Page 328 - Chemical process engineering design and economics

Separator Design 307

Vacuum, P v
t
/ / S / / / / / / S

FtterCake

WMerFlow

Figure 6.11 Section of a filter cake.

where dm is the differential amount of dry cake in a layer of thickness dx and the
volume fraction of solids in the wet cake is (1 - e).
After substituting Equation 6.18 into Equation 6.17 to eliminate da, we ob-
tain
2
dP ks |av s (l-s)
(6.19)
dm p s s A F
Define a specific resistance, a.

2
ks (l-s)
(6.20)

The specific resistance, which has units of m/kg, depends on the characteristics of
the cake. As the pressure across the cake increases, the porosity of the cake de-
creases because the cake becomes compressed. Consequently, the specific resis-
tance increases. The specific resistance at any point in a compressible cake can
be expressed as

n (6.21)
a = a 0 P s

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