Nonhomogeneous flow

Term Sf is the sum of forces caused by various inertial effects and by effects of flow nonhomogeneity. When there are concentrated suspensions, an analytical expression for this term has been so far obtained only for fine spherical particles whose Reynolds number is smaller than unity [24]. In the case of fine suspensions, the inertial part of Sf includes 1) an inertial force due to acceleration of the virtual fluid mass by the moving particle, 2) a contribution to the buoyancy which is caused by the field of inertial body forces in the same way as buoyancy is usually caused by the field of external body forces, 3) a hereditary force whose strength and direction depend on the flow history (Basset force), and 4) a new force due to frequency dispersion of the suspension effective viscosity. As the suspension concentration comes to zero, the first three force constituents of the inertial part of Sf tend to manifest themselves as forces similar to those experienced by a single... 

Nonconventiona.1 Solder Systems. Nonconventional solder systems are developed for use with newer alloys, especially base metal alloys. They are few in number and will probably remain the exception rather than the rule. Some new solder systems consist of metallic particles either pressed to form a rod or suspended in a paste flux. The metallic composition is close to that of the alloy to be joined. If the particles are nonhomogeneous, the solder has particles with melting points lower and higher than that of the alloy. For nonhomogeneous solders, once the flame has been placed on the parts to be joined and the soldering material, it should not be removed until the flow process is completed. 

Hansen, S., and Ottino, J. M., Aggregation and cluster size evolution in nonhomogeneous flows. ]. Colloid Interface Sci. 179, 89-103 (1996b). 

However, bubble nonhomogeneous distribution exists in two-phase shear flow. As yet, the following general trends in void fraction radial profiles are being identified for bubbly upward flow (Zun, 1990) concave profiles (Serizawa et al., 1975) convex profiles (Sekoguchi et al., 1981), and intermediate profiles (Sekoguchi et al., 1981 Zun, 1988). Two theories are currently dominant ... 

The frictional pressure gradient is obtained by different correlations described in following sections. In a horizontal flow, (dp/dz)elev = 0, it is an ideal case to perform experiments excluding the term of elevation pressure drop. Because of nonhomogeneity of the slug flow, the acceleration pressure gradient term is different from that shown above it is given in Section 3.5.2.2. 

In principle, the energy dissipation (friction loss) associated with the gas-liquid, gas-wall, and liquid-wall interactions can be evaluated and summed separately. However, even for distributed (nonhomogeneous) flows it is common practice to evaluate the friction loss as a single term, which, however, depends in a complex manner on the nature of the flow and fluid properties in both phases. This is referred to as the homogeneous model ... 

A successor to PESTANS has recently been developed which allows the user to vary transformation rate and with depth l.e.. It can describe nonhomogeneous (layered) systems (39,111). This successor actually consists of two models - one for transient water flow and one for solute transport. Consequently, much more Input data and CPU time are required to run this two-dimensional (vertical section), numerical solution. The model assumes Langmuir or Freundllch sorption and first-order kinetics referenced to liquid and/or solid phases, and has been evaluated with data from an aldlcarb-contamlnated site In Long Island. Additional verification Is In progress. Because of Its complexity, It would be more appropriate to use this model In a hl er level, rather than a screening level, of hazard assessment. 

Three main independent contributions to band spreading inside the column have been identified (32) as longitudinal molecular diffusion, the unevenness of flow through the nonhomogeneous packing, and the resistances to mass transfer in the mobile and stationary phases. 

General Generally, from a macroscopic point of view, maldistribution can be divided into two different phenomena (Stanek, 1994). The first one is small-scale maldistibution, which is connected mainly to the so-called preferred paths. It is the case where the liquid follows specific paths through bed and travels with velocities considerably higher than the mean. The same phenomenon is characterized as chaneling. The second case is large-scale maldistribution, which is connected to the nonhomogeneous (nonunifonn) initial distribution of the liquid and is referred to as wall effects. The concepts of distributor quality and liquid maldistribution in fixed beds are frequently found in the related technical literature, and these concepts are connected to each other—the better die distributor quality, the better the liquid distribution and flow into bed (Klemas and Bonilla, 1995). 

Despite considerable success in some fields of application, the CFD simulations are still not fully mastered, especially where the considered processes reveal clearly nonhomogeneous, segregated fluid flow patterns. The latter are usually the basic phenomenon in packed or filmlike units used in reactive and non-... 

One-dimensional flow models are adopted in the early stages of model development for predicting the solids holdup and pressure drop in the riser. These models consider the steady flow of a uniform suspension. Four differential equations, including the gas continuity equation, solids phase continuity equation, gas-solid mixture momentum equation, and solids phase momentum equation, are used to describe the flow dynamics. The formulation of the solids phase momentum equation varies with the models employed [e.g., Arastoopour and Gidaspow, 1979 Gidaspow, 1994], The one-dimensional model does not simulate the prevailing characteristics of radial nonhomogeneity in the riser. Thus, two- or three-dimensional models are required. 

In Sections 4.4 and 4.5, we dealt briefly with particulate flow instabilities in hoppers and the nonhomogeneous stress distributions created under uniaxial loading of a particulate assembly. In this section, we will expand on the discrete nature of such assemblies, and refer the reader to the computational and experimental tools that have been developed, and are rapidly advancing, to study such phenomena. 

With a homogeneous reaction and mechanical equilibrium (VP = 0), consider a reactor consisting of a large number of n subsystems with equal volumes and the same reaction taking place in all subsystems. We assume that the subsystems have a uniform composition and temperature. The reaction flow in subsystem k is Jrk and the driving force is AGk/T. The total system is a nonhomogeneous reactor with variations in temperature and composition... 

Is this expectation really realistic In sharp contrast to a packed bed, a monolithic reactor has no flow in the radial direction there is no flow from one charmel to an adjacenf one. When the initial distribution of liquid in fhe radial direction is nonhomogeneous, this distribution will propagate down the reactor unchanged. In a packed-bed reactor, there is always some radial flow. Therefore, in a design of a monolith reactor, the inlet design is more critical than that for a packed-bed reactor. In scale-up of a monolifh reacfor, fhe reacfor inlef system has to be designed such that the distribution of fhe liquid af fhe enhance of fhe reactor is ideal. 

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