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dv
pfD a€-f = Ti - opgD ,(43)
where of is the velocity of an element of _a liquid ligament at z. And the
interfacial shear stress Ti is given in terms of interfacial friction factor
fias
Ti = fi
1 pgvg•(44)
When the gravity term is negligible compared'with the interfacial term, Eq.
(43) can be rewritten as
dvf---------------
= dt =dz(45)
1g 1 f v2f
p 2 pfD i g
At z = £, this velocity is equal to the initial velocity of the droplet, that
is
vf(z=t) = vi(46)
Integrating Eq. (45) from z = 0 to z = z,, one can obtain
2pfviD=2fi p9v29£I(47)
Equation (47) implies that the kinetic energy of the droplet entrained is
equal to the work exerted on the element of a liquid ligament by gas flow.
The ligament of liquid at the pool interface, as shown in Fig . 2, can be
regarded as a sequence of several droplets which are about to be entrained .
Therefore, the interfacial shear stress may be related to the drag coefficient
for a droplet in the wake regime, i.e., Eq. (33), thus
-0.5
fi CD--ReD(48)
The length of the liquid ligament is assumed to be proportional to the width
of the ligament which is on the order of the droplet diameter in analogy with
the Rayleigh instability of a liquid jet. Then,
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