Mass diffusivities radial, defined

The conventional two-dimensional pseudo-homogeneous reactor model consists of the continuity equation (11.1) and the simplified momentum equation (11.3) defined in connection with the pseudo-homogeneous dispersion model. The species mass and temperature equations are extended to 2D by adding postulated diffusion terms in the radial space dimension [3]. 

The following assumptions were made in formulating this model 1) there is no solute adsorption to the stationary phase, 2) the porous particles which form the stationary phase are of uniform size and contain pores of identical size, 3) there are no interactions between solute molecules, 4) the mobile phase is treated as a continuous phase, 5) the intrapore diffusivity, the dispersion coefficient and the equilibrium partition coefficient are independent of concentration. The mobile phase concentration. Cm, is defined as the mass (or moles) per interstitial volume and is a function of the axial coordinate z and the angular coordinate 0. The stationary phase concentration, Cs, is defined as the mass per pore volume and depends on z, 6 and the radial coordinate, r, of a spherical coordinate system whose origin is at the center of one of the particles. 

Often the global reaction rate of heterogeneous catalytic reactions is affected by the diffusion in the pore and the external mass-transfer rate of the reactants and the products. When the diffusion in the pores is not fast, a reactant concentration profile develops in the interior of the particle, resulting in a different reaction rate at different radial locations inside the catalytic pelet. To relate the global reaction rate to various concentration profiles that may develop, a kinetic effectiveness factor is defined [1, 3,4,7, 8] by... 

The radial variable r is dimensionalized to isolate the Damkohler number in the mass balance. It is important to emphasize that dimensional analysis on the radial coordinate must be performed after implementing the canonical transformation from Ca to iJia- If the surface area factors of and 1/r are written in terms of as defined by equation (13-9), prior to introducing the canonical transformation given by equation (13-4), then the mass transfer problem external to the spherical interface retains variable coefficients. If diffusion and chemical reaction are considered inside the gas bubble, then the order in which the canonical transformation and dimensional analysis are performed is unimportant. Hence,... 

The model discussed here uses the effective transport concept, this time to formulate the fiux of heat or mass in the radial direction. This flux is superposed on the transport by overall convection, which is of the plug flow type. Since the effective diffusivity is mainly determined by the flow characteristics, packed beds are not isotropic for effective diffusion, so that the radial component is different from the axial mentioned in Sec. 11.6.b. Experimental results concerning D are shown in Fig. 11.7.a-l [61, 62,63]. For practical purposes Pe may be considered to lie between 8 and 10. When the effective conductivity, X , is determined from heat transfer experiments in packed beds, it is observed that X decreases strongly in the vicinity of the wall. It is as if a supplementary resistance is experienced near the wall, which is probably due to variations in the packing density and flow velocity. Two alternatives are possible either use a mean X or consider X to be constant in the central core and introduce a new coefficient accounting for the heat transfer near the wall, a , defined by ... 

The lower limit for is determined practically by radial losses of ions to the walls of the drift tube the upper limit is defined by electrical breakdown of gases in the supporting atmosph e inside the drift tube. An important property of an ion mobility spectrometer operating in the low-field region is that ion losses to the walls by radial diffusion do not introduce mass discrimination in the collected ion signal because the ratio of the radial spreading distance to the drift distance is indep doit of ion mass [24]. 

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