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308 Chapter 6

Table 6.17 Filter-Cake Specific-Resistance Parameters (Source Ref. 27).

10
Substance a 0(10 )m/kg a Exponent, n
Asbestos —
Calcium carbonate 0.19
Celite — 0.14
Crushed limestone — ——
Gairome clay 282 0.60
Ignition plug clay — 0.56
Kaolin — —
Kaolin, Hong Kong pink 101 0.33
Solkofloc 0.0024 1.01
Talc 8.66 0.51
Titanium dioxide 32 0.32
Zinc sulfide 14 0.69
8
General range Ixl0 tolxl0 3 0 to 1.2

a) To convert to ft/lb multiply bv 1.488.

where P = P - P is equal to the pressure drop across the cake at any point. The
s 0
exponent, n, usually varies from 0.2 to 0.8. If n = 0, the cake is incompressible.
Values of the specific resistance and n are given in Table 6.17.
After substituting Equation 6.20, 6.21, and dP s = - dP into Equation 6.19,
and after separating variables, we obtain,

dP s a 0 u v s dm
(6.22)
PS" A F

The limits of integration for Equation 6.22 are: at Xi = 0, PS = 0, m = 0 and at x =
x 2, PS = P 0 - Pi, and m = iris, where P, is the pressure at the interface of the cake
and the filter medium, as shown in Figure 6.11. Thus, after integrating Equation
6.22 across the cake, we obtain

0
(Po-Pi) " 0
(6.23)

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