External transfer

Boeh-Ocansey O., Freeze-drying in a fluidized-bed atmospheric dryer and in a vacuum dryer evaluation of external transfer coefficients, /. Food Eng., 7 (1988) 127-146. 

The dependence of Sh on Pe/(1 + k) at high Pe results because the Hadamard -Rybczynski analysis gives dimensionless velocities iiJU, iio/V) proportional to (1 + k) within and close to the particle (Eqs. (3-7) and (3-8)). Similar dependence is encountered for unsteady external transfer (Section B.2), and for internal transfer at all Pe (Section C.4). These results do not give the rigid sphere values as /c x, because of fundamental diflerences between the boundary layer approximations for the two cases (see Chapter 1), and arc only valid for /c < 2. 

External transfer transfer of the absorbate from bulk fluid to outer surface of particle by molecular and convective diffusion. 

External transfer transfer of energy from the surface of the particle into the fluid stream. The properties of flowing fluids are such that the resistance to heat transfer can be larger than that for mass transfer, so that a negligible concentration difference may exist between bulk fluid and particle surface and yet the corresponding temperature difference will be significant. 

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

Assessment of external transfer effects on measured rates requires the knowledge of the corresponding transfer coefficients. 

Mass transport, whether external (transfer from the bulk to the external surface of the photocatalyst) or internal (transfer within the pores of the... 

So far in this section we have considered only the adsorption, desorption, and surface reaction. Let us next set these in the context of the transfer and diffusion steps for the same reaction. As has been mentioned above, the catalyst will often be held on porous particles so that the reactants and products have to diffuse to and from the surface of the particle and also within it. For external transfer from the flowing reaction mixture to the exterior of the particle we shall reserve the term mass transfer (more particularly, external mass transfer), and for the diffusion within the particle the term diffusion (or internal diffusion). Both are, of course, concurrently examples of mass transfer and of diflTusion so that the choice of language is an arbitrary one but it draws a useful distinction. 

It is obvious from the conditions defined above that the rate-based model equations and variables are more numerous and complex than those in the equilibrium stage model described in Chapter 13. Other features of the rate-based model are that the exiting liquid and vapor from a stage can be at different temperatures since separate balance equations are written for each phase. Each phase on a stage can have a different externally transferred heat duty. The exiting phases in general are not at equilibrium the liquid may be subcooled and the vapor may be superheated. In a rate-based model the phase interface must be defined. The variables defining the interface include the liquid and vapor compositions and the temperature at the interface, and the molar flux across the interface. 

The theoretically simplest approach is to assume that no external boundary layer exists, thus obtaining the highest average values for the external transfer coefficients. Experience proves this assumption to hold for many important practical applications (D8, H8, HI3, W3, and others), where the Reynolds number and viscosity ratio Hcl ld are high. Boussinesq (BIO) was the first to... 

In that case, M- 0 since AT,->0 and Colburn s equation (M6, Eq. 11), derived for piston flow (apparent external transfer coefficient), reduces to... 

E21.3 The hydrogenation of a diol is performed in a slurry bed reactor by adding 0.500 g of catalyst powder into reactor and the initial concentration of the diol is 2.5mol/cm. The reaction is first order with respect to both H2 and diol H2 is bubbled through distributor at 1 atm and 35°C. The concentration of H2 in equilibrium conditions is 0.01 mol/cm and the constant specific reaction rate is 4.8 x 10 (cm /(cm x s)). The flow rate of catalyst is 0.1 kg/m, the particle diameter is 0.01 cm, and its density is equal to 1.5 g/cm. Calculate the overall reaction rate. The pore diffusion can be neglected Verify if the mass transfer in the pores and the external transfer can be negligible (Adapted from Fogler, 2000). 

Figure 16.29 (Continued) (b) The Perseus TGA-DSC-FTIR system with a vertical arrangement of the FTIR and thermal analysis system, with no external transfer line. (Courtesy of NETZSCH Instruments, Inc., Burlington, MA, www.netzsch-hermal-analysis.com.)...

The mass spectrum of evolved gases (up to MWs of 1024 Da) can be obtained to provide identification of the structure with no condensation during transfer between the thermal analyzer and the mass spectrometer. (Courtesy of Setaram Instmmentation, SA, Caluire, France, www. setaram.com.) (b) A different commercial thermogravimetry (TG)-GC-MS system, showing the Netzsch TG 209 on the right, connected to a GC-MS via an external transfer line. (Courtesy of NETZSCH Instruments, Inc., Burlington, MA, www.netzsch-thermal-analysis.com.)... 

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