Chapter 1 Physical properties of powder particles 1.1 Characterization of single particle 1.2 Flow behavior of single particle 1.3 Particle size distribution and mean equivalent diameter 1.4 particles aggregation 1.5 Particle density 1.6 Particle voidage 1.7 Angle of powder particles

1.3 Particle size distribution and average equivalent diameter Particle size distribution The most commonly used method for classifying powders is to sieve the particles through a series of screens with standardized mesh size by shifting, swirling, shaking or vibrating. There are different kinds of standard mesh sizes and the most commonly used is the Tyler sieve size. The mesh number of a sieve refers to the number of parallel wires per inch in the weave of the screen.

Standard mesh sizes ： Tyler sieve size Mesh number ： The number of parallel wires per inch in the wave of the screen Sieve excess ： the amount of particles pass through the sieve sieve residue ： the amount of particles trapped in the sieve 1 、 sieve analysis and the standard mesh sizes Question ： what is the mean diameter of the trapped particles between adjacent two mesh?

1.3.1 Particle size distribution There are two kinds of methods to calculate the mean aperture distance between two adjacent mesh. The most commonly used is the geometric mean value geometric mean value ： arithmetic mean value ：

1.3.1 Particle size distribution When the particle is very small, less than 100  m, the sieve analysis can not accurately measure the particle diameter. The commonly instrumental analysis methods includes : Electric Conductivity technique (such as the Coulter counter, Elzone particle size analyzer), Sedimentation technique (such as the series of SediGraph tester of Micromeritics’), Microscopy technique (optical or electron microscopy), The image technique (such as the series of AccuSizer tester of PSS’) and laser diffraction technique.

1.3.1 Particle size distribution Electric Conductivity technique ： suspend particles in an electrolyte, force the particles through a small aperture,then determine the particle diameter according to the conductivity change. Sedimentation technique obtain the particle size distribution by measuring the terminal settling velocity in the fluid. Microscopy technique and image analysis measures particle size by optical or electronic microscopy. Laser diffraction technique measures particle diameter according to different diffraction effects by different particle sizes.

1.3.1Particle size distribution 描述颗粒群的粒度分布有不同的基准，如质量基准、体积基准、 颗粒数基准等。例如，质量基准是用颗粒群中各个粒度范围的颗粒 质量在颗粒群总质量中所占的份额（质量百分数）来描述分布的。 按一定基准测得的粒度分布数据有 3 种表示形式：即表格形式、图 示形式和函数形式。

1.3.1Particle size distribution Table is the most simple, the curve of particle size distribution is intuitive comparatively and the function is easier to handle. There are two kinds of curves to express the particle size distribution. The first curve shows the percentage of particles in different size d i and directly reflects the size distribution; the other gives the cumulative particle size distribution.

Particle size distribution can be conveniently expressed as a cumulative distribution in the terms of particle size versus weight, volume, or number fraction of particles smaller or larger than the stated particle size.

 Probability function f of distribution 0 频率函数 f 粒径 d p d p,i fifi Definition ： The weight fraction of particles in a certain size range is equal to the area under the frequency curve in this range of particle size; sieve analysis results d i-1 <d p <d i-2 d i <d p <d i-1 d i+1 <d p <d i Question :total area under the curve equals to ?

 function of Particle size distribution F 0 Distribution function F Particle size d p d p,i d p,max 1.0 FiFi Definition ： The value of F i indicates the mass fraction of the particles with a diameter less than d p,i 0 Frequency function f Particle size d p d p,i fifi Question :1. What’s the value at the maximum diameter d p,max 2 、 What is the relationship between the probability function f and distribution function F? d 50

1.3.2 equivalent mean diameter( 颗粒群的平均当量直径 ) The equivalent mean diameter calculated by particle size distribution is not only related to the expression form of particle size composition (such as in the terms of particle size versus weight, volume, or number fraction of particles), but also related to mathematical methods which used to calculate the mean diameter. What people concern about is the mass fraction or volume fraction of particles in the fluidized bed. And the mass fraction is the most accessible, so the most commonly used is the mean diameter in the terms of weight.

1.3.2 Equivalent mean diameter Suppose in a certain amount of particulate material, the mass fraction of particles with diameter d1 d1 is x1 x1 ; the mass fraction of particles with diameter d2 d2 is x2 x2 …… the mass fraction of particles with diameter dn dn is xn xn. The method to express the equivalent mean diameter are: Arithmetic mean equivalent diameter ： Mean surface equivalent diameter ：

1.3.2 equivalent mean diameter volume equivalent diameter ： specific surface equivalent diameter ： Which form of equivalent mean diameter to be chosen depends on its practical application. For the fluidized bed, mean specific surface area equivalent diameter is generally used. Because the one people concerned most in the chemical reaction is the surface area,and the amount of packing in the fluidized bed is often calculated in the terms of volume (or mass). The specific surface area is the key parameter to contact both of them.

