Influence of the Particle Diameter

Two experiments were carried out at a gas inlet temperature of 130 °C and 160 °C to investigate the influence of the diameter of the bed material on reactive absorption. 

In the investigated diameter range, there were no significant differences between the conversions and outlet temperatures (Figs. 16.27-16.30). An increase in the 

The larger Re-number is contained in the empirical Sh-approximation for the calculation of the mass transfer coefficient gas-particle. Increases in the Re-number, Ar-number and Sh-number do not provide a large gas mass transfer coefficient, as this will decrease due to diameter growth and thus lead to larger Sh-numbers. This dependency is illustrated by the equation from Rowe [78] 

The transport of sulfur dioxide in the gas phase to the particles, as well as transport of water vapor from the particles, is a convective mass transfer. Both mass transfer coefficients can be described by Sh-approximations. Thus, progression of the Sh-numbers and the mass transfers coefficients must be qualitatively identical (Fig. 16.31). 

It is clear from Fig. 16.32 that for the quantitative evaluation of convective mass transfer, the product of the two quantities - mass transfer surface and mass transfer coefficient - is crucial. As a result, a constant product of mass transfer coefficient and mass transfer surface under the conditions of a constant fluidization mass flow has a constant number of transfer units (NTU). 

---

Influence of the particle diameter and density in the gas velocity in jet spouted beds... 

The wear rate increased directly proportionally up to = wt.-5%, above which it decreased. The cause is the ever greater collision frequency between the particles themselves. The influence of the particle diameter dp on the wear rate is considerable p oc dp. This relationship can also be proven theoretically [274]. 

The basic influence of the number of stages and the particle diameter on productivity and eluent consumption is illustrated and compared with batch elution chromatography. Based on this work, Biressi et al. (2000) presented a method to optimize operating parameter and investigate the influence of the particle diameter as well as the feed concentration on process performance. Ludemann-Hombourger, Bailly, and Nicoud (2000a) have also analyzed the influence of particle diameter on the productivity. 

Figure 3.4.3 shows the influence of the particle diameter on the pressure drop per meter length for a flow of air with a superficial velocity... 

This correlation gives, for perfectly wettable solids, fairly good estimates of the static holdup for different particle-geometries and sizes. Saez and Carbonnel [26] used the hydraulic diameter, instead of the nominal particle diameter, as the characteristic length in the Eotvos number, to include the influence of the particle geometry on the static hold-up. However, no improvement could be obtained in correlating the data with this new representation. 

Many commercial activated carbons have been prepared with various sources of raw materials and different processing conditions. As a result, the micropore structures and specific surface areas of activated carbons, which are the most profound influences on the extent of adsorption, vary, and in general, activated carbons have a surface area of up to 3000 m2/g. The rate of adsorption increases with some function of the inverse of the radius of the activated carbon even though the adsorption capacity (i.e., equilibrium adsorption) is relatively independent of the particle diameter. However, for a highly porous adsorbent such as activated carbon, the... 

From the volume-surface diameter (dvs) the dispersion of the supported phase (D) can be evaluated. For this purpose a relationship between this parameter and D is required. Different authors have suggested an influence of the particle shape on this relationship (389390). To check this point, a series of models of metal particles with shapes more or less close to those observed in the experimental HR M miages (octahedron, cube-octahedrons, cube, sphere) and of increasing size were built using the Rhodius program (184). For each model the total number of atoms (Nt) and the number of surface atoms (Ns) were counted up, and from their ratio (N /Nt) the dispersion (D) was calculated. 

The main consequence of grinding is a significant decrease of the particle diameter and consequently, an increase of the specific surface area. Looking at the evolutions of both particle size and specific surface area, it appears clearly that the nature of the additive influences significantly the kinetics of muscovite grinding. The most efficient is pentanedioic acid (PAA dimer), especially from the point of view of the particle size reduction. The less active is the PAA itself which is even less efficient than pure water. 

