644 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Empty •Pipe With "' ,.•,• d i(fi Inlet o• iO -I 0 5 I0 15 L/d Figure 5. Intensity of segregation vs. relative length of the mixer Before mixing, I is equal to one and for a complete, uniform mixture I is equal to zero. Figure 5 shows the relation between I and the relative length of the device. Figure 6 shows the pressure drop as a function of the relative length. It can be seen that with 6 elements (which corresponds to L/D= 7.5) the intensity of segregation is 2 x 10 -4 and the pressure drop is only 0.037 psi. Analysis of Pressure Drop and Power Consumption Since there are no moving parts in the device, only the processed materials are in motion. Consequently, the only energy required for the mixer unit is the energy required to overcome the pressure drop. The general equation for calculating pressure drop in an empty pipe for isothermal incompressible fluids is known as the Darcy equation, which can be written as: •P=/D P, gc (4)

CONTINUOUS MIXING AND PROCESSING 645 0.•I9 0.146 Scllaschlik Mixer STATIC MIXER © J Unit Pipe With ß Radial Inlet ß ß ß ß J Empty Pipe .... 0.0?3 0 I0 20 50 40 50 L/d Pressure drop vs. relative length of the mixer Figure 6. Pressure drop vs. relative length of the mixer Where Ap = pressure drop in empty pipe f = Darcy's friction factor L = length of pipe D = inside diameter of pipe v = velocity of fluid go = gravitational acceleration p = density of fluid Pressure drop in the device of the same length and diameter as an empty pipe is determined by multiplying the calculated pressure drop in the empty pipe by a oeaetor, K. That is: AP•s,.• -- K AP (5) where APs•t is the pressure drop in the device. The factor, K, is a function of the geometry of the mixer elements and the Reynolds number. The values of K were determined under different conditions. To facilitate the calculation of pressure drop in the device, the values are tabulated and plotted for different conditions (Figs. 7, 8, and Table I). The factor, K, is determined according to the range of the Reynolds number,