کتاب مهندسی شیمی کالسون و ریچاردسون

کتاب مهندسی شیمی کالسون و ریچاردسون

 CHEMICAL ENGINEERING//// Coulson and Richardson’s
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CHAPTER 1
Particulate Solids
1.1. INTRODUCTION
In Volume 1, the behaviour of fluids, both liquids and gases is considered, with particular
reference to their flow properties and their heat and mass transfer characteristics. Once
the composition, temperature and pressure of a fluid have been specified, then its relevant
physical properties, such as density, viscosity, thermal conductivity and molecular diffusivity,
are defined. In the early chapters of this volume consideration is given to the
properties and behaviour of systems containing solid particles. Such systems are generally
more complicated, not only because of the complex geometrical arrangements which are
possible, but also because of the basic problem of defining completely the physical state
of the material.
The three most important characteristics of an individual particle are its composition, its
size and its shape. Composition determines such properties as density and conductivity,
provided that the particle is completely uniform. In many cases, however, the particle
is porous or it may consist of a continuous matrix in which small particles of a second
material are distributed. Particle size is important in that this affects properties such as
the surface per unit volume and the rate at which a particle will settle in a fluid. A
particle shape may be regular, such as spherical or cubic, or it may be irregular as, for
example, with a piece of broken glass. Regular shapes are capable of precise definition by
mathematical equations. Irregular shapes are not and the properties of irregular particles
are usually expressed in terms of some particular characteristics of a regular shaped
particle.
Large quantities of particles are handled on the industrial scale, and it is frequently
necessary to define the system as a whole. Thus, in place of particle size, it is necessary
to know the distribution of particle sizes in the mixture and to be able to define a mean
size which in some way represents the behaviour of the particulate mass as a whole.
Important operations relating to systems of particles include storage in hoppers, flow
through orifices and pipes, and metering of flows. It is frequently necessary to reduce the
size of particles, or alternatively to form them into aggregates or sinters. Sometimes it
may be necessary to mix two or more solids, and there may be a requirement to separate
a mixture into its components or according to the sizes of the particles.
In some cases the interaction between the particles and the surrounding fluid is of little
significance, although at other times this can have a dominating effect on the behaviour of
the system. Thus, in filtration or the flow of fluids through beds of granular particles, the
characterisation of the porous mass as a whole is the principal feature, and the resistance
to flow is dominated by the size and shape of the free space between the particles. In
such situations, the particles are in physical contact with adjoining particles and there is
1
2 CHEMICAL ENGINEERING
little relative movement between the particles. In processes such as the sedimentation of
particles in a liquid, however, each particle is completely surrounded by fluid and is free to
move relative to other particles. Only very simple cases are capable of a precise theoretical
analysis and Stokes’ law, which gives the drag on an isolated spherical particle due to
its motion relative to the surrounding fluid at very low velocities, is the most important
theoretical relation in this area of study. Indeed very many empirical laws are based on
the concept of defining correction factors to be applied to Stokes’ law.
1.2. PARTICLE CHARACTERISATION
1.2.1. Single particles
The simplest shape of a particle is the sphere in that, because of its symmetry, any
question of orientation does not have to be considered, since the particle looks exactly
the same from whatever direction it is viewed and behaves in the same manner in a fluid,
irrespective of its orientation. No other particle has this characteristic. Frequently, the
size of a particle of irregular shape is defined in terms of the size of an equivalent sphere
although the particle is represented by a sphere of different size according to the property
selected. Some of the important sizes of equivalent spheres are:
(a) The sphere of the same volume as the particle.
(b) The sphere of the same surface area as the particle.
(c) The sphere of the same surface area per unit volume as the particle.
(d) The sphere of the same area as the particle when projected on to a plane perpendicular
to its direction of motion.
(e) The sphere of the same projected area as the particle, as viewed from above, when
lying in its position of maximum stability such as on a microscope slide for example.
(f) The sphere which will just pass through the same size of square aperture as the
particle, such as on a screen for example.
(g) The sphere with the same settling velocity as the particle in a specified fluid.
Several definitions depend on the measurement of a particle in a particular orientation.
Thus Feret’s statistical diameter is the mean distance apart of two parallel lines which are
tangential to the particle in an arbitrarily fixed direction, irrespective of the orientation of
each particle coming up for inspection. This is shown in Figure 1.1.
A measure of particle shape which is frequently used is the sphericity, ψ, defined as:
ψ = surface area of sphere of same volume as particle
surface area of particle
(1.1)
Another method of indicating shape is to use the factor by which the cube of the size of
the particle must be multiplied to give the volume. In this case the particle size is usually
defined by method (e).
Other properties of the particle which may be of importance are whether it is crystalline
or amorphous, whether it is porous, and the properties of its surface, including roughness
and presence of adsorbed films.