Particle solid/fluid

What this shows is that, from the definition of off-bottom motion to complete uniformity, the effect of mixer power is much less than from going to on-bottom motion to off-bottom suspension. The initial increase in power causes more and more solids to be in active communication with the liquid and has a much greater mass-transfer rate than that occurring above the power level for off-bottom suspension, in which slip velocity between the particles of fluid is the major contributor (Fig. 18-23). 

If force P is greater than zero, the particle will be in motion relative to the continuous phase at a certain velocity, w. At the beginning of the particle s motion, a resistance force develops in the continuous phase, R, directed at the opposite side of the particle motion. At low particle velocity (relative to the continuous phase), fluid layers running against the particle are moved apart smoothly in front of it and then come together smoothly behind the particle (Figure 14). The fluid layer does not intermix (a system analogous to laminar fluid flow in smoothly bent pipes). The particles of fluid nearest the solid surface will take the same time to pass the body as those at some distance away. 

An ideal particle moves relative to the fluid with velocity, v, dependent on just four quantities viz. fluid viscosity and density p and p respectively (i.e. fluid properties), and particle solid density and characteristic size ps and d respectively (i.e. particle characteristics), subject to the forces of buoyancy and friction, as illustrated in Figure 2.1. 

Consider a thin layer solid bowl centrifuge as shown in Figure 4.20. In this device, particles are flung to the wall of the vessel by centrifugal force while liquor either remains stationary in batch operation or overflows a weir in continuous operation. Separation of solid from liquid will be a function of several quantities including particle and fluid densities, particle size, flowrate of slurry, and machine size and design (speed, diameter, separation distance, etc.). A relationship between them can be derived using the transport equations that were derived in Chapter 3, as follows. 

We should mention here one of the important limitations of the singlet level theory, regardless of the closure applied. This approach may not be used when the interaction potential between a pair of fluid molecules depends on their location with respect to the surface. Several experiments and theoretical studies have pointed out the importance of surface-mediated [1,87] three-body forces between fluid particles for fluid properties at a solid surface. It is known that the depth of the van der Waals potential is significantly lower for a pair of particles located in the first adsorbed layer. In... 

In general, adsorption is a surface phenomenon, where gas or liquid is concentrated on the surface of solid particles or fluid interfaces. There are many adsorption systems. 

The solid-liquid separation of shinies containing particles below 10 pm is difficult by conventional filtration techniques. A conventional approach would be to use a slurry thickener in which the formation of a filter cake is restricted and the product is discharged continuously as concentrated slurry. Such filters use filter cloths as the filtration medium and are limited to concentrating particles above 5 xm in size. Dead end membrane microfiltration, in which the particle-containing fluid is pumped directly through a polymeric membrane, is used for the industrial clarification and sterilisation of liquids. Such process allows the removal of particles down to 0.1 xm or less, but is only suitable for feeds containing very low concentrations of particles as otherwise the membrane becomes too rapidly clogged.2,4,8... 

Simulations of multiphase flow are, in general, very poor, with a few exceptions. Basically, there are three different kinds of multiphase models Euler-Lagrange, Euler-Euler, and volume of fluid (VOF) or level-set methods. The Euler-Lagrange and Euler-Euler models require that the particles (solid or fluid) are smaller than the computational grid and a finer resolution below that limit will not give a... 

In settling processes, particles are separated from a fluid by gravitational forces acting on the particles. The particles can be liquid drops or solid particles. The fluid can be a gas, vapor or liquid. 

Gr Grashof number D2pg Ap/p)/v2 Dp = particle diameter g = acceleration due to gravity Ap = solid-fluid density difference p = fluid density... 

Many engineering operations involve the separation of solid particles from fluids, in which the motion of the particles is a result of a gravitational (or other potential) force. To illustrate this, consider a spherical solid particle with diameter d and density ps, surrounded by a fluid of density p and viscosity /z, which is released and begins to fall (in the x = — z direction) under the influence of gravity. A momentum balance on the particle is simply T,FX = max, where the forces include gravity acting on the solid (T g), the buoyant force due to the fluid (Fb), and the drag exerted by the fluid (FD). The inertial term involves the product of the acceleration (ax = dVx/dt) and the mass (m). The mass that is accelerated includes that of the solid (ms) as well as the virtual mass (m() of the fluid that is displaced by the body as it accelerates. It can be shown that the latter is equal to one-half of the total mass of the displaced fluid, i.e., mf = jms(p/ps). Thus the momentum balance becomes... 

