Relative Importance of the Effects of Seed and Feed Stage ...

368 Krishnan et al.
is proportional to the square root of the power input per unit volume (Koh
et al., 1984; Kusters et al., 1997; Lowry et al., 1984, 1986):
g avg ¼
2P 0:5
ð14Þ
15mV R
where P is the power-input, V R is the volume of the liquid in the reactor,
and m, the viscosity of the fluid. For a 40, 45, and 50% solids batch
emulsion copolymerizations of vinyl chloride and ethyl acrylate in a 2
gallon reactor, Lowry et al. (1984, 1986) found that the amounts of
coagulum at the end of the polymerization could be correlated to the
agitation power-inputs using Eqs. 12 and 14. Similarly, for semibatch
emulsion polymerization of BMA and its copolymerization with NMA,
Dave (1998) found that the mass of coagulum was proportional to P 0.5 ,as
expected from Eqs. 13 and 14.
Some experimental results that do not conform to Eqs. 9 or 13 must
also be pointed out. Eq. 13 indicates that amount of coagulum is directly
proportional to the time to which the suspension is subjected to the shear
rate g. However, using viscosity measurements, Utracki (1973) has found
that the high rate macrocoagulation process was preceded by an induction
period called the coagulation time, t c , during which the coagulation energy
necessary to overcome the threshold energy of coagulation, accumulated in
the system. Microcoagulation (formation of doublets and triplets) occurred
during the induction period. Instead of the exponential decrease of the
particle number with time as suggested by Eq. 11, Utracki proposed that the
number of particles decreased linearly with time during the induction
period. His theoretical equation relating t c to the shear rate, g, and volume
fraction of dispersed phase, f, was confirmed by the experimental data for
poly(vinyl chloride) and poly(vinyl acetate) latexes. Also, Zollars and Ali
(1987) found that when the repulsive forces (arising from adsorbed
surfactant, or chemically bound surface groups) between the latex particles
were high, the shear coagulation rate decreased with an increase in the
particle volume fraction, f, in contrast to Eq. 10. This unusual result was
attributed to the decrease in the collisional efficiency with increasing
particle volume fraction. However, when the latex particles possessed only
weak repulsive forces, the coagulation rate increased linearly with f, as
expected. Their work involved very low particle volume fractions, ranging
from 4.2910 5 to 6.8610 4 . Matejicek et al. (1988) have reported that
during a 52% solids semibatch emulsion terpolymerization of styrene, n-
butyl acrylate, and acrylic acid, in a 25 dm 3 stirred reactor, the amount of
coagulum decreased with an increase in P/V R below a specific power-input
(P/V R ) of 80 W/m 3 . They attributed this coagulum formation to poor