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3.9 P article Analysis 233
Table 3.15
The density def initions
Density Volume included in definition
Symbol Solid Open pore Closed pore Interparticle
olume material v volume volume void volume
Bulk b √ √ √ √
Particle p √ √ √
Skeletal s √ √
True t √
where is the fluid densityis introduced . In the present book, the term “hydraulic density”
f
in order to highlight the use of this kind of density in hydrodynamic calculations in olv- v
ing suspension of particles.
Despite the fact that this hydraulic density is essential to many calculations in olving v
fluidization and the suspension of particles, it is characteristic that in the related literature,
authors use the terms “particle density” or “solid density” without specifying if the fluid
in the pores has been taken into account. Ho the subject of hydraulic density has
v
er
we
,
been analyzed in studies of the behavior of impermeable aggreates in fluids. As these g
aggregates could be seen as porous particles, the releant analysis is interesting and will v
be presented here.
The case of hydraulic density
g
The case of impermeable spherical aggreates has been analyzed by Johnson et al .
ork,
(Johnson et al ., 1996). In this w the settling velocity of aggreates in liquids using g
Stoke’s law has been studied and a modified Stokw has been introduced. The dif s la fer- e’
ence from the classical Stokw is that the density difference is expressed in terms of e’
s la
g the aggreate density.
(1 ) (3.559)
a a f s a
where:
a the aggreate porosity g
the aggregate density
a
the density of the particles composing the aggre g ate.
s
Thus, the aggreate–fluid density dif ference becomes g
(1
)
a f a f s a f (3.560)
(1 (1 f ) a (1 )( ) s
)
f
a
a
s
To highlight the difference from the classical Stoks equation, the density difference in
e’
the latter is ( ), where is the skeletal density of the rigid particle. No it is easy to w ,
s f s
illustrate the analogy to a porous particle. A porous particle can be viewed as an aggregate,