Particle size distribution ： (understood ） Summary ： Particle size distribution and equivalent mean diameter Tyler sieving 、 geometric mean value 、 arithmetic mean value equivalent mean diameter: arithmetic mean equivalent diameter mean surface area equivalent diameter mean volume equivalent diameter mean special surface area equivalent diameter

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1.5 agglomeration ( 颗粒的团聚性 ) The behavior of particles is largely no longer subject to gravity when the interaction between particles is much larger than the particle gravity. Advantages :improve the fluidity of particles ; reduce dust ; easy packing. Disadvantage : the particles must be mixed before operation interaction between particles ： Van der Waals force; capillary force; electrostatic force, etc.

When there is no gas adsorption effect on the FCC catalyst, the change of agglomeration number over particle size is shown in the figure below. The agglomeration will be more serious when the particle size becomes smaller. The agglomeration number is greater than 10 6 for the particle of size less than 1μm. Therefore, smaller particles are more likely to form agglomerates with the interaction between particles. 1.5 agglomeration ( 颗粒的团聚性 )

10nm FCC 颗粒的聚团强度可高达 10 8 Pa ，可见 10nm 的 FCC 颗粒将以聚团的形 式存在。 1μm FCC 颗粒的聚团强度约为 10 4 Pa ，即约为 lm 水柱。 The smaller the particle,the more easily the agglomeration 所形成的聚团强度越大！ 1.5 agglomeration ( 颗粒的团聚性 )

Bulk density of particles, ρ b

Bulk density  b ： 1.5 Several definitions of the particle density and the measurement 充气密度：将已知质量的催化剂装入量筒中颠倒摇动，然后将量筒直 立，待样品全部落下时读其体积，此时测得的密度为充气密 度，又称松装密度 沉降密度：依上述方法将量筒静置 2min ，读其体积，此时测得的密度为 沉降密度，又称自由堆积密度 敦实密度：将装有已知质量颗粒的量筒在特定仪器上振动数次，直至体 积不变为止，读其体积，此时测得的密度为压紧密度，又称 敦实密度

1.6 Several definitions of the particle density and the measurement

1.6 Voidage of the particles Voidage of the particles  ： The voids volume V v divided by particle’s overall volume V B voidage of the particles depends on the particle shape, size distribution and the packing arrangement. The loose packing voidage and the compact packing voidage are commonly used.

Impact of particle size and shape on the loose packing voidage: the voidage of irregular particle is bigger than that of spherical particles. The following table shows the influence of particle size distribution on the loose packing voidage, we can find that the voidage of the particles with a wide size distribution is smaller than that of the particles with a narrow one. 1.6 Voidage of the particles

When powders are poured on a horizontal plane, the accumulation volume will increases but the repose angle α remain unchanged. When the cylinder rotates, the surface of the powders is not to maintain horizontal, but keep an angle α with the horizontal plane When lift the container which filled with powders, powders remain motionless until the angle between the container and the flat surface reaches α. Differences between fluid and powders: 1.7 Repose angle

Repose angle Experiments show that for the same powders, the angles mentioned above are equivalent (angle between the top of a pile of powders and the horizontal plane 、 angle between the particles in the container and the horizontal surface 、 angle between the particles in the rotation cylinder and the horizontal surface). This angle is referred to as the repose angle. The measurement methods of the repose angle are shown as below

The repose angle of spherical particles is relatively small and generally between 23 ～ 28 o, and these particles have good flow properties.The repose angle of regular particles is about 30 o, the irregular particle is about 35 o, the extremely irregular is about 40 o and the flow properties of these particles is bad.

Repose angle compressibility and agglomeration of the fine particles are strong, the repose angle is related to the process variables, such as the outflow velocity of powder from the container 、 lifting speed of the container and rotational speed of the cylinder. So the repose angle is not the physical property.

Angle of collapse The angle of repose resulting from a jarring effect Angle of difference The difference between the angle of repose and the angle of fall Angle of slide The angle from the horizontal of an inclined surface on which an amount of particles will slide downward due to the influence of gravity. Why the catalyst circulation line is tilt ？ Why does the feeding line to be designed with a larger radius of curvature of the elbow? Why dose the bottom of the fluidized bed be designed to be conical? What’s the factors that affect cone angle?

1.7 Summary definition and measurement of the angle of repose The angle of repose for spherical particles is relatively small and generally between 23 ～ 28 o, and these particles have good flow properties The angle of repose for regular particles is about 30 o The angle of repose for irregular particle is about 35 o The angle of repose for the extremely irregular particle is about 40 o and the flow property is bad