Particles linear velocity

This reaction is carried out in tall fluidized beds of high L/dt ratio. Pressures up to 200 kPa are used at temperatures around 300°C. The copper catalyst is deposited onto the surface of the silicon metal particles. The product is a vapor-phase material and the particulate silicon is gradually consumed. As the particle diameter decreases the minimum fluidization velocity decreases also. While the linear velocity decreases, the mass velocity of the fluid increases with conversion. Therefore, the leftover small particles with the copper catalyst and some debris leave the reactor at the top exit. 

The results obtained were probably as accurate and precise as any available and, consequently, were unique at the time of publication and probably unique even today. Data were reported for different columns, different mobile phases, packings of different particle size and for different solutes. Consequently, such data can be used in many ways to evaluate existing equations and also any developed in the future. For this reason, the full data are reproduced in Tables 1 and 2 in Appendix 1. It should be noted that in the curve fitting procedure, the true linear velocity calculated using the retention time of the totally excluded solute was employed. An example of an HETP curve obtained for benzyl acetate using 4.86%v/v ethyl acetate in hexane as the mobile phase and fitted to the Van Deemter equation is shown in Figure 1. 

The column length, as well as providing the required efficiency, is also defined by the D Arcy equation. The D Arcy equation describes the flow of a liquid through a packed bed in terms of the particle diameter, the pressure applied across the bed, the viscosity of the fluid and the linear velocity of the fluid. The D Arcy equation for an incompressible fluid is given as follows. 

The primary section of the chamber is characterized by its cross-sectional area (W X H) and by its length (L). The cross-sectional area is designed to be larger than the inlet and exit ducts in order to reduce substantially the gas stream s inlet linear velocity. The length of the chamber determines the amount of time the particles remain at the redueed rate. This starving of the gas s forward motion allows the partieles sufficient time to settle out into the hoppers. 

There are data showing that at the same contact time, but different linear velocities, there is no difference in the performance of a carbon system. It is obvious then that the effect of linear velocity on the diffusion through the film around the particle and the ratio of the magnitude of the film diffusion to the pore diffusion are the factors that determine the effects, if any, that occur. Therefore, the linear velocity cannot be ignored completely when evaluating a system. Systems at the higher linear velocity (LV) treat more liquid per volume of carbon at low-concentration levels and the mass-transfer zone (MTZ) is shorter. 

Peclet number Np = uL/D, where u is a linear velocity, L is a linear dimension, and is die dispersion coefficient. In packed beds, Npg = udp/Dg, where u is die intersddal velocity and dp is die particle diameter. 

Kinematics is based on one-dimensional differential equations of motion. Suppose a particle is moving along a straight line, and its distance from some reference point is S (see Figure 2-6a). Then its linear velocity and linear acceleration are defined by the differential equations given in the top half of Column 1, Table 2-5. The solutions... 

The absolute linear velocity of the particles u s The absolute linear velocity of the liquid The slip velocity = u L — u s The hold-up of the solids 65 The hold-up of the liquid e/, = 1 —... 

The first pseudo force, Fi, is called the Coriolis force, and its magnitude is directly proportional to the angular velocity of the rotating frame of reference and the linear velocity of the particle in this frame. By definition, this force is perpendicular to the plane where vectors Vi and o are located, Fig. 2.3a, and depends on the mutual position of these vectors. The second fictitious force, F2, is called the centrifugal force. Its magnitude is directly proportional to the square of the angular velocity and the distance from the particle to the center of rotation. It is directed outward from the center and this explains the name of the force. It is obvious that with an increase of the angular velocity the relative contribution of this force... 

Electrophoresis The physical situation of relative motions of a solution and another (insulating) phase during electrophoresis is exactly the same as in electroosmosis. Hence, the linear velocity of a cylindrical particle (which is the equivalent of a cylindrical pore) is given by the value following from Eq. (31.4). With particles of dilferent shape, this velocity can be written as... 

The factors to consider in the selection of crossflow filtration include the flow configuration, tangential linear velocity, transmembrane pressure drop (driving force), separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, low protein-binding ability, and 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. 

We begin with a consideration of a classical particle i with mass mt rotating in a plane at a constant distance r, from a fixed center as shown in Figure 5.2. The time r for the particle to make a complete revolution on its circular path is equal to the distance traveled divided by its linear velocity Vi... 

Correlation was found between domain size and attainable column efficiency. Column efficiency increases with the decrease in domain size, just like the efficiency of a particle-packed column is determined by particle size. Chromolith columns having ca. 2 pm through-pores and ca. 1pm skeletons show H= 10 (N= 10,000 for 10 cm column) at around optimum linear velocity of 1 mm/s, whereas a 15-cm column packed with 5 pm particles commonly shows 10,GOO-15,000 theoretical plates (7 = 10—15) (Ikegami et al., 2004). The pressure drop of a Chromolith column is typically half of the column packed with 5 pm particles. The performance of a Chromolith column was described to be similar to 7-15 pm particles in terms of pressure drop and to 3.5 1 pm particles in terms of column efficiency (Leinweber and Tallarek, 2003 Miyabe et al., 2003). Figure 7.4 shows the pressure drop and column efficiency of monolithic silica columns. A short column produces 500 (1cm column) to 2500 plates (5 cm) at high linear velocity of 10 mm/s. Small columns, especially capillary type, are sensitive to extra-column band... 

Effect of particle size and linear velocity on conversion. [Reprinted with permission from the contribution of D. A. Dowden and G. W. Bridger to Advances in Catalysis, 9 (669). Copyright 1957, Academic Press.]... 

A van Deemter plot for a given particle size dp and diffusion coefficient Du shows the relation of the theoretical peak height H to the linear velocity u that can be expressed as column length L... 

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