For easy separation of crystals from a solution, it is important that the crystals are sufficiently large. This can be shown by the Kozeny-Carman equation derived for laminar flow through an incompressible bed of particles, which describes the pressure drop in the bed. The pressure drop relates inversely to the square of the quadratic particle size and directly to the dynamic viscosity of the fluid. The influence of the particle size and solution viscosity on the pressnre required in filtration can be estimated as follows. If the viscosity increases tenfold, the pressnre drop also inCTeases tenfold. If, on the other hand, the particle diameter drops to 10% of its original valne, the pressnre drop increases by 100-fold. 

The hydrodynamic influence on the suspension stored at different time intervals in different reactors, results in a similar decrease of the particle size. This can be observed in the parallel shift of the graphs showing the dependence of the particle diameter of calcium stearate upon storage time under different synthesis conditions (Figure... 

Figure 4.22 Dependence of the particle diameter, formed in a volume reactor, on suspension storage time in the absence of mixing (4). Influence on the particles, preliminarily formed in a volume reactor (1), tubular turbulent reactor of cylinder (2) and diffuser-confusor (3) construction, and in situ (5)...

Rgure 2 Influence of sediment particle diameter on light absorbance by samples of different concentrations. Note how a given concentration effects much greater absorbance at the smaller particle diameters. (Reproduced with permission from Ward PRB and Chikwanha R (1980) Laboratory measurement of sediment turbidity. Proceedings of the American Society of Civil Engineers, Journal of the Hydraulics Division 106 1041-1053.)... 

Secondly, the influence of the liquid-to-solid mass transfer as well as of pore diffusion must be excluded by variation of the particle diameter. For dp < 100 p,m, the... 

Assessment of the performance of several types of flush valves was accomplished at the pilot plant, with particular attention paid to the minimization of the pressure drop through the control device. The flush valve initially was viewed as a containment and transfer device but rapidly evolved to be a control device. Fluid mechanics calculations demonstrated the precise condition required to achieve atomization. The atomization was modeled as an effervescent atomizer due to the influence of the orifice diameter and the pressure drop on the size of the collected particles (87-90). 

Figure 3 Influence of the average diameter of particles on concentration of poly(ethylene oxide) in the copolymerizing mixture of 1,3,5-trioxane ([1,3,5-trioxane] = 7.0 mol kg" ) and 1,3-dioxolane ([1,3-dioxolane] = 0.35 mol kg" ). Concentration of BF3OBU2 initiator was equal to 1.75 x 10 mol kg " (o), 3.50 X 10 mol kg"" ( ), and 4.50 x 10" mol kg"" (A). Reproduced with permission from Penczek, S. Fejgin, J. Sadowska, A. Tomaszewicz, M. Makromol. Chem. 1968, 116, 203." ...

The correct treatment of boundaries and boundary effects is crucial to simulation methods because it enables macroscopic properties to be calculated from simulations using relatively small numbers of particles. The importance of boundary effects can be illustrated by considering the following simple example. Suppose we have a cube of volume 1 litre which is filled with water at room temperature. The cube contains approximately 3.3 X 10 molecules. Interactions with the walls can extend up to 10 molecular diameters into the fluid. The diameter of the water molecule is approximately 2.8 A and so the number of water molecules that are interacting with the boundary is about 2 x 10. So only about one in 1.5 million water molecules is influenced by interactions with the walls of the container. The number of particles in a Monte Carlo or molecular dynamics simulation is far fewer than 10 -10 and is frequently less than 1000. In a system of 1000 water molecules most, if not all of them, would be within the influence of the walls of the boundary. Clecirly, a simulation of 1000 water molecules in a vessel would not be an appropriate way to derive bulk properties. The alternative is to dispense with the container altogether. Now, approximately three-quarters of the molecules would be at the surface of the sample rather than being in the bulk. Such a situation would be relevcUit to studies of liquid drops, but not to studies of bulk phenomena. 

---