Particle permeametry

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. 

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. 

Volume shape coefficients may be determined from knowledge of the number, volume mean size, weight and density of the particles comprising a fraction graded between close limits e.g. by sieving. Further, if surface areas are also determined by permeametry, surface shape coefficients may... 

Correlation between specific surface areas measured using a simple and robust technique such as gas permeametry and SSA determined by more sophisticated techniques such as PSD, MIP and BET have been carried out. A good agreement between Sbf (surface measured by gas permeametry, Blaine Fisher, Sbf) and measured Sbet was obtained. This is due to the fact that the DS studied does not exhibit intraparticular microporosity (both Krypton and air can access all the surface developed by the powder). Sbf compared with estimated Sng (estimated from MIP results) and Spsd (estimated from PSD results) show a good linearity, but Shb and Spsd values are overestimated. This arises due to the simplifying approximations for particles shape included in the theoretical models for PSD and PIM... 

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. 

Permeametry is generally suitable for powders of average particle size between 0.2 and 50 microns but it can be also used with coarser powders, say up to 1000 microns using a suitably scaled-up test equipment. 

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. 

Permeametry ) Surface area measurement useful for particle sizes smaller than Gas adsorption) about 50 pm ... 

The Fisher sub-seive sizer employs permeametry in a relatively quick and simple technique to determine the volume specific surface area, 5, of a powder compact. In combination with the pore volume of the compact, V, the mean equivalent radius, r, of the macropores (>1000 A radius) in a dense green powder compact composed of micron-size particles can be estimated from... 

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... 

In fluidised and fixed beds, knowledge of particle density is necessary for calculation of the effective void bed volume (Ergun equation Ergun 1952) and specific surface areas of solids by permeametry using the Kozeny-Carman equation (BS 4359 Pt 2 1982 Carman 1937). Kozeny-Carman equation... 

Harris [17] discussed the role of adsorbed fluid in permeametry but prefers the term immobile fluid. He stated that discrepancies usually attributed to errors in the porosity function or non-uniform packing are, in truth, due to the assumption of incorrect values for e and S. Associated with the particles is an immobile layer of fluid that does not take part in the flow process. The particles have a true volume vj and an effective volume v a true surface S and an effective surface 5 a true density p, and an effective density p. The true values can be... 

The settling of particles, constrained to fixed positions, in a stagnant liquid is analogous to the permeametry situation where the liquid is moving and the bed is fixed. For a sedimenting suspension, the pressure head may be replaced by the gravitational minus the buoyant force on the particles ... 

Permeametry, the measurement of the rate of flow of a fluid through a porous medium under a known pressure gradient, is a technique by means of which a mean particle size (but not a particle size distribution) can be determined. The equation for the rate of fluid flow through a packed bed of uniform spheres is the semiempirical Ergun equation... 

A mean particle size can be calculated from permeametry measurements using the Ergun equation provided that... 

If conditions (1) and (2) are met, but the interstices are much smaller than the mean free path of the molecules, then the dusty gas model of Mason and coworkers [23] can be used to calculate a mean particle size from permeametry measurements. There is a major experimental difficulty involved in using permeametry at very small particle sizes, however. The fluid may channel through fissures in the agglomerate, which, although large compared with the interstices, may well pass unnoticed to the eye. 

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. 

---