Mass transfer local

Here a conflict can arise in an agitated vessel. High power input per unit mass is required to enhance mass transfer area and heat transfer coefficient, but this will result in a high degree of gas recircniation, reducing Ihe mean gas phase concentration driving force for mass transfer. Local shear rates will also increase with power inpnt. The balance will vary with scale. 

The high rate of mass transfer in SECM enables the study of fast reactions under steady-state conditions and allows the mechanism and physical localization of the interfacial reaction to be probed. It combines the usefid... 

In many types of contactors, such as stirred tanks, rotary agitated columns, and pulsed columns, mechanical energy is appHed externally in order to reduce the drop si2e far below the values estimated from equations 36 and 37 and thereby increase the rate of mass transfer. The theory of local isotropic turbulence can be appHed to the breakup of a large drop into smaller ones (66), resulting in an expression of the form... 

The role of coalescence within a contactor is not always obvious. Sometimes the effect of coalescence can be inferred when the holdup is a factor in determining the Sauter mean diameter (67). If mass transfer occurs from the dispersed (d) to the continuous (e) phase, the approach of two drops can lead to the formation of a local surface tension gradient which promotes the drainage of the intervening film of the continuous phase (75) and thereby enhances coalescence. It has been observed that d-X.o-c mass transfer can lead to the formation of much larger drops than for the reverse mass-transfer direction, c to... 

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

The general expression given by Eq. (14-8) is more complex than normally is required, but it must be used when the mass-transfer coefficient varies from point to point, as may be the case when the gas is not dilute or when the gas velocity varies as the gas dissolves. The values of yi to be used in Eq. (14-8) depend on the local hquid composition Xi and on the temperature. This dependency is best represented by using the operating and equilibrium lines as discussed later. 

Solution. By assuming that the mass-transfer coefficient varies as the 0.8 power of the local gas mass velocity, we can derive the following relation ... 

Methods for analysis of fixed-bed transitions are shown in Table 16-2. Local equilibrium theoiy is based solely of stoichiometric concerns and system nonlinearities. A transition becomes a simple wave (a gradual transition), a shock (an abrupt transition), or a combination of the two. In other methods, mass-transfer resistances are incorporated. 

Combined Pore and Solid Diffusion In porous adsorbents and ion-exchange resins, intraparticle transport can occur with pore and solid diffusion in parallel. The dominant transport process is the faster one, and this depends on the relative diffusivities and concentrations in the pore fluid and in the adsorbed phase. Often, equilibrium between the pore fluid and the solid phase can be assumed to exist locally at each point within a particle. In this case, the mass-transfer flux is expressed by ... 

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

The relationships between the local and overall mass transfer coefficients are ... 

Sparrow, E. M., and Kalejs, J. P. (1977). Local convective transfer coefficients in a channel downstream of a partially constricted inlet. Int. ]. Heat Mass Transfer 20, 1241-1249. 

The energy of large and medium-size eddies can be characterized by the turbulent diffusion coefficient. A, m-/s. This parameter is similar to the parameter used by Richardson to describe turbulent diffusion of clouds in the atmosphere. Turbulent diffusion affects heat and mass transfer between different zones in the room, and thus affects temperature and contaminant distribution in the room (e.g., temperature and contaminant stratification along the room height—see Chapter 8). Also, the turbulent diffusion coefficient is used in local exhaust design (Section 7.6). 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

As our first approach to the model, we considered the controlling step to be the mass transfer from gas to liquid, the mass transfer from liquid to catalyst, or the catalytic surface reaction step. The other steps were eliminated since convective transport with small catalyst particles and high local mixing should offer virtually no resistance to the overall reaction scheme. Mathematical models were constructed for each of these three steps. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

From the c s, the local mass transfer was calculated by the formula... 

The proposed technique will be used here to illustrate the case of interfacial heat and multicomponent mass transfer in a perfectly mixed gas-liquid disperser. Since in this case the holding time is also the average residence time, the gas and liquid phases spend the same time on the average. If xc = zd = f, then for small values of t, the local residence times tc and td of adjacent elements of the continuous and dispersed phases are nearly of the same order of magnitude, and hence these two elements remain in the disperser for nearly equal times. One may conclude from this that the local relative velocity between them is negligibly small, at least for small average residence times. Gal-Or and Walatka (G9) have recently shown that this is justified especially in dispersions of high <6 values and relatively small bubbles in actual practice where surfactants are present. Under this domain, Eqs. (66), (68), (69) show that as the bubble size decreases, the quantity of surfactants necessary to make a bubble behave like a solid particle becomes smaller. Under these circumstances (pd + y) - oo and Eq. (69) reduces to... 

Characteristic length [Eq. (121)] L Impeller diameter also characteristic distance from the interface where the concentration remains constant at cL Li Impeller blade length N Impeller rotational speed also number of bubbles [Eq, (246)]. N Ratio of absorption rate in presence of chemical reaction to rate of physical absorption when tank contains no dissolved gas Na Instantaneous mass-transfer rate per unit bubble-surface area Na Local rate of mass-transfer per unit bubble-surface area Na..Average mass-transfer rate per unit bubble-surface area Nb Number of bubbles in the vessel at any instant at constant operating conditions N Number of bubbles per unit volume of dispersion [Eq. (24)] Nb Defined in Eq. (134)... 

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