Centrifugal force can also be used to separate solid particles from fluids by inducing the fluid to undergo a rotating or spiraling flow pattern in a stationary vessel (e.g., a cyclone) that has no moving parts. Cyclones are widely used to remove small particles from gas streams ( aerocyclones ) and suspended solids from liquid streams ( hydrocyclones ). 

In fast-fluidized beds, which use extremely small catalyst particles, the flow of particles and fluid is cocurrent, and nearly PF, leading to high conversion and selectivity. However, severe erosion of equipment is common, and thus, the design of the solids recovery and recirculation system is important. 

Calculate the pressure drop (-AP/kPa) for flow of fluid through a fluidized bed of solid particles based on the following data the difference in density between solid particles and fluid is 2500 kg m-3 at mf conditions, the bed voidage (em/) is 0.4, and the bed depth (Lm ) is 1.2 m. State any assumptions) made. 

Particle boundary location, 18 148 Particle capture mechanisms, in depth filtration theory, 11 339-340 Particle changes, in solid-fluid reactions, 21 344... 

For the most part, solid particles in fluid streams have Reynolds numbers which are much lower than 500. 

For solid particles a sufficient set of boundary conditions is provided by the no slip condition, the requirement of no flow across the particle surface, and the flow field remote from the particle. For fluid particles, additional boundary conditions are required since Eqs. (1-1) and (1-9) apply simultaneously to both phases. Two additional boundary conditions are provided by Newton s third law which requires that normal and shearing stresses be balanced at the interface separating the two fluids. 

In solid—fluid separation, the fine particles are most difficult to separate, ie, Re is low, almost inevitably below 0.2, owing to low values of x and v. Therefore, only the Stokes region has to be considered. 

Heat-transfer resistance Across two-phase interface in fast reactions Gas side of tube wall in liquid-cooled gas-phase or G/S reactors Within solid particles in solid-fluid reactions... 

Consider a fluidized bed operated at an elevated temperature, e.g. 800°C, and under atmospheric pressure with ah. The scale model is to be operated with air at ambient temperature and pressure. The fluid density and viscosity will be significantly different for these two conditions, e.g. the gas density of the cold bed is 3.5 times the density of the hot bed. In order to maintain a constant ratio of particle-to-fluid density, the density of the solid particles in the cold bed must be 3.5 times that in the hot bed. As long as the solid density is set, the Archimedes number and the Froude number are used to determine the particle diameter and the superficial velocity of the model, respectively. It is important to note at this point that the rale of similarity requires the two beds to be geometrically similar in construction with identical normalized size distributions and sphericity. It is easy to prove that the length scales (Z, D) of the ambient temperature model are much lower than those in the hot bed. Thus, an ambient bed of modest size can simulate a rather large hot bed under atmospheric pressure. 

Properties of the particles (size, density, shape, solid, fluid, hygroscopicity, and electric charge)... 

Owing to reduced salt solubility, the formation of metal oxides and, eventually, the presence of stable solid-matter particles, these are all present in the SCWO processes. These particles can cause equipment-fouling and erosion. However the reduced solubility of salts under supercritical conditions introduces the possibility of a solid fluid separation. 

Vol. 9 Hydrophile-Lipophile Balance of Surfactants and Solid Particles. Physicochemical Aspects and Applications. By P.M. Kruglyakov Vol. lO Particles at Fluid Interfaces and Membranes. Attachment of Colloid Particles and Proteins to Interfaces and Formation of Two-Dimensional Arrays. 

One approach to describe the kinetics of such systems involves the use of various resistances to reaction. If we consider an irreversible gas-phase reaction A — B that occurs in the presence of a solid catalyst pellet, we can postulate seven different steps required to accomplish the chemical transformation. First, we have to move the reactant A from the bulk gas to the surface of the catalyst particle. Solid catalyst particles are often manufactured out of aluminas or other similar materials that have large internal surface areas where the active metal sites (gold, platinum, palladium, etc.) are located. The porosity of the catalyst typically means that the interior of a pellet contains much more surface area for reaction than what is found only on the exterior of the pellet itself. Hence, the gaseous reactant A must diffuse from the surface through the pores of the catalyst pellet. At some point, the gaseous reactant reaches an active site, where it must be adsorbed onto the surface. The chemical transformation of reactant into product occurs on this active site. The product B must desorb from the active site back to the gas phase. The product B must diffuse from inside the catalyst pore back to the surface. Finally, the product molecule must be moved from the surface to the bulk gas fluid. 

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