Limitations

For very fine powders, the basic Kozeny-Carman equation is not accurate. This is because the laminar flow assumption on which it is based is no longer valid. Compressed fine particles result in a powder bed with very small channel widths. If these widths are comparable to the mean free path length of the gas molecules, laminar flow conditions are not maintained.

Such a situation, involving molecular flow or diffusion conditions, is known as Knudsen flow (Ref 26) and can occur with very fine powders or with coarser particles at low pressures. Figure 7 shows a typical apparatus used to measure find particles under molecular flow conditions (Ref 27, 28). In some powders, both laminar and molecular flow may be significant. This is known as the transitional region.

Mercury reservoir ft— -MM

Valve or damp

— Graduated Manometer cylinder g

Fig. 7 Modified Pechukas and Gage apparatus for fine powders. Source: Ref 27

Evaluating surface areas with steady-state flow conditions historically excluded noninterconnected blind pores. A method for including blind pores by utilizing transient-state flow measurements is the principle behind the apparatus shown in

Fig. 8(a) (Ref 29, 30). A typical flow rate curve, showing extrapolation of the steady-state portion to determine the time lag is given in Fig. 8(b). The basic principle of the permeability analysis has not changed much during the last several years; even so, instruments now use more sophisticated pressure transducer and flowmeter or flow controller. Combined with a computerization of the instrument and an improved data analysis software, the instrument offer a wider variety of analysis tasks and computational methods.

Fig. 8(a) (Ref 29, 30). A typical flow rate curve, showing extrapolation of the steady-state portion to determine the time lag is given in Fig. 8(b). The basic principle of the permeability analysis has not changed much during the last several years; even so, instruments now use more sophisticated pressure transducer and flowmeter or flow controller. Combined with a computerization of the instrument and an improved data analysis software, the instrument offer a wider variety of analysis tasks and computational methods.

Fig. 8(a) Transient flow apparatus

Fig. 8(b) Flow rate curve for the transient flow apparatus

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