Particle pressure

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

When a fluid flows upward through a bed of solid particles, pressure drop across the bed increases as the flow rate increases. Eventually the pressure drop equals the weight of the bed (per unit horizontal area) at which point the particles are... 

Number of fine particles Pressure along screw (Pa)... 

Boride Binder nature and content (wt%) Mean Compacting particle pressure size xIO" Sintering T ( O Holding time (min) Sintering atmosphere or Vacuum V (pressure in torrP Relative density (%) Remarks Ref. 

Binder nature particle pressure Sintering Holding vacuum V Relative ... 

One of the strengths of the KTGF, although still under development, is that it can offer a very clear physical picture with respect to the key parameters (e.g., particle pressure, particle viscosity, and other transport coefficients) that are used in the TFMs. The TFMs based on KTGF requires less ad hoc adjustments compared to the other two types of models. Therefore, it is the most promising framework for modeling engineering-scale fluidized beds. 

Note that the mass and momentum equations for the gas phase can simply be obtained by replacing ss-> , ps >p, u5-mi in Eqs. (84) and (85), and dropping the terms concerning the particle-pressure gradient. 

After the new solid volume fractions have been obtained from Eq. (93), new particle pressures are calculated, where after new velocities can be obtained from the coupled momentum equations. Next, new granular temperatures are calculated from the granular energy equations by an iterative procedure described in Section IV.E.l. Finally, the new mass residuals (D ijk and (T>s)v,i are computed and the convergence criteria are checked again. 

At least three approaches have been proposed to solve for the mean pressure field that avoid the noise problem. The first approach is to extract the mean pressure field from a simultaneous consistent39 Reynolds-stress model solved using a standard CFD solver.40 While this approach does alleviate the noise problem, it is intellectually unsatisfying since it leads to a redundancy in the velocity model.41 The second approach seeks to overcome the noise problem by computing the so-called particle-pressure field in an equivalent, but superior, manner (Delarue and Pope 1997). Moreover, this approach leads to a truly... 

In Section 6.8 we will discuss how particle fields such as (U U X > can be estimated from the notional particles. However, it is important to note that since the particle-pressure field is found by solving (6.179), the estimate of (U U X must be accurate enough to allow second-order derivatives. As noted after (6.61), the problem of dealing with noisy estimates of P(x, t) is one of the key challenges in applying (6.178).134... 

As noted above, in the applications of Lagrangian PDF methods to inhomogeneous flows, evaluation of the particle-pressure field can be problematic. In order to avoid this difficulty, hybrid PDF methods have been developed (Muradoglu, et al. 1999 Jenny et al. 

The principal advantage of using (6.184) to determine u is that the feedback of statistical noise through the particle-pressure field in (6.178) will be minimized by solving (6.185) for (U). Indeed, for homogeneous turbulence, (6.184) is independent of X ... 

Equilibrium composition of a solution in presence of CaCC>3(s) (calcite) at constant particle pressure of C02 (Pco2 = 10 3 5 atm) at 25° c-,f no ac d or base is added-the equilibrium composition is indicated by the arrow. The calcite at this composition is characterized by a net surface charge of zero. 

Equation (2.2.19) implies that at the surface of the particles pressure is constant and equal to p0 + e1 + e-<> — 2. This in turn implies that the total pressure force on the particle vanishes. The second force component is the electric force. As indicated in (2.2.13a), this component may be computed as follows (assuming independence of the dielectric constant on the density of the liquid [21]) ... 

One should note, that in a real industrial process there are de-pressurization processes accompanied by fast intra-particle pressure drop, and the morphology of particles might be changed by stress created by fastly evaporating liquid gases stored in the pores and sorbed by the polymer. 

The nature and sizing of equipment depends on the economic values and proportions of the phases as well as certain physical properties that influence relative movements of liquids and particles. Pressure often is the main operating variable so its effect on physical properties should be known. Table 11.1 is a broad classification of mechanical processes of solid-liquid separation. Clarification is the removal of small contents of worthless solids from a valuable liquid. Filtration is applied to the recovery of valuable solids from slurries. Expression is the removal of relatively small contents of liquids from compressible sludges by mechanical means. 

In Chapter 6 we gave a brief account of the normal manner of filling voids. By such a procedure we may reduce the void space to very small amounts. In powder metallurgy the void space is reduced partly by a deformation of particles and partly by a diffusion through slippage of the finer particles to the void spaces. This may be termed particle-pressure diffusion. 

Isothermal-isobaric ensemble IIE (each system has constant P, T, and N the walls between systems are flexible and diathermal each system keeps its number of particles, pressure, and temperature, but can trade both volume and energy with neighboring systems). The relevant partition function is the isothermal-isobaric partition function A (P,T,N) ... 

The particle pressure of a vapor at the surface of its parent liquid. 

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