The particle size may also be described as the diameter of a sphere of the same surface area as the particle or again as the diameter of a sphere of volume (or weight) equal to that of the particle. In the case of sedimenta- tion methods, Stokes Law, of course, refers to spheres. Here the usual description of particle size is the diameter of a sphere of the same density