Permeability particle diameter

There are various methods for the determination of the surface area of solids based on the adsorption of a mono-, or polymolecular layer on the surface of the solid. These methods do not measure the particle diameter or projected area as such, but measure the available surface per gram or milliliter of powder. The surface measured is usually greater than that determined by permeability methods as the latter are effectively concerned with the fluid taking the path of least resistance thru the bed, whereas the adsorbate will penetrate thru the whole of the bed as well as pores in the powder particles. These methods appear to be more accurate than surface areas calculated from weight averages or number averages of particle size because cracks, pores, and capillaries of the particles are included and are independent of particle shape and size... 

It is seen from figure 2 that changing the particle diameter from I to 20 micron results in an efficiency change from about 3500 theoretical plates to nearly 1.5 million theoretical plates and furthermore, this very high efficiency is achieved at an inlet pressure of only 3000 p.s.i.. It is also seen that the maximum available efficiency increases as the particle diameter increases. This is because, as already discussed, if the pressure is limited, in order to increase the column length to accommodate more theoretical plates the permeability of the column must be increased to allow the optimum mobile phase velocity to be realized. It is possible to increase the inlet pressure to some extent, but ultimately the pressure will be limited and the effect of particle diameter will be the same but at higher efficiency levels. 

Small particles should be used in gas chromatographic columns since the HETP is directly proportional to particle diameter. However, column permeability is proportional (and pressure drop is inversely proportional) to the square of the particle diameter. Therefore, if particles are too small pressure requirements increase tremendously. 

In the 300-gallon-per-day plant the mean ice particle sizes have been calculated from measurements of ice bed permeability and porosity made on the ice harvested at the top of the column. From these results the important design parameters can be calculated, such as particle diameters, linear ice velocities, residence time of ice in the column, frictional losses in the wash water flowing down the column and in brine flowing toward the screens in the bottom of the coltam, and the fraction of voids occupied by air above the liquid level in the column. Typical ranges for some of these measured or calculated quantities are shown in Table III from measurements in the 12-inch diameter column. 

If flow is the dominant mechanism bringing a velocity bias to an end, then S will be the average length of the channel having a consistently higher or lower than average permeability, ultimately responsible for that bias. Channel lengths, like other distances in the packed bed, are scaled to particle diameter dp. Thus the S value based on a flow mechanism is proportional to... 

We now have a fairly adequate understanding of the different properties, including the particle diameter i/p, the pore size, the degree of permeability, and the chemical composition of the surface of the support matrix, to know which type of stationary phase can be successfully used with a particular class of peptides. Most of the HPLC packing materials now in use for peptide separations are based on the wide pore microparticulate silica gels with polar or nonpolar carbonaceous phases chemically bonded to the surface of the matrix. Methods for the preparation of these chemically bonded stationary phases, their available sources of supply. 

The velocity we can obtain at a given pressure will also be limited by the resistance to flow presented by the column, known as the specific column permeability. In equation (17-16) the permeability is broken up into its two main components the flow resistance parameter, ( ), and the particle diameter squared, dl, and can be expressed as... 

The Kf values for the particulate silica columns indicate a decrease of the permeability with increasing average mesopore diameter, increasing total porosity and increasing pore connectivity at constant average particle diameter of 10 pm. The monolithic column show a slight increase of the permeability with increasing macropore diameter at constant total porosity which is to be expected. 

The constant Bo characterises the permeability of the column, which depends on the interstitial porosity of the column, c, (with regularly packed columns, e, is usually close to 0.40) and increases with the second power of the mean particle diameter, dp. From the Koz.eny-Carman equation [16.171 it follows ... 

A specific permeability of 4 x IO mm was calculated in Problem 18. To what particle diameter does this K° value correspond ... 

Prefer batch when cake formation rate is <0.01 mm/s (low concentrations of small diameter particles). OK for higher liquid viscosities and higher temperatures. Batch can be vacuum or pressure operation. Prefer vacuum operation for particle diameter >30 pm, if there is a small mass of tines (<50% with diameter <5 pm) and bed has permeability between 0.1 to 1000 pm. Prefer pressure filters for particle diameter 1 to 70 pm, if there is a large mass of fines (with >50% w/w with diameter <10 pm) and bed has permeability between 0.001 to 0.1 pm. ... 

Permeability can be increased by increasing the particle diameter, since K° dp (Equation 7.26). 

Since equation 12 is valid when Darcy s law is applicable, the equivalent spherical particle diameter, ds, and the intrinsic permeability, k, can be related by... 

In terms of the permeability, k, rather than the particle diameter, we have... 

Multidimensional Effects. In the previous section, we studied the wall effect on the shear factor. To give a full account of the wall effects, we now look at the no-slip flow effect posed by the containing wall (multidimensional effect) on the total pressure drop. For simplicity, let us rewrite the normalized pressure drop factor, fv, based on the permeability of the medium rather than the particle diameter,... 

Permeability is one other method for obtaining information about particle diameters. If one packs a tube with a weight of powder exactly equal to its density, and applies a calibrated gas pressure tbrough 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 ji. 

The Taylor-Aris result for the dispersion coefficient (Eq. 4.6.35) has been applied to the empirical correlation of measured and calculated longitudinal dispersion coefficients in flow through packed beds and porous media (see Eidsath et al. 1983). Typically, the velocity in the Peclet number of the Taylor-Aris formula is identified with the superficial velocity, and the capillary diameter with the hydraulic diameter for spherical particles. An alternative velocity suggested by the capillary model is the interstitial velocity, and an alternative length is the square root of the permeability. In an isotropic packing of particles is about one-tenth the particle diameter (Probstein Hicks... 

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