Fluid-phase mass transport

In the literature on turbulent two-phase flow (Minier Peirano, 2001 Peirano Minier, 2002 Simonin et al, 1993), the fluid phase is usually treated using a separate distribution function whose integral over phase space leads to the fluid-phase mass density. Here, we use a different approach starting from n(f, x, Vp, p, Vf, f). In this approach, we let the internal coordinate be equal to the fluid mass seen by a particle. The fluid-phase mass density is then given by 

We also define a corresponding fluid-mass-average disperse-phase velocity by 

Using this definition and starting from Eq. (4.39) with g = the transport equation 

A consistent model for the change in fluid mass seen by the particles 

As with the fluid volume seen by a particle, we implicitly assume that the fluid mass seen by each particle is distinct. In this context, Eqs. (4.75) and (4.81) are consistency constraints on the definition of ff2. The simplest case is when = g t x, fp2), where g is a function that satisfies Eq. (4.75). In this case, the NDF can be written as n(t,x, Vp,fp2, Vf, ff2) = n(t,x, Vp,fp2, Vf) 5(ff2 -g(f, x,fp2)). If we choose the linear function g(f, x, (p2) = Pffp2/pp, then each particle has associated with it a mass of fiuid that is proportional to its mass fp2. even simpler model is 

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Caro and Nerem [5] measured the uptake of labeled cholesterol bound to serum lipoprotein in excised dog arteries under well-defined conditions in which the L v que solution (Equation 9.19) described the fluid phase mass transport process. If the transport of lipoprotein to the surface had been controlled by the fluid phase, they should have observed a decrease in uptake with distance from the vessel entrance following a law (Equation 9.19). They did not, however, observe any significant spatial variation of... 

Rates and selectivities of soHd catalyzed reactions can also be influenced by mass transport resistance in the external fluid phase. Most reactions are not influenced by external-phase transport, but the rates of some very fast reactions, eg, ammonia oxidation, are deterrnined solely by the resistance to this transport. As the resistance to mass transport within the catalyst pores is larger than that in the external fluid phase, the effectiveness factor of a porous catalyst is expected to be less than unity whenever the external-phase mass transport resistance is significant, A practical catalyst that is used under such circumstances is the ammonia oxidation catalyst. It is a nonporous metal and consists of layers of wire woven into a mesh. 

To be able to predict the release of SVOCs from a material to the indoor environment it is important to understand the fundamental mechanisms in order to mathematically model the emissions. The emission behavior of DEHP from PVC in the FLEC and CLIMPAQ experiments (Clausen et al., 2004) have now been successfully modeled (Xu and Little, 2006). Fluid building materials such as paints (Clausen, 1993 Xu and Little, 2006) and wood oil (Clausen, 1997) may also emit SVOCs and are usually used on large indoor surfaces such as walls, ceilings and floors. Such wet materials may be applied on substrates like wood or plaster board. The emission of for example, Texanol from water-based paint was found likely to be limited by gas phase mass transport (Clausen, 1993) similar to the DEHP emission from PVC (Clausen et al., 2004). 

These properties allow SCW to provide an environment and an opportunity to conduct chemistry in a single fluid phase that would otherwise occur in a multiphase system under more conventional conditions. The advantages of a single supercritical-phase reaction medium are that (i) higher concentrations of reactants can often be attained and (ii) there are no inter-phase mass transport processes to hinder reaction rates. 

Dixon A, Di Costanzo M, Soucy B (1984) Fluid-phase radial transport in packed beds of low tube-to-particle diameter ratio. Int J Heat Mass Transfer 27(10) 1701-1713... 

Referring to Figure 9.1, we will assume that the species of interest is transported from the blood vessel lumen, where its bulk concentration is Q, to the blood vessel surface, where its concentration is Cs, by a convective-diffusive mechanism which depends on the local fluid mechanics and can be characterized by a fluid-phase mass transfer coefficient ki (see Reference 6 for further background). The species flux in the blood phase is given by... 

Table 12.1 clearly reveals that for a straight aorta, transport is in the entry or L v que regime (x < lO ). For albumin and LDL, Da Sh, and transport is expected to be wall-limited. For Oj and ATP, Da Sh, and the possibility of fluid phase-limited transport exists. At the lowest possible rates of wall mass transport in a straight vessel (Sh = 3.66-4.36), transport is still expected to be wall-limited for albumin and LDL, whereas it would be fluid-phase limited for oxygen and ATP. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

The liquid-liquid extraction process is based on the specific distribution of dissolved components between two immiscible fluids, for instance, between aqueous and organic liquids. The process refers to a mass exchange processes in which the mass transport of component (j) from phase (1) to phase (2) by means of convection or molecular diffusion acts to achieve the chemical potential (p) equilibrium (134) ... 

Solution We suppose that the mass transfer and diffusion steps are fast compared with bulk transport by convection. This is the design intent for ion-exchange columns. The reaction front moves through the bed at a speed dependent only on the supply of fluid-phase reactants. Assuming piston... 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

Data for the bulk fluid, line A, indicate that vz varies as a function of z but maintains a value near 0.75 of maximum velocity. The periodicity of vx and vy is clearly evident in the graph of line A and a 1800 out of phase coupling of the components is seen with one positive when the other is negative. This indicates a preferred orientation to the plane of the oscillatory flow and this feature was seen in all the biofilms grown throughout this study. The secondary flow components are 0.1-0.2 of the maximum axial velocity and are spatially oscillatory. The significant non-axial velocities indicate non-axial mass transport has gone from diffusion dominated, Pe = 0, in the clean capillary, to advection dominated, Pe 2 x 103, due to the impact of the biofilm. For comparison, the axial Peclet number is Pe L 2x 10s. Line B intersects areas covered by biomass and areas of only bulk... 

The same types of catalyst have been employed in 1-octene hydroformylation, but with the substrates and products being transported to and from the reaction zone dissolved in a supercritical fluid (carbon dioxide) [9], The activity of the catalyst is increased compared with liquid phase operation, probably because of the better mass transport properties of scC02 than of the liquid. This type of approach may well reduce heavies formation because of the low concentration of aldehyde in the system, but the heavies that do form are likely to be insoluble in scC02, so may precipitate on and foul the catalyst. The main problem with this process, however, is likely to be the use of high pressure, which is common to all processes where supercritical fluids are used (see Section 9.8). 

As depicted in Figure 2.8, mass transport of substrate from the bulk water phase takes place through a fluid boundary layer (liquid film) and into a biofilm followed by a combined diffusion and utilization of the substrate in the biofilm. 

The transport of an adsorbable species from the bulk fluid flowing around an individual bead is a problem of molecular diffusion. With the fluid in motion the rate of transport to the surface of a bead or pellet of adsorbent material is generally treated as a linear driving force. Eor gas phase separations there are a variety of correlations available to describe the mass transport to the surface in terms of the particle Reynolds number, the Schmidt number, the size of the adsorbent particle and of course the binary diffusivity of the species of interest. 

The thermochemical conversion of biofuels takes place in the conversion system and belongs to the science of two-phase phenomena (fluid-solid dynamics), that is, heat and mass transport processes take place inside and between a solid phase and a gas phase. This phenomenology is well illustrated by Balakrishnen and Pei [49], see Figure 40. 

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