Interaction between Particles and Fluids

The fluid-particle and particle-particle interactions dominate the fluid dynamics of particle systems and are of major importance in predicting the behaviour of complex operations, such as fluidisation, pneumatic transport and flow of slurries. In this section, the simple case study of a single particle immersed in a fluid is the starting point for the subsequent examination of the behaviour of fluidisation processes, which involve many particles in up-flowing fluids. This extends what is presented in Chapter 3, in which the concepts of Fluid Flow are 

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Detailed consideration of the interaction between particles and fluids is given in Volume 2 to which reference should be made. Briefly, however, if a particle is introduced into a fluid stream flowing vertically upwards it will be transported by the fluid provided that the fluid velocity exceeds the terminal falling velocity m0 of the particle the relative or slip velocity will be approximately o- As the concentration of particles increases this slip velocity will become progressively less and, for a slug of fairly close packed particles, will approximate to the minimum fluidising velocity of the particles. (See Volume 2, Chapter 6.)... 

Compared to small molecules the description of convective diffusion of particles of finite size in a fluid near a solid boundary has to account for both the interaction forces between particles and collector (such as van der Waals and double-layer forces) and for the hydrodynamic interactions between particles and fluid. The effect of the London-van der Waals forces and doublelayer attractive forces is important if the range over which they act is comparable to the thickness over which the convective diffusion affects the transport of the particles. If, however, because of the competition between the double-layer repulsive forces and London attractive forces, a potential barrier is generated, then the effect of the interaction forces is important even when they act over distances much shorter than the thickness of the diffusion boundary layer. For... 

This section will first deal with the phases in particle-fluid two-phase flow by developing a mathematical model to quantify local hydrodynamic states. This analysis will reveal the insufficiency of the conditions for the conservation of mass and momentum alone in determining the hydrodynamic states of heterogeneous particle-fluid systems, and calls for a methodology different from what is used in analyzing dilute uniform flow. For this purpose the concept of multi-scale interaction between particles and fluid and the principle of energy minimization are proposed. 

The interaction between particles and fluids is important in many industrial processes. The most relevant size distribution in such cases is, therefore, based on the sedimentation behavior of particles in fluids and the applicable size is the settling or Stokes diameter. 

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