In this section,g is assumed constant. This means either that no
surfactant is present (then single drops are considered) or that there is a
large excess of surfactant. Furthermore, when speaking about drops,
bubbles are also implied. Most of the theory discussed is only valid for small
volume fractions.
11.3.1 Regimes
The relations governing the size of the drops obtained depend on
hydrodynamic conditions. Accordingly, some different regimes can be
distinguished, and in each regime equations can be derived that predict
parameters like local stress, resulting drop size, and time scales of various
events. The main factors determining what the regime is are the type of force
and the flow type. The reader is assumed to be familiar with the material in
Section 5.1.1.
Thetypes of forcescausing disruption of drops can be
Frictional, generally called viscous, forces, which are due to the
continuous liquid flowing along the drop surface, hence the force
acts for the most partparallelto the drop surface. (Some authors
speak of shear forces.) The local stress would equal viscosity times
local velocity gradientðZ?CÞ.
Inertialforces, due to local pressure fluctuations, which in turn are
generally evoked by local velocity fluctuations according to the
Bernoulli equation (5.4). They act for the most partperpendicularto
the drop surface. The local stress would equalrvvDv, wherevvis the
average liquid velocity andDvis the local velocity difference.
Flow Types. The main distinction is between:
Laminarflow, occurring if Re<2000. The Reynolds number is
given in Eq. (5.5); see also Table 5.1.
Turbulentflow for Re>2500.
These variables give rise to threeregimesfor droplet (or bubble) break-
up:
- Laminar/viscousforces (LV), i.e., breakup by viscous forces in a
laminar flow field - Turbulent/viscousforces (TV)
- Turbulent/inertialforces (TI)
Whether in turbulent flow viscous or inertial forces are predominant
depends on the drop Reynolds number Redr (Table 5.1), where the