Theory

As mentioned earlier, an expanded bed is a fluidized bed that is devoid of or shows low back-mixing of liquid and adsorbent. The stability of the expanded bed makes it resemble a packed bed in that it shows an almost constant flow velocity profile and yields a bed with an increased number of theoretical plates (relative to a fully mixed fluid-ized bed). These characteristics are achieved by a combination of column and adsorbent design.

Column

The liquid flow in a column used for expanded-bed adsorption must be uniform over the entire cross-section of the bed. A conventional packed-bed chromatography column with one or a few inlets cannot meet this criterion. In a packed bed, the bed itself creates a pressure drop that achieves the desired plug flow. In an expanded bed, there is a very low pressure drop over the column, thus requiring a specially designed flow distributor at the bottom of the column (50). This distributor must ensure that the flow is directed in a vertical direction only, because radial flow inside the column will cause disturbances in the expanded bed. It must also prevent the adsorbent particles from leaving the column while allowing cells and debris to pass through. Other requirements are that it must not create high shear stresses, or cells and shear sensitive molecules may break, and it should be designed to facilitate cleaning. There should be no stagnant zones in the column where cells and other contaminants can accumulate and, in the worst case, escape cleaning.

Adsorbent

The adsorbents used for expanded-bed adsorption must exhibit additional properties to those required of an adsor bent used in packed-bed chromatography. The density of the particles must be relatively high to enable high liquid flow velocities through the expanded bed without the adsorbent particles packing against the adaptor. The adsorbent particles in a fluidized/expanded bed are in constant motion; however, an efficient protein adsorption process requires that the solid dispersion (the movement of the adsorbent particles) is reduced to a minimum. This can be achieved if the adsorbent is polydispersed with respect to size, that is, the particles exhibit a size distribution. When such a polydispersed adsorbent with a small variation in particle density is expanded, each particle will find its equilibrium position in the upward flow. The result is called a classified bed (51), and at a closer look the larger particles will be found at the bottom of the bed and the smaller ones at the top. A distribution of density with size (a large particle exhibiting a larger density than a small particle) will further enhance the classification of the bed. One way of describing the behavior of such an adsorbent in an expanded bed is the Richardson-Zaki (52) model for monodispersed particles:

where u0 is the superficial velocity of the fluid, ut is the terminal falling velocity of a particle in infinite dilution, e is bed voidage, and " is an index. The model describes expansion for a bed that has reached equilibrium (the expansion height is constant). The terminal falling velocity ut is described by Stoke's law:

ut = ((dp)2g(pp - q))/18i where dp is particle diameter, g is acceleration due to gravity, pp is particle density, p is fluid density, and i is fluid viscosity. Stoke's law can only be used for particles with a Reynold number lower than 0.2. The Reynold number Rep for a particle in a fluid is defined by:

The Richardson-Zaki model is corrected for the particle size distribution of the adsorbent by using the perfectly classified bed model (51):

where H0 is sedimented bed height, e0 is sedimented bed voidage, DFv is the proportion of the total volume of particles having the diameter within the interval d — Dd/2 < d < d + Dd/2, and e is bed voidage for the particles within that interval. This means that the particle size group between d and (d — Dd) is found within the expanded bed between heights h and (h + Dh). Thus, each segment of height is considered a bed with a specific void-age that can be calculated using the Richardson-Zaki equation. The total bed height is obtained by adding up the heights of each segment.

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