Porous particles

A separation method in which a mixture passes through a bed of porous particles, with smaller particles taking longer to pass through the bed due to their ability to move into the porous structure. 

SI units stands for Systeme International d Unites. These are the internationally agreed on units for measurements, (p. 12) size-exclusion chromatography a separation method in which a mixture passes through a bed of porous particles, with smaller particles taking longer to pass through the bed due to their ability to move into the porous structure, (p. 206)... 

Solid Density. SoHds can be characterized by three densities bulk, skeletal, and particle. Bulk density is a measure of the weight of an assemblage of particles divided by the volume the particles occupy. This measurement includes the voids between the particles and the voids within porous particles. The skeletal, or tme soHd density, is the density of the soHd material if it had zero porosity. Fluid-bed calculations generally use the particle... 

A second convention is the placement of an imaginaiy envelope around the outermost boundaiy of a porous particle, so that all solute and nonadsorbing fluid contained within the pores of the particle is considered adsorbed. 

Early suspension polymers, although less contaminated, were supplied as more or less spherical particles with a diameter in the range 50-100 p,m. Such materials had a much lower surface/volume ratio than the emulsion polymers and, being of low porosity, the materials were much slower in their gelation with plasticisers. The obvious requirement was to produce more porous particles and these became available about 1950 as easy-processing resins. 

The skeletal density, p, also called the true density, is defined as the density of a single particle excluding the pores. That is, it is the density of the skeleton of the particle if the particle is porous. For nonporous materials, skeletal and particle densities are equivalent. For porous particles, skeletal densities are higher than the particle density. 

FIGURE 1.5 Cumulative pore volume curves of 5-/j.m monosized porous particles. [Reprinted from T. Ellingsen et al. (1990). Monosized stationary phases for chromatography. J. Chromatogr. 535, 147-161 with kind permission from Elsevier Science-NL, Amsterdam, The Netherlands.]... 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

When the resistance to mass transfer to the external surface of the pellet is significant compared with that within the particle, part of the concentration driving force is required to overcome this external resistance, and the concentration of reacting material at the surface of the pellet Cm is less than that in the bulk of the fluid phase Cao- In Sections 10.7.1-10.7.3, the effect of mass transfer resistance within a porous particle... 

Pore diffusion With porous particles, pore diffusion is likely to limit reaction rates at the internal surface. 

Reaction, diffusion, and catalyst deactivation in a porous catalyst layer are considered. A general model for mass transfer and reaction in a porous particle with an arbitrary geometry can be written as follows ... 

Whitaker, S, Diffusion in Packed Beds of Porous Particles, AlChE Journal 34, 679, 1988. Whitaker, S, The Development of Fluid Mechanics in Chemical Engineering. In One Hundred Years of Cheical Engineering Peppas, NA, ed. Kluwer Academic Dordrecht The Netherlands, 1989 47. 

Figure 1. A, porous particle used to illustrate slow mass trarlsfer due to diffusion in the stag-nant mobile phase within the particle. B, illustration of a porous layer bead.

The precision in retention from injection to injection will often be better than 1%. Over longer periods of time such precision requires the following (a) good flow control from the pump (b) constant mobile and stationary phases and (c) temperature control of the column. The critical question of reproducibility from column to column is still a matter of concern, especially when dealing with the more sophisticated packing materials, e.g. small porous particles, bonded phases While frequently this reproducibility is quite good, workers should recognize that care must be exercised to achieve and/or maintain reproducible columns. Undoubtedly, with experience, this need not be a severe problem. 

Where u, is the mobile phase velocity at the column outlet, Fg the column volumetric flow rate, and Ag the column cross-sectional area available to the mobile phase. In a packed bed only a fraction of the column geometric cross-sectional area is available to the mobile phase, the rest is occupied by the solid (support) particles. The flow of mobile phase in a packed bed occurs predominantly through the interstitial spaces the mobile phase trapped within the porous particles is largely stagnant (37-40). 

Totally porous particles of relatively large particle sizes were widely used in low pressure liquid chromatography for many years. These column packings had good sample capacity but only limited efficiency accompanied by long separation times, due to the large size and unfavorable size distribution of the particles and the presence of relatively deep pores within the particles through whick sample molecules diffused in and out of very slowly. 

Tab. 3.3.1 Physical properties of the packed porous particles. The relaxation times were determined at a Larmor frequency of 300 MHz for protons of water adsorbed into saturated catalyst pellets (average error 2%). The equivalent diameter is defined by 6 Vp/Ap where Vp and Ap are volume and external surface of the particles, respectively.

Stegeman, G., Kraak, J. C., and Poppe, H., Hydrodynamic and size-exclusion chromatography of polymers on porous particles, ]. Chromatogr., 550, 721, 1991. 

---