TECHNIQUES FOR ASSESSING RHEOLOGICAL PROPERTIES 447 Figure 8 The Calculation of Creep Compliance (Fig. 3) the surfaces of both cylinders are finely ribbed to prevent sample slippage. The outer cylinder is kept stationary while the inner cylinder is rotated slowly by a pulley-weight arrangement. Angular rotation of

448 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS the inner cylinder is measured optically by reflection of a light beam from a lamp via a mirror affixed to the inner cylinder suspension wire on to a graduated scale. Strain (+) -- r•a (II) r• - r• where r• and rs are the respective radii of the inner and outer cylinders, and a is the angular rotation. Shear stress (S) = mgD (III) x(r• + rs) d where m is the weight acting over each pulley of diameter D, and g (981 dynes) is acceleration due to gravity. Creep compliance -- + --r• ax (r• + rs) d = K a (IV) S (r•.- r•) mg m since a and m are the only variables. From the way in which creep compliance changes with time, it is possible to make a detailed rheological analysis. The calculations involved are discussed in full in the section dealing with the parallel plate viscoelasto- meter. PENETROMETERS A needle or cone (or sphere) penetrates the sample with a given force for a predetermined time, and the depth of penetration is measured. The main difficulties with this technique are that the area of contact between penetrometer and sample does not remain constant during the test, and that sample is displaced in a direction opposite to that in which the penetrometer moves. Yield value (So) for a cone penetrometer, e.g. Hutchinson, which is operated by a release mechanism is calculated from depth of penetration (p cm) by S O K• mg - (v) (gm/cm') pn where m is the weight (gms) of the cone plus mobile parts, and n is a constant with a value depending on the properties of the sample being tested, and usually approximating to 2 (8). K• 1 = -cos 2 • cot • (VI) where 2• is the cone angle.