Particles permeability

The introduction of large pore supports, which are able to increase particle permeability and hence mass transfer, represented a turning point in protein analysis [113]. Around 1990, anew HPLC technique, using nonporous supporting materials characterized by presenting two set of pores, was introduced by Afeyan et al. [114]. A brief description of this HPLC technique, which is gaining still more popularity in protein analysis, is discussed in the next section. 

Kinetic factors will lead to dispersion of the fronts being much more important for favorable isotherms. Intraparticle mass-transfer resistance can be eliminated or decreased by using peUicular packings, reducing particle size or increasing particle permeability as shown in Fig. 3.4-4. 

At low velocities /(A) <= 1 and both equations lead to similar results. However, at high superficial velocities, /(A) <= 3/A and so the last term in Rodrigues equation becomes a constant since the intraparticle convective velocity Vq is proportional to the superficial velocity u. The HETP reaches a plateau that does not depend on the value of the solute diffusivity but only on the particle permeability and pressure gradient (convection-controlled limit). 

Schon and Georgi (2003) developed a capillary-based model for dispersed shaly sand that shows an analogy to the Waxman-Smits equation (Section 8.5.3) for electrical properties. This model (Fig. 2.32) accounts for the reduction in porosity and decrease in the pore cross-sectional area with the content of clay and the associated immobile water. Starting with Hagen-Poiseuille s law, the flow rate for a cross-section is reduced by a film of clay particles. Permeability for dispersed shaly sand can be written as a functimi of the clean sand permeability sd and the dispersed shale content Fsh... 

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

In special cases (as in colloidal solutions) some particles can be considered as essential and other particles as irrelevant , but in most cases the essential space will itself consist of collective degrees of freedom. A reaction coordinate for a chemical reaction is an example where not a particle, but some function of the distance between atoms is considered. In a simulation of the permeability of a lipid bilayer membrane for water [132] the reaction coordinate was taken as the distance, in the direction perpendicular to the bilayer, between the center of mass of a water molecule and the center of mass of the rest of the system. In proteins (see below) a few collective degrees of freedom involving all atoms of the molecule, describe almost all the... 

An additional benefit of prethickening is reduction in cake resistance. If the feed concentration is low, there is a general tendency of particles to pack together more tightly, thus leading to higher specific resistances. If, however, many particles approach the filter medium at the same time, they may bridge over the pores this reduces penetration into the cloth or the cake underneath and more permeable cakes are thus formed. 

Because gravity is too weak to be used for removal of cakes in a gravity side filter (2), continuously operated gravity side filters are not practicable but an intermittent flow system is feasible in this arrangement the cake is first formed in a conventional way and the feed is then stopped to allow gravity removal of the cake. A system of pressure filtration of particles from 2.5 to 5 p.m in size, in neutralized acid mine drainage water, has been described (21). The filtration was in vertical permeable hoses, and a pressure shock associated with relaxing the hose pressure was used to aid the cake removal. 

Deterrnination of the specific surface area can be made by a variety of adsorption measurements or by air-permeability deterrninations. It is customary to calculate average particle size from the values of specific surface by making assumptions regarding particle size distribution and particle shape, ie, assume it is spherical. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Leaching is the removal of a soluble fraction, in the form of a solution, from an insoluble, permeable sohd phase with which it is associated. The separation usually involves selective dissolution, with or without diffusion, but in the extreme case of simple washing it consists merely of the displacement (with some mixing) of one interstitial liquid by another with which it is miscible. The soluble constituent may be solid or liquid and it may be incorporated within, chemically combined with, adsorbed upon, or held mechanically in the pore structure of the insoluble material. The insoluble sohd may be massive and porous more often it is particulate, and the particles may be openly porous, cellular with selectively permeable cell walls, or surface-activated. 

The factors to consider in the selection of cross-flow filtration include the cross-flow velocity, the driving pressure, the separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, and the hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

Of particular interest in the usage of polymers is the permeability of a gas, vapour or liquid through a film. Permeation is a three-part process and involves solution of small molecules in polymer, migration or diffusion through the polymer according to the concentration gradient, and emergence of the small particle at the outer surface. Hence permeability is the product of solubility and diffusion and it is possible to write, where the solubility obeys Henry s law,... 

In suspension processes the fate of the continuous liquid phase and the associated control of the stabilisation and destabilisation of the system are the most important considerations. Many polymers occur in latex form, i.e. as polymer particles of diameter of the order of 1 p.m suspended in a liquid, usually aqueous, medium. Such latices are widely used to produce latex foams, elastic thread, dipped latex rubber goods, emulsion paints and paper additives. In the manufacture and use of such products it is important that premature destabilisation of the latex does not occur but that such destabilisation occurs in a controlled and appropriate manner at the relevant stage in processing. Such control of stability is based on the general precepts of colloid science. As with products from solvent processes diffusion distances for the liquid phase must be kept short furthermore, care has to be taken that the drying rates are not such that a skin of very low permeability is formed whilst there remains undesirable liquid in the mass of the polymer. For most applications it is desirable that destabilisation leads to a coherent film (or spongy mass in the case of foams) of polymers. To achieve this the of the latex compound should not be above ambient temperature so that at such temperatures intermolecular diffusion of the polymer molecules can occur. 

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