Spherical beads

Use of the peUetted converter, developed and used by General Motors starting in 1975, has declined since 1980. The advantage of the peUetted converter, which consists of a packed bed of small spherical beads about 3 mm in diameter, is that the pellets were less cosdy to manufacture than the monolithic honeycomb. Disadvantages were the peUetted converter had 2 to 3 times more weight and volume, took longer to heat up, and was more susceptible to attrition and loss of catalyst in use. The monolithic honeycomb can be mounted in any orientation, whereas the peUetted converter had to be downflow. AdditionaUy, the pressure drop of the monolithic honeycomb is one-half to one-quarter that of a similar function peUetted converter. 

Because most widely used methods used to prepare classical styrene/divinylben-zene copolymers have always been based on suspension polymerization, it seemed logical that a series of porous PDVB gels using similar methodologies could be developed. In suspension polymerization, divinylbenzene is suspended as a dispersion of small droplets in a continuous phase of water and polymerized by classical free radical initiation. This process produces the spherical beads... 

Hard, attrition-resistant, insoluble synthetic polymers (typically a copolymer of styrene with divinylbenzene). The resins are manufactured in a spherical bead shape that contain either exchangeable anion or cation portions, capable of exchanging with other anions or cations and usually in an aqueous medium. Typically cation resins for water softening will have a practical operating capacity of 20,000 gpg (at 6 lb NaCl per cu ft) rising to 30,000 gpg (at 15 lb NaCl per cu ft). 

Figure 5.255. The finite differencing of the spherical bead geometry.

Diffusion and reaction within a spherical bead Constant D=3.0E-06 Diffusion coefficient (m2/h) Constant R=0.1 rRadius of aggregate (m)... 

Fig. 6.2. Illustration of the mapping procedure for a 2 1 mapping where the repeat unit of a BPA-PC chain is replaced by two monomers of a generalized bead spring chain. The geometrical centers of the carbonate group and the geometrical center of the isopropyli-dene group, respectively, are mapped onto the centers of the new spherical beads. From [43]...

When the mesophase pitch is heated, tiny spherical beads having a radial orientation of the graphite embryo form and grows in the mother pitch. When the size of the beads in the pitch reaches an appropriate size (10-30 pm), the pitch is cooled down and the beads can be collected by dissolving the pitch matrix with an appropriate solvent. The beads are then heat-treated in an oxygen/water gas mixture to produce the protective skin, as for the MCF, and then graphitized, as depicted in Figure 10. 

Allum and co-workers 110) studied several polymer types and focused on macroreticular, high surface area, cross-linked polystyrene. The best polymer found was AMBERLITE XAD-2, spherical beads with a high surface area of 120 m2/g. A linkage for rhodium was provided by attachment of a —CH2PPh2 group ... 

Rimbock et al.125 prepared microcrystalline cellulose tribenzoate powders and Francotte et al.126 128 prepared spherical beads of cellulose tribenzoate derivatives they found that these derivatives are useful CSPs with a high loading capacity. 

Polymerisation proceeds to 100 per cent conversion and the product formed is obtained as spherical beads or pearls, because of this it is sometimes known as bead or pearl polymerisation. 

The lowest theoretical interparticular volume of perfectly packed uniformly sized spherical beads is calculated to be about 26% of the total available volume. In practice, even the best packed columns still contain about 30-40% void volume in addition to the internal porosity of the beads. The problem of interparticular volume does not exist in systems in which a membrane is used as the separation medium. Both theoretical calculations and experimental results clearly document that membrane systems can be operated in a dead-end filtration... 

The oxygen concentration is zC at the outer surface of the bead, and is essentially zero at the burning front for this high-temperature burning. For a spherical bead of radius a with coke core of radius, the solution of... 

Coarse-grained molecular d5mamics simulations in the presence of solvent provide insights into the effect of dispersion medium on microstructural properties of the catalyst layer. To explore the interaction of Nation and solvent in the catalyst ink mixture, simulations were performed in the presence of carbon/Pt particles, water, implicit polar solvent (with different dielectric constant e), and ionomer. Malek et al. developed the computational approach based on CGMD simulations in two steps. In the first step, groups of atoms of the distinct components were replaced by spherical beads with predefined subnanoscopic length scale. In the second step, parameters of renormalized interaction energies between the distinct beads were specified. 

The designer now needs to make some estimates of mass transfer. These properties are generally well known for commercially available adsorbents, so the job is not difficult. We need to re-introduce the adsorber cross-section area and the gas velocity in order to make the required estimates of the external film contribution to the overall mass transfer. For spherical beads or pellets we can generally employ Eq. (7.12) or (7.15) of Ruthven s text to obtain the Sherwood number. That correlation is the mass transfer analog to the Nusselt number formulation in heat transfer ... 

This chapter will focus exclusively on cross-linked vinyl polymer supports either in a spherical bead or resin form, or in some other macroscopic format. These essentially insoluble materials lead to considerably simplified reaction work-up and product isolation procedures when used e.g. in solid phase synthesis or as catalyst or... 

In an early attempt to model the dynamics of the chromatin fiber, Ehrlich and Langowski [96] assumed a chain geometry similar to the one used later by Katritch et al. [89] nucleosomes were approximated as spherical beads and the linker DNA as a segmented flexible polymer with Debye-Huckel electrostatics. The interaction between nucleosomes was a steep repulsive Lennard-Jones type potential attractive interactions were not included. 

---