Bed of Porous Particles

FIGURE 6.10. Theoretical uptake curves for a biporous adsorbent calculated according to Eqs. (6.39)-(6.42) showing the transition from micropore to macropore diffusion control and the difference in the shape of the uptake curve for intermediate values of (From ref. 16 with permission.) 

It is obvious if the sorption curve is to be followed by monitoring the composition of the fluid phase the experimental conditions must be chosen to ensure that A 0. 

In the measurement of micropore diffusivities by the uptake rate method it is generally necessary to use an assemblage of microparticles (such as zeolite 

FIGURE 6.11. Idealized bed of unifonn spherical microporous crystals. 

It should be noted that p is always real but u may be either real or imaginary. When u is imaginary (m h), Eq. (6.50) becomes 

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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)... 

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... 

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. 

Bulk density, A ml l A, which corresponds to the mass of a bed of porous particles, granules, tablets, etc., related to the volume of the whole bulk VA including the pores between granules in a PS bed... 

Glaser, M. B. and Litt, M. A.I.Ch.E.Jl. 9 (1963) 103. A physical model for mixed phase flow through beds of porous particles. 

Nienow (1983a) observed a delay in the start of particle growth when binder was added to a bed of porous particles and stable fluidization under conditions which produced quenching with non-porous particles. Nitrogen adsorption measurements showed that the pore surface area of alumina decreased as spraying proceeded, indicafing that an effective reduction in pore volume was taking place. 

Several tracers have been used in experiments describing axial mixing in fluidized beds of porous particles, e.g. acetone [37,57], Tryptophane [47], NaCl [49,56], radioactive tracers [58] and dextrane blue [59], It should be noted at this point, that measurement of RTD is not only important for determining possible domination of the chromatographic result by liquid mixing, Bo may as well be taken as a measure for the existence of a stable classified fluidized bed which is ready for sample application. Measurement of RTD in this case will provide a rational basis for the decision to start a large scale protein purification using a fluidized bed or to take measures for improvement of bed stability before application of valuable material. 

Fig. 1.13. Schematic illustration of intra- and interparticle EOF through a packed bed of porous particles in CEC.

Even in a column that is packed very tightly with small particles, this porosity can be as high as 0.80 to 0.84 for a porous material that is, a tightly packed bed of porous particles is still about 80% empty ... 

The extraction of toluene and 1,2 dichlorobenzene from shallow packed beds of porous particles was studied both experimentally and theoretically at various operating conditions. Mathematical extraction models, based on the shrinking core concept, were developed for three different particle geometries. These models contain three adjustable parameters an effective diffusivity, a volumetric fluid-to-particle mass transfer coefficient, and an equilibrium solubility or partition coefficient. K as well as Kq were first determined from initial extraction rates. Then, by fitting experimental extraction data, values of the effective diffusivity were obtained. Model predictions compare well with experimental data and the respective value of the tortuosity factor around 2.5 is in excellent agreement with related literature data. 

Chromatography is a complex phenomenon, which results from the superimposition of a number of different effects. A mobile phase percolates through a bed of porous particles. It carries the components of a mixture that interact to different degrees with the stationary phase. These components diffuse in and out of the particles, undergo molecular interactions with the stationary phase or form transient chemical bonds with it, and are eventually swept out of the colimm. Fluid dynamics, mass transfer phenomena, and equilibriiun thermodynamics play an... 

Each particle in a bed of porous particles is surroimded by a laminar sublayer (Figure 5.4), through which mass transfer takes place only by molecular diffusion. On one side, this layer is exposed to the flowing mobile phase and is entirely accessible. On the other side, it wraps the particle wall and is accessible from the particle inside only at the pore openings. The thickness of this layer, hence the mass transfer coefficient, is determined by hydrodynamic conditions and depends on the flow velocity. The mass transfer rates can be correlated in terms of the effective mass transfer coefficient, fcy, defined according to a linear driving force equation ... 

Gel permeation chromatography (GPC) is essentially a process for the separation of polymer molecules according to their size. The separation occurs as the solute molecules in a flowing liquid move through a stationary bed of porous particles. The method has been used extensively in biochemistry to separate biological polymer molecules from small molecule contaminants (with the use of Sephadex column). Application of the method to synthetic polymer chemistry in the 1970s has revolutionized the procedures for polymer characterization and molecular weight determination. 

We can now put the whole van Deemter equation together, including the coefficients that we can use as a rule of thumb to estimate the HETP for a normal packed bed of porous particles ... 

Size exclusion (SEC) or gel permeation chromatography (GPC) is the most widely used chromatographic method in biochemistry. The biomolecules are separated by size during elution through a neutral and hydrophilic packed bed of porous particles. Large molecules are excluded from the pores and elute first, whereas small molecules totally invade the pores and elute last. 

Whitaker, S., Diffusion in packed beds of porous particles, AIChE J., 34(4), 679-683 (1988). 

For a bed of porous particles, the total liquid holdup can be represented as the sum of partial holdups ... 

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