Single Particles in a Fluid

The free-fall or terminal settling velocity of a single particle in a fluid, wq, can be calculated by equating the drag force (equation 9.109) with the gravitational force. Thus for a spherical particle of density p ... 

The hydrodynamic drag experienced by the diffusing molecule is caused by interactions with the surrounding fluid and the surfaces of the gel fibers. This effect is expected to be significant for large and medium-size molecules. Einstein [108] used arguments from the random Brownian motion of particles to find that the diffusion coefficient for a single molecule in a fluid is proportional to the temperature and inversely proportional to the frictional coefficient by... 

In a particle-fluid flow, the particle velocity Vp generally differs from the fluid velocity V. The slip velocity, V — Vp, leads to unbalanced pressure distribution as well as viscous stresses on the particle surface, which yield a resulting force known as the drag force. The drag force of a single particle in a uniform flow field can be generally... 

This chapter deals with the motion of single solid particles in fluids. The objective here is to develop an understanding of the forces resisting the motion of any such particle and provide methods for the estimation of the steady velocity of the particle relative to the fluid. The subject matter of the chapter will be used in subsequent chapters on the behaviour of suspensions of particles in a fluid, fluidization, gas cyclones and pneumatic transport. 

The nature of the hlter medium is critical to the filtration process, and the various types of media will be described in Section 2. Suffice it to say here that there are ten broad types of media material to be considered. Of these ten types only one does not have a version that is hbrous in structure. All the rest are entirely fibrous, or have a significant component in fibrous format. It follows that, to find how filtration works, it is necessary to examine the way in which a bed of fibres can stop a particle moving towards and through it. The process is illustrated in Figure 1.3, which shows the cross-section of a single fibre in a fluid flow from left to right, carrying some particles in suspension. 

The general consensus, however, is that the behavior of a single particle in a turbulent fluid flow is strongly determined by the ratio of various times scales ... 

Spouted beds are used for coarse particles that do not fluidize well. A single, high velocity gas jet is introduced under the center of a static particulate bed. This jet entrains and conveys a stream of particles up through the bed into the vessel freeboard where the jet expands, loses velocity, and allows the particles to be disentrained. The particles fall back into the bed and gradually move downward with the peripheral mass until reentrained. Particle-gas mixing is less uniform than in a fluid bed. 

So far the relative motion between a fluid and a single particle has been considered. This process is called free settling. When a fluid contains a concentration of particles in a vessel, the settling of an individual particle may be hindered by the other particles and by the walls. When this is the case, the process is called hindered settling. Interference is negligible if the particles are at least 10 to 20 diameters away from each other and the vessel wall [Larian (1958)]. In this case the particles can be considered to be free settling. 

Several expressions of varying forms and complexity have been proposed(35,36) for the prediction of the drag on a sphere moving through a power-law fluid. These are based on a combination of numerical solutions of the equations of motion and extensive experimental results. In the absence of wall effects, dimensional analysis yields the following functional relationship between the variables for the interaction between a single isolated particle and a fluid ... 

The result of experiments on heat transfer between a single particle and a flowing fluid are usually expressed in the form... 

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