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3.9 P article Analysis 235

the latter is practically equal to the hydraulic densityThis is the reason why in gas–solid .
fluidization, the particle density is used in all hydraulic calculations. The complication is
found only in the case where porous solids are found in suspension in a liquid–solid sys-
tem, e.g. fluidization and suspension/sedimentation in agitated vessels. In any case, one
w
should be aare of the type of density used or that should be used. For e Menoud xample,
et al . (1998) used two different densities for modeling the fluidized bed operation, i.e. the
resin particle density for mass balances and relevant calculations, and the hydraulic density
for the relevant hydraulic calculations (e.g. for the evaluation of Archimedes number).
Special reference should be made to resin–liquid systems, where the phenomenon of
swelling makes the case more complex. A resin’s matrix is flexible and when immersed in
xpands,
a liquid, its volume e leading to an increase in its particle diameter and in turn, to
a decrease in particle density (mass of dry resin per volume of swollen particle).
Furthermore, the loading of the resin with ions results in further changes in its v olume
(Helfferich, 1995). Thus, in these cases, the particle density and diameter as well as the
hydraulic density should be referred to for the swollen and loaded resin. In practice, a
mean value is frequently used.

3.9.7 Terminal velocity of a single particle

The forces that are present when an isolated porous particle is suspended in a fluid are the
following.
The gravitational force F , g
F g M g p (3.564)

the byant force uo F , b
F b V g f (3.565)

and the drag force F . d
AC
F d F g F b f pr D u ter 2 (3.566)
2

where:
M p the mass of the particle
V f the volume of fluid displaced by the particle
A pr the area of the particle projected on a plane normal to the direction of
flow (projected area perpendicular to flo w)
u ter the terminal v elocity
C D an empirical drag coef icient. f
Then,
M V V (3.567)
p p p p f p