Particle size distribution prediction

The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

The heat-transfer coefficient depends on particle size distribution, bed voidage, tube size, etc. Thus a universal correlation to predict heat-transfer coefficients is not available. However, the correlation of Andeen and Ghcksman (22) is adequate for approximate predictions ... 

The two steps in the removal of a particle from the Hquid phase by the filter medium are the transport of the suspended particle to the surface of the medium and interaction with the surface to form a bond strong enough to withstand the hydraulic stresses imposed on it by the passage of water over the surface. The transport step is influenced by such physical factors as concentration of the suspension, medium particle size, medium particle-size distribution, temperature, flow rate, and flow time. These parameters have been considered in various empirical relationships that help predict filter performance based on physical factors only (8,9). Attention has also been placed on the interaction between the particles and the filter surface. The mechanisms postulated are based on adsorption (qv) or specific chemical interactions (10). 

The general form of the population balance including aggregation and rupture terms was solved numerically to model the experimental particle size distributions. While excellent agreement was obtained using semi-empirical two-particle aggregation and disruption models (see Figure 6.15), PSD predictions of theoretical models based on laminar and turbulent flow considerations... 

Tailoring of the particle size of the crystals from industrial crystallizers is of significant importance for both product quality and downstream processing performance. The scientific design and operation of industrial crystallizers depends on a combination of thermodynamics - which determines whether crystals will form, particle formation kinetics - which determines how fast particle size distributions develop, and residence time distribution, which determines the capacity of the equipment used. Each of these aspects has been presented in Chapters 2, 3, 5 and 6. This chapter will show how they can be combined for application to the design and performance prediction of both batch and continuous crystallization. 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

Figure 8.24 Predicted transient particle size distribution during the hatch precipitation of calcium carbonate crystals (Wachi and Jones, 1992)...

Each of the PLgel individual pore sizes is produced hy suspension polymerization, which yields a fairly diverse range of particle sizes. For optimum performance in a chromatographic column the particle size distribution of the beads should be narrow this is achieved by air classification after the cross-linked beads have been washed and dried thoroughly. Similarly, for consistent column performance, the particle size distribution is critical and is another quality control aspect where both the median particle size and the width of the distribution are specified. The efficiency of the packed column is extremely sensitive to the median particle size, as predicted by the van Deemter equation (4), whereas the width of the particle size distribution can affect column operating pressure and packed bed stability. 

JR Crison, GL Amidon. The effect of particle size distribution on drug dissolution A mathematical model for predicting dissolution and absorption of suspensions in the small intestine. Pharm Res 10 S170, 1992. 

Perhaps the greatest difficulty in predicting fluidization performance via the Geldart (1973) classification is deciding on a single diameter to represent the complete material, especially if the product possesses a wide particle size distribution. This is supported to some extent by the more recent bulk density approach proposed by Geldart et al. (1984). 

Model simulations of particle volume concentrations in the summer as functions of the particle production flux in the epilimnion of Lake Zurich, adapted from Weilenmann, O Melia and Stumm (1989). Predictions are made for the epilimnion (A) and the hypolimnion (B). Simulations are made for input particle size distributions ranging from 0.3 to 30 pm described by a power law with an exponent of p. For p = 3, the particle size distribution of inputs peaks at the largest size, i.e., 30 pm. For p = 4, an equal mass or volume input of particles is in every logaritmic size interval. Two particle or aggregate densities (pp) are considered, and a colloidal stability factor (a) of 0.1 us used. The broken line in (A) denotes predicted particle concentrations in the epilimnion when particles are removed from the lake only in the river outflow. Shaded areas show input fluxes based on the collections of total suspendet solids in sediment traps and the composition of the collected solids. 

The form of the above equations suggests that the only properties of the bed on which the pressure gradient depends are its specific surface S (or particle size d) and its voidage e. However, the structure of the bed depends additionally on the particle size distribution, the particle shape and the way in which the bed has been formed in addition both the walls of the container and the nature of the bed support can considerably affect the way the particles pack. It would be expected, therefore, that experimentally determined values of pressure gradient would show a considerable scatter relative to the values predicted by the equations. The importance of some of these factors is discussed in the next section. 

PK-Map and PK-Sim (Bayer Technology Services, Wuppertal, Germany), that are based on the models described by Willman et al. [54], In these software packages, the intestinal permeability coefficient can be calculated using a compound s lipophilicity and molecular weight [52,54] and hence, no experimental permeability data is needed. Different to the model described by Willman et al. [54], the commercial prediction tools model the dissolution rate taking the particle size distribution of the solid particles into account (www.pk-sim.com). 

Raman spectroscopy s sensitivity to the local molecular enviromnent means that it can be correlated to other material properties besides concentration, such as polymorph form, particle size, or polymer crystallinity. This is a powerful advantage, but it can complicate the development and interpretation of calibration models. For example, if a model is built to predict composition, it can appear to fail if the sample particle size distribution does not match what was used in the calibration set. Some models that appear to fail in the field may actually reflect a change in some aspect of the sample that was not sufficiently varied or represented in the calibration set. It is important to identify any differences between laboratory and plant conditions and perform a series of experiments to test the impact of those factors on the spectra and thus the field robustness of any models. This applies not only to physical parameters like flow rate, turbulence, particulates, temperature, crystal size and shape, and pressure, but also to the presence and concentration of minor constituents and expected contaminants. The significance of some of these parameters may be related to the volume of material probed, so factors that are significant in a microspectroscopy mode may not be when using a WAl probe or transmission mode. Regardless, the large calibration data sets required to address these variables can be burdensome. 

---