Inner mass transfer

Let us now study the inner mass transfer problems involving a volume chemical reaction. We assume that the diffusion process is quasi-stationary and takes place inside a solid spherical inclusion or a drop of radius a filled with a stagnant or moving medium. 

In general, the intrinsic kinetic parameters of a catalytic reaction under study are unknown. Therefore, the relationships based on the Thiele modulus cannot be used to estimate the influence of inner mass transfer on the measured overall reaction rate. Observed is the experimentally accessible efficient reaction rate, In... 

Dashed Lines Calculations without mass transfer limitations Solid lines Calculations with inner mass transfer limitations... 

Yagi and Wakao (1959) used mass transfer measurement results to estimate the heat transfer coefficient at the tube wall. Material was coated on the inner surface of the packed tubes and the dissolution rate was measured. 

The basic differential equation for mass transfer accompanied by an nth order chemical reaction in a spherical particle is obtained by taking a material balance over a spherical shell of inner radius r and outer radius r + Sr, as shown in Figure 10.12. 

This is the first reactor reported where the aim was to form micro-channel-like conduits not by employing microfabrication, but rather using the void space of structured packing from smart, precise-sized conventional materials such as filaments (Figure 3.25). In this way, a structured catalytic packing was made from filaments of 3-10 pm size [8]. The inner diameter of the void space between such filaments lies in the range of typical micro channels, so ensuring laminar flow, a narrow residence time distribution and efficient mass transfer. 

Equation (5b), in Table VII, established by Lin et al. (L9) for coaxial flow in annuli with k = 0.5, was originally taken by them to be a striking confirmation of the theoretically derived correlation, Eq. (27), with 0=1. The latter condition, however, corresponds only to the limiting case of Eq. (27), at /c->0, that is, mass transfer to the wall of an outer cylinder, without an inner cylinder present. On these grounds, and because of other experimental conditions, the correlation of Lin et al. (L9) was criticized by Friend and Metzner (F9), who calculated that the constant in Eq. (5b) of... 

The model is most vulnerable in the way it accounts for the number of particles that collide with the electrode [50, 115], In the model, the mass transfer of particles to the cathode is considered to be proportional to the mass transfer of ions. This greatly oversimplifies the behavior of particles in the vicinity of an interface. Another difficulty with the model stems from the reduction of the surface-bound ions. Since charge transfer cannot take place across the non-conducting particle-electrolyte interface, reduction is only possible if the ion resides in the inner Helmholtz layer [116]. Therefore, the assumption that a certain fraction of the adsorbed ions has to be reduced, implies that metal has grown around the particle to cover an identical fraction of the surface. Especially for large particles, it is difficult to see how such a particle, embedded over a substantial fraction of its diameter, could return to the plating bath. Moreover, the parameter itr, that determines the position of the codeposition maximum, is an artificial concept. This does not imply that the bend in the polarisation curve that marks the position of itr is illusionary. As will be seen later on, in the case of copper, the bend coincides with the point of zero-charge of the electrode. 

Finally, it must be noted that tensides that are adsorbed at the interface cause a stiffening of the interface. They hinder or even stop the inner circulation and oscillation of drops, and reduce the mass transfer intensity. Moreover, they form a barrier against the mass transfer, so that a further resistance term should be considered in the overall mass transfer process [28] in Eq. (9.33). Since the nature and concentration of tensides in industrial processes cannot be predicted, such phenomena cannot be taken into consideration during equipment calculations. 

We first give a rather general mass-transfer model, which is useful for most processes of porous-solid extraction with dense gases. Two cases are possible [43] for a single particle loaded with solute. In (a), the solute is adsorbed over the internal surface of the particle, and is desorbed from the sites and diffuses out to the external surface, (b) The solute fills in the pore-cavities completely, and is dissolved from an inner core that moves progressively to the centre of the particle. 

These thin-film evaporators are equipped with rotating elements that create a thin, liquid film of high turbulence along the inner surface of the heated tube (see Figure 1). Consequently, favorable heat and mass-transfer conditions (I), (2) and short residence times result owing to the small holdup (3,4). 

Although new types of columns will undoubtedly continue to be introduced, at present much research is being performed for the purpose of improving the existing ones. For packed columns the primary goal is the reduction in the number of active sites, while for capillaries it is the reproducible and uniform coating of capillaries with inner diameters closer to the theoretical optimum for mass transfer, the latter will unfortunately require further improvements in sample introduction and detection before the predicted improvements in resolution can be fully realized. 

The membrane system considered here is composed of two aqueous solutions wd and w2, separated by a liquid membrane M, and it involves two aqueous solution/ membrane interfaces WifM (outer interface) and M/w2 (inner interface). If the different ohmic drops (and the potentials caused by mass transfers within w1 M, and w2) can be neglected, the membrane potential, EM, defined as the potential difference between wd and w2, is caused by ion transfers taking place at both L/L interfaces. The current associated with the ion transfer across the L/L interfaces is governed by the same mass transport limitations as redox processes on a metal electrode/solution interface. Provided that the ion transport is fast, it can be considered that it is governed by the same diffusion equations, and the electrochemical methodology can be transposed en bloc [18, 24]. With respect to the experimental cell used for electrochemical studies with these systems, it is necessary to consider three sources of resistance, i.e., both the two aqueous and the nonaqueous solutions, with both ITIES sandwiched between them. Therefore, a potentiostat with two reference electrodes is usually used. 

Guo F, Zhao Y, Cui J, Guo K, Chen J, Zheng C. Effect of inner packing support on liquid controlled mass transfer process in rotating packed beds. In Gough M, ed. 4th International Conference on Process Intensification in Practice. London BHR Group, 2001 107-113. 

The effectiveness of the gas-solid mass transfer in a circulating fluidized bed (see Chapter 10) can be reflected by the contact efficiency, which is a measure of the extent to which the particles are exposed to the gas stream. As noted in Chapter 10, fine particles tend to form clusters, which yield contact resistance of the main gas stream with inner particles in the cluster. The contact efficiency was evaluated by using hot gas as a tracer [Dry et al., 1987] and using the ozone decomposition reaction with iron oxide catalyst as particles [Jiang etal., 1991], It was found that the contact efficiency decreases as the particle concentration in the bed increases. At lower gas velocities, the contact efficiency is lower as a result of lower turbulence levels, allowing a greater extent of aggregate formation. The contact efficiency increases with the gas velocity, but the rate of increase falls with the gas velocity. 

Using coal-based sorbents, Sivasamy et al. [62] evaluated their ability to remove fluoride from water. On equilibrium basis, Langmuir and Freundlich models were used to describe the data points, while the kinetic data points were interpreted in terms of reaction and mass transfer processes. Kaolinite, adioctahedral two-layered (silica and alumina) silicate (1 2 type), has also been tested in drinking water defluoridation. Recently, Sugita etal. [58] and earlier Kau etal. [63] and Weerasooriya et al. [10] presented fluoride adsorption results of kaolinite. The fluoride-binding sites in kaolinite consist of aluminol and silinol sites. The authors explained that the fluoride-kaolinite interaction led to the formations of both the inner- and outer-sphere complexes. 

The picture is completely different when the reaction is very fast. Now the mass transfer cannot cope with the rate of reacting molecules. Mass transfer cannot supply the new molecules to the inner part of the catalytic particle as fast, with the result that the concentration in the particle is much lower than in the bulk fluid phase. If, from the mass transfer phenomena, pore diffusion is the slowest step, additionally a falling concentration profile is formed in the particle. In both cases, the reaction occurs with a concentration much lower than the one we believe occurs, namely the one in the bulk fluid phase. 

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