SOME APPLICATIONS OF RIGIDITY AND YIELD VALUES 429 Air pressure 2a ____ (o) (b) Figure I Arrangement of apparatus. (a) at rest, (b) under applied air pressure (2). gel to the wall of the tube was sufficient to prevent slip. The rigidity is calculated using the formula PR4 c,, = 8La2h where G----rigidity modulus, Nm-2. P=net pressure (corrected for the back pressure of displaced mercury). R=radius of tube, cm. L--length of gel column, cm. a=radius of mercury capillary, cm. h=displacement of mercury, cm. The formula is valid for the condition that L R. Rheological measurements A Ferranti-Shirley cone and plate viscometer fitted with an automatic programming unit and an X-Y recorder was used to obtain shear stress versus rate of shear curves. The cone was enclosed in a special vapour hood to prevent evaporation of the sample (3). Measurements were made at 25 ø + 0.1 ø using a 7 cm cone (0.3 ø) and a 600 g torque spring. A standardised procedure was used for plotting the flow curves of the gels. All were sheared from zero to 1 759 s-t and back to zero in 120 s as a preliminary. The flow curves were then recorded after allowing the gel to age in the viscometer for varying periods. For assessing the rate of breakdown of the gel, the decrease in shearing stress at a constant rate of

430 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 15-- c o • I ._ 0 I 0 20 5[0 40 50 60 Glycerin, % w/w Figure g The effect of glycerine concentration on the rigidity of gelafine/glycerine gels (25øC__ O.IøC) Gelatine (99 Bloom) % w/w b •o% c shear (17.59 s-l) was recorded on the X-Y recorder with a time from 0-10 s recorded on the Y axis. RESULTS The effect of glycerin concentration on the rigidity of glycerin/gelatin gels is shown in Figs. oe and $. For gels containing less than 40}/0 w/w glycerin the expression: G=Go+m C . . . (II) held where G=rigidity, Go=rigidity at zero glycerin concentration, m=slope, C=% concentration of glycerin. Above 40% glycerin the non linear increase in the viscosity of the gel interlattice fluid was reflected by a similar non-linear increase in rigidity. The values of Go and m in equation {2) have been found to obey the straight line relationships given under {1). G O = oc q- ip Z 2 . . . (III) m _- I• q- % Z ............ (IV) where Z=% gelatin concentration and oc and [• are intercepts on their respective axes and 9 and % the slopes. Substituting these values equation (II) becomes