Entrainment rate of droplets in the ripple-annular regime for small vertical tubes Page: 8 of 28
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e a pf?7 R(a) (15)
Taylor obtained an analytic solution for the growth rate of capillary waves. When the
liquid viscosity is small the asymptotic solution is the same as Kelvin-Helmholtz's inviscid
model. The growth rate of the fastest growing waves is:
R(a) = 0.384 kou, (16)
Pf
where
ko = pg- (17)
0-
is a wave number associated with the fastest growing waves. For water and Freon-113
equation (16) is applicable. However for more viscous fluids the coefficient in equation
(16) is not constant for very viscous fluids, but becomes a function of the liquid viscosity,
and in such cases the complete solution obtained by Taylor should be used. The criterion
for the low viscosity range where equation (16) is valid is
P100 (18)
Combining equations (15) through (17):
eD oc P-u2DPfUg Pg (19)
Jtf 6 Pf Pf
Equation (19) may be written as:
eD x We, Re / [Pg (20)
puf ~ h ufypf
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Lopez de Bertodano, M.A.; Assad, A. & Beus, S.G. Entrainment rate of droplets in the ripple-annular regime for small vertical tubes, article, June 1, 1998; West Mifflin, Pennsylvania. (https://digital.library.unt.edu/ark:/67531/metadc706213/m1/8/: accessed May 15, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.