Particle-fluid interaction

A relationship between these four variables is required in order to prediet partiele veloeity in a variety of eireumstanees. In doing so, it is noted that as a partiele moves through a fluid it experienees drag and viee versa as the fluid moleeules move aeross and around the surfaee of the partiele. There is thus a fluid-particle interaction due to interfaeial surfaee drag. 

Di Felice, R., 1994. The voidage function for fluid-particle interaction systems. International Journal of Multiphase Flow, 20, 153-159. 

Let us consider an V-component fluid in a volume V, at temperature T, and at chemical potentials /r = mi, > Mv - The fluid is in contact with an impermeable solid surface. We assume that the fluid particles interact between themselves via the pair potential denoted by u pir), and interact with the confining surface via the potential (a,f3= 1,2,. ..,V). The potential v ir) contains a hard-wall term to ensure that the solid surface is impermeable. For the sake of convenience, the hard-wall term is assumed to extend into the bulk of the solid [46,47], such that the Boltzman factor (r), and the local density Pa r) are cutoff at a certain distance z = z, ... 

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

Either a liquid or a gas can be used as the carrier fluid, depending on the size and properties of the particles, but there are important differences between hydraulic (liquid) and pneumatic (gas) transport. For example, in liquid (hydraulic) transport the fluid-particle and particle-particle interactions dominate over the particle-wall interactions, whereas in gas (pneumatic) transport the particle-particle and particle-wall interactions tend to dominate over the fluid-particle interactions. A typical practical approach, which gives reasonable results for a wide variety of flow conditions in both cases, is to determine the fluid only pressure drop and then apply a correction to account for the effect of the particles from the fluid-particle, particle-particle, and/or particle-wall interactions. A great number of publications have been devoted to this subject, and summaries of much of this work are given by Darby (1986), Govier and Aziz (1972), Klinzing et al. (1997), Molerus (1993), and Wasp et al. (1977). This approach will be addressed shortly. 

The procedure for determining APs that will be presented here is that of Molerus (1993). The basis of the method is a consideration of the extra energy dissipated in the flow as a result of the fluid-particle interaction. This is characterized by the particle terminal settling velocity in an infinite fluid in terms of the drag coefficient, Cd ... 

The fluid-particle interaction force, omitting the virtual mass term and combining the pressure terms in the equation of motion becomes... 

The volumetric fluid-particle interaction force F0 in Eq. (28) is calculated from the forces acting on the individual particles in a cell ... 

Note that depending on the manner in which the drag force and the buoyancy force are accounted for in the decomposition of the total fluid particle interactive force, different forms of the particle motion equation may result (Jackson, 2000). In Eq. (36), the total fluid-particle interaction force is considered to be decomposed into two parts a drag force (fd) and a fluid stress gradient force (see Eq. (2.29) in Jackson, 2000)). The drag force can be related to that expressed by the Wen-Yu equation, /wen Yu> by... 

In addition to flow, thermal, and bed arrangements, an important design consideration is the amount of catalyst required (W), and its possible distribution over two or more stages. This is a measure of the size of the reactor. The depth (L) and diameter (D) of each stage must also be determined. In addition to the usual tools provided by kinetics, and material and energy balances, we must take into account matters peculiar to individual particles, collections of particles, and fluid-particle interactions, as well as any matters peculiar to the nature of the reaction, such as reversibility. Process design aspects of catalytic reactors are described by Lywood (1996). 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

As discussed in Section 4.3, the linear-eddy model solves a one-dimensional reaction-diffusion equation for all length scales. Inertial-range fluid-particle interactions are accounted for by a random rearrangement process. This leads to significant computational inefficiency since step (3) is not the rate-controlling step. Simplifications have thus been introduced to avoid this problem (Baldyga and Bourne 1989). 

Khan, A. R. and Richardson, J. F. Chem. Eng. Comm. 78 (1989) 111. Fluid-particle interactions and flow characteristics of fluidized beds and settling suspensions of spherical particles. 

Apart from the specific classes of motion discussed above, understanding of unsteady fluid-particle interaction is not well advanced. Torobin and Gauvin... 

Equations (5.139) to (5.142) are the basic equations for a gas-solid flow. More detailed information on both the fluid-particle interacting force Fa and the total stresses T and Tp must be specified before these equations can be solved. One approach to formulate the fluid-particle interacting force FA is to decompose the total stress into a component E representing the macroscopic variations in the fluid stress tensor on a scale that is large compared to the particle spacing, and a component e representing the effect of detailed variations of the point stress tensor as the fluid flows around the particle [Anderson and... 

The particle mobility B is defined as B = U. Generally, the particle velocity is given in terms of the product of the mobility and a force F acting externally on the particle, such as a force generated by an electrical field. Under such conditions, the particle motion is called quasi-stationary. That is, the fluid particle interactions are slow enough that the particle behaves as if it were in steady motion even if it is accelerated by external forces. Mobility is an important basic particle parameter its variation with particle size is shown in Table II along with other important parameters described later. 

In a packed bed, the fluid-particle interaction force is insufficient to support the weight of the particles. Hence, the fluid that percolates through the particles loses energy due to frictional dissipation. This results in a loss of pressure that is greater than can be accounted for by... 

Most fluidisation processes are operated at high temperatures and pressures. It is important, therefore, to be able to predict changes in fluidisation with the operating conditions. Using Equations (35) and (36), the effect of temperature and pressure can be determined. With increasing temperature, gas viscosity increases while gas density decreases. For small particles, the fluid-particle interaction is dominated by the viscous effects. Equation (35) shows that varies with 1 jp, and wmf should therefore decrease with temperature. For large particles, the inertial effects dominate Equation (36) predicts that wn,r will vary with (1 /p/)0 5, should therefore increase with temperature. 

The viscous effects dominate the fluid-particle interaction of small particles (below 100 pm), thus the inertial term of the Ergun equation can be neglected. Hence, the minimum fluidisation velocity can be obtained from ... 

Although particles in two-phase flow are not uniformly distributed, the dense and the dilute phases can be considered, each in its own, as uniform suspensions, and the global system can thus be regarded as consisting of dense clusters dispersed in a broth of separately distributed discrete particles, as shown in Fig. 1. The preceding correlations will therefore be used respectively in the dilute and the dense phases, for calculating micro-scale fluid-particle interaction, and also for evaluating meso-scale interphase interaction between clusters and the broth, as shown in Table I, for CD, CD[ and CD. ... 

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