ratio. The relation for droplet size then becomes
dmax&ge^1 =^2 Zc^1 =^2 ð 11 : 14 ÞThis is again a very simple relation. It has not been as well tested as Eq.
(11.11), to the author’s knowledge.
Notice that in the regime TV the viscosity of the viscous phase is a
variable governing droplet size, but not in TI. Of course, the magnitude ofZc
would determine whether the regime is TI or TV. If the conditions are such
that Redris close to unity, the relations governing drop size will be between
those given in Eqs. (11.11) and (11.14), and viscosity will have some effect,
say,d! 1 =Z^1 C=^4.
11.3.4 Complications
The discussion given in Section 11.3 is to some extent an oversimplification,
not so much because the relations given are approximations, but rather
because several conditions must be fulfilled for them to be applicable, since
foam and emulsion formation may involve a number of other variables. A
few will be mentioned by way of illustration.
Theviscosity of the disperse phaseZDis not a variable in any of the
equations for the turbulent regimes. Nevertheless, it is often
observed that a higher value ofZDleads to a higher average drop
size. This is because the time needed for deformation of a drop may
be longer than the lifetime of the eddies that would cause its
disruption. The latter is given by Eq. (11.9). Table 11.2 gives the
stress acting on a droplet, and Eq. (11.6) can then be used to
calculate the deformation time. For example, forE¼ 1010 W?m^3 ,d
¼ 1 mm, andZD¼ 0 :1Pa?s, we would obtain for the deformation
time 5ms and for the eddy lifetime 0.5ms (try to check these
calculations). This is clearly impossible and the drops can only be
broken up by eddies larger than 1mm, which have a longer lifetime
but provide a smaller stress; hencedmaxwould be larger than 1mm.
The value of thepower density may greatly vary among sitesin the
apparatus. Near the tip of a stirrer,ewould have a much higher
value than further away. It means that the effective volume for
droplet disruption is much smaller than the total volume of stirred
liquid. This has two consequences. First, part of the mechanical
energy is dissipated at a level where it cannot disrupt drops (and is
thereby wasted). Second, droplet breakup takes a long time, because