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medium viscosity  m is universally dependent on  irrespective of the particle radius
[48, 52]. The  eff of four CB aggregates ( eff ) was evaluated by comparing the
/ m ratios of the CB aggregates and the universal  / m versus  curve for the
hard-core silica particles. The results are shown in Figure 16. From the abscissa
coordinates of the plot for the CB aggregates (open symbols), the  value was
estimated to be 2.6, 2.6, 5.5, and 16 for the CB-76, CB-24-1, CB-15-2, and AcB
suspensions, respectively. This result indicates that the  value or the effective
volume is an important parameter to characterize CB aggregates. With increasing
shear rate, the density of the three-dimensional network of the CB aggregates is
decreased. Under sufficient high shear, the size of flow unit becomes the CB
aggregate size. In this shear region, the second Newtonian flow appears. Therefore,
the CB aggregates are considered to be a flow unit corresponding to “effective
volume”. The  value increases with increasing the DBP absorption value,
suggesting that  eff depends mainly on aggregate structure morphology irrespective
of particle size. This result indicates that the CB aggregates behave as a flow unit at
high shear rates and the difference between  eff and  reflects mainly the non-
spherical shapes of the aggregates.
Figure 16. Relative viscosity  r versus effective volume fraction  eff plots of the
CB-76/(PS/DBP), CB-24-1/(PS/DBP), CB15-2/(PS/DBP), and AcB/(PS/DBP)
suspensions. The  eff values were determined in a way that the  / m versus  eff for four
suspensions were superposed on the universal  / m versus  plots obtained for unimodal
hard-core particles [32].
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