Drugs and the pharmaceutical sciences

Pore Sizes and Distributions 71
pressure differential of 1.66 bar. The simultaneous solution of Eqs. (3) and (5), which is
graphically solved in Figure 5, is about 8.5 mm. The calculated hydrodynamic pore size of
this filter is smaller than the maximum pore size, as determined by bubble point
measurement. If this was reversed, it would indicate that the block had a nonuniform
structure such as that produced by a dense surface skin. This means that the assumption
that the capillary length is equal to the thickness of the medium is incorrect. In this block
the flow radially through the filter resulted in the same pore size being calculated. There
was obviously no skin or surface densification. When there is surface densification, there
can be a discrepancy between the maximum pore size and the calculated hydrodynamic
pore size. The value of L must be adjusted to take the densification into account.
Sometimes it is difficult to make a conclusion that can be supported by data in the
determination of L for a dense surface.
In membrane filters this can be very important in the determination of pore size and
retention characteristics. It is possible to measure the pore size distribution independently
of surface densification. A rigorous analysis of this process requires the solution of the
flow equation for a wetted filter medium. For membrane filters in the pore size range of
about 0.1–3 mm, the following equation has been developed:
PV ¼ pD4 PP
128 L
¼ nRT ð8Þ
This represents the viscous portion of the gas flow. An additional term must be
added to this equation when the Knudsen number, Kn, is greater than zero. The flow
equation for small capillaries is (Carman, 1956):
PV ¼ pD4 DPP
128hL
1 þ 4Kn 2
f
FIGURE 6 Carbon block filter dimensions.
1 ð9Þ
Kn is the Knudsen number, the ratio of the mean free path of the gas molecules to
the diameter of the capillary. In membrane filters the value of Kn cannot be ignored. In
this equation f is a reflection factor. This factor is absent from the viscous flow equation
because the molecules never reach the surface of the capillary, because a layer of