Permeametry methods

Some of the methods of analysis of porosity are based on specific properties of porous and disperse materials, namely, thermoporometiy method is based on shifts of the temperature of phase transitions and permeametry methods are based on characteristics of mass transfer through porous media. Each method has its advantages, for example low cost of equipment and high performance. Each has its own range of optimal measurements. But, all the methods are really doomed for coexistence, and in many cases they supplement each other. 

Permeametry Method This method is based on the fact that the flow rate of a fluid through a bed of particles depends on the pore space, the pressure drop across the bed, the fluid viscosity, dimensional factors such as the area of the bed, and specific surface area (S. The determination of permeability can be made either under continuous steady-state flow (constant flow rate) or under variable-flow (constant-volume) conditions. 

All of the permeametry methods are based on the Carman-Kozeny equation given in Fig. 4 which relates the approach velocity u to the porosity of the powder e and the specific surface of the sample Sw. The specific surface calculated involves only the walls of the pores of the bed which are swept by the flow and it does not take into account the pores within the particles which do not contribute to the flow. The surface measured, therefore, is an envelope surface area and it can be very much smaller than the total surface area of the particles as measured, say, by gas adsorption. 

Particles consist of both internal and external surface area. The external surface area represents that caused by exterior topography, whereas the internal surface area measures that caused by microcracks, capillaries, and closed voids inside the particles. Since the chosen surface area technique should relate to the ultimate use of the data, not all techniques are useful for fine powders. The commonly used approaches are permeametry and gas adsorption according to the Brunauer, Emmet, and Teller (BET) equation [9]. Because of simplicity of operation and speed of operation, permeametry methods have received much attention. The permeametry apparatus consists of a chamber for placing the material to be measured and a device to force fluid to flow through the powder bed. The pressure drop and rate of flow across the powder bed are measured and related to an average particle size and surface area. Especially for porous powders, permeametry data include some internal surface area, thus decreasing their value. 

Surface Area Determination. Specific surface areas were required to determine the fraction of adsorbent surface covered by the virus at equilibrium. This in turn is required for adsorption free-energy evaluations. BET-N2 (21) methods were used where applicable and Kozeny (22) permeametry methods were used for confirmation. Values are listed in Table I. Although the values measured by the two methods are not directly comparable, trends shown by the two sets of values are similar. The BET method measures all surface accessible to adsorbing N2 molecules and generally is considered to be the most reliable... 

Permeability is another method for obtaining information about pcirticle diameters. If one packs a tube with a weight of powder exactly equal to its density, and applies a calibrated gas pressure through the tube, the pressure drop can be equated to an average particle size. The instrument based on this principle is called the "Fisher Sub-Sieve Sizer ". Only one value can be obtained but the method is fast and reproducible. The instrument itself is not expensive and the method can be applied to quality control problems of powders. Permeametry is usefiil in the particle range of 0.5 to 50 n. 

Viscous flow permeametry measured near atmospheric pressure offers the advantages of experimental simplicity and a means of measuring the external or envelope area of a powder sample which is otherwise not readily available by any adsorption method. The usefulness of measuring the external surface area rather than the BET or total surface area becomes evident if the data is to be correlated with fluid flow through a powder bed or with the average particle size. 

The concept of the surface diameter may be mostly used in the field of adsorption and reaction engineering, where the equivalent surface exposure area is important. The determination of the surface area depends on the method of measurements for example, permeametry can give a much lower area than does gas adsorption. The latter often includes the contribution of pore surface area, which is accessible to the gas molecules. The determination of particle surface area by gas adsorption is given in 1.2.2.4. The fundamentals of gas adsorption are further covered in 1.4.1. 

One method which is known under the name of permeametry [131] or Poiseuille-Knudsen method [124] is based on the law of gas permeability in a porous media in the two flow regimes molecular flow (Knudsen) and laminar or viscous flow (Poiseuille). According to Darcy s law, the gas flux through a membrane with a thickness / can be written as / = KAP/l, where K is the permeability coefficient and AP (AP = Pi - P2) the pressure difference across the membrane. If the membrane pore diameter is comparable to the mean free path of the permeating gas, K can be expressed as a stun of a viscous and a non-vis-cous term... 

Some other techniques involving membrane permeability have been developed that have not yet been extensively used. Concerning gas permeability, a method called permeametry has been developed [41], based on Adzumi equation. It consists of measuring the variation in membrane permeability when favoring either molecular (Knudsen) or laminar (Poiseuille) flow regime. A mean pore radius is obtained with this method. 

In cake filtration, where the surface volume diameter is of interest, methods for surface area determination are relevant (these measure only mean sizes) particularly, permeametry, gas diffusion and hindered settling methods. 

The volume equivalent sphere diameter or equivalent volume sphere diameter is a commonly used equivalent sphere diameter. We will see later in the chapter that it is used in the Coulter counter size measurements technique. By definition, the equivalent volume sphere diameter is the diameter of a sphere having the same volume as the particle. The surface-volume diameter is the one measured when we use permeametry (see Section 1.8.4) to measure size. The surface-volume (equivalent sphere) diameter is the diameter of a sphere having the same surface to volume ratio as the particle. In practice it is important to use the method of... 

It should be clear from the above remarks that permeametry is an auxiliary, rather than primary, method for determining particle size. It is useful when other evidence (e.g., microscopy) confirms the applicability of the Ergun equation. 

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