Particle shape factor

Particle shape factor = (surface of sphere)/ Dimensionless Dimensionless Dimensionless... 

R reaction rate s catalyst particle shape factor t time (min)... 

These equations are similar to those shown in Table 8.1. The only difference is the experimental particle shape factor (aSjI/v) used instead of n (only valid for spheres). In their model, the better fit was achieved considering a constant value for h, above a certain particle size. 

An equivalent sphere is defined as the sphere with the same value of one of the above measures. The commonest referent is the volume-equivalent sphere, which many authors describe as the equivalent sphere without further definition. The particle shape factor is defined as the ratio of another measure from the above list to the corresponding value for the equivalent sphere. Of the many possible shape factors, those which have proved most useful are described below. All shape factors are open to the criticism that a range of bodies with different forms may have the same shape factor, but this is inevitable if regular or complex shapes are to be described by a single parameter. 

For the operation of the cold model ambient air was chosen as fluidising gas for the riser, and in order to match the required density ratio the gasifier was fluidized with a gas mixture of 55 45 % helium to air. Sj erical bronze particles with a density of 8900 kg/m and a mean particle diameter of 180 pm were chosen as bed material. The geometric scale factor between the two units was five and the normalised particle size distributions of the bronze particles and the sand used on the plant were comparable. The one scaling parameter it was not found possible to match was the particle shape factor 4). In the cold model the particles were spherical (( p1) w4iereas sand particles are normally considered to be broken solids for which ( 0.63 (6) in option in the CFB however attrition will be likely to increase this to nearer unity. 

One of the earliest particle shape factors used in the pharmaceutical industry was WadeU s true spheritcity, The true sphericity defines the proximity of the irregular particle measured to a perfect sphere and the relationship between the iiregular particles to the perfect sphere is given by ... 

CCT, critical cracking thickness Boltzmann constant (1.381x10 local permeability [m ] fracture resistance [N m ] average permeability in/of compact [m ] particle shape factor compact thickness [m] initial particle number concentration [m refractive index of particle material refractive index of dispersion material number density of ion i dimensionless number dimensionless number Stokes number Peclet number capillary pressure [N-m ] dynamic pressure [N m ] local liquid pressure in the compact [N-m local solid pressure in the compact [N-m ] superficial fluid velocity [m-s q gas constant [J K ] centre to centre distance [m]... 

These relationships assume that the particle shape factors C2 and C3 are independent of particulate size. For homogeneous suspensions (for example, clays) and for many heterogeneous aqueous particulates, this appears to be a reasonable assumption (10,21). When fibrous or unusually shaped particulates are present in large numbers, appropriate corrections to this assumption must be made. 

Deposition in the thoracic region is the sum of aerodynamic and thermodynamic deposition of particulate material. Aerodynamic deposition depends on aerodynamic particle size, total volumetric flow rate, anatomical dead space, tidal volume, functional residual capacity (FRC) (combined residual and expiratory reserve volume or the amount of air remaining in the lungs after a tidal expiration) and diameter of the airways. Thermodynamic deposition depends on anatomical and physical characteristics, such as tidal volume, anatomical dead space, functional residual capacity and the transit time of air within each region. Thermodynamic particle size, which is derived from the diffusion coefficient, particle shape factor and the particles mass density, influence thermodynamic deposition. 

The particle shape factor (%) is a dimensionless constant used to relate drag force on an irregular particle moving in air to the particle s equivalent volume diameter (ICRP, 1994). The shape factor and the mass density are used to determine the particle s thermodynamic diameter in the model but in practice, the thermodynamic diameter can be measured for small particles. The shape factor is assumed to have a triangular distribution ranging from 1.1 to 1.9 with a mode of 1.5 (ICRP, 1994). The ICRP 66 default for the X is 1-5. 

For irregular particles produced by crushing or grinding, the external surface is larger than for spheres of the same nominal size, which tends to increase the effectiveness factor but also increases the pressure drop through a bed of particles. Shape factors based on pressure drop are given for some typical granular solids [23], but these shape factors are not used for pore diffusion calculations, and R in the Thiele modulus is taken as 0.5 times the nominal or screen size. 

In-phase and out-of-phase characteristic functions for macro-particle shape factor sm... 

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