Mass transfer across boundary

Thus the driving force for fuming is approximately equal to that for free evaporation. Using dre experimental data, and the normal expression for mass transfer across a boundary layer, it is concluded that the boundary layer thickness which would account for this rate should be about 2 x 10 cm (Turkdogan et al., 1963). 

MASS TRANSFER ACROSS PHASE BOUNDARIES Agitation and Oxygen Transfer... 

What are the general principles underlying the two-film, penetration and film-penetration theories for mass transfer across a phase boundary Give the basic differential equations which have to be solved for these theories with the appropriate boundary conditions. 

Explain the basis of the penetration theory for mass transfer across a phase boundary. What arc the assumptions in the theory which lead to the result that the mass transfer rate is inversely proportional to the square root of the time for which a surface element has been expressed (Do not present a solution of the differential equal ion.) Obtain the age distribution function for the surface ... 

On the. assumptions involved in the penetration theory of mass transfer across a phase boundary, the concentration Ca of a solute A at a depth v below the interface at a time l after the formation of the interlace is given by ... 

Wbat is the penetration theory for mass transfer across a phase boundary Give deiails of she underlying... 

The mass transfer coefficients, Kg and Ky, are overall coefficients analogous to an overall heat transfer coefficient, but the analogy between heat and mass transfer breaks down for mass transfer across a phase boundary. Temperature has a common measure, so that thermal equilibrium is reached when the two phases have the same temperature. Compositional equilibrium is achieved at different values for the phase compositions. The equilibrium concentrations are related, not by equality, as for temperature, but by proportionality through an equilibrium relationship. This proportionality constant can be the Henry s law constant Kh, but there is no guarantee that Henry s law will apply over the necessary concentration range. More generally, Kyy is a function of composition and temperature that serves as a (local) proportionality constant between the gas- and liquid-phase concentrations. 

The rate of mass transfer across a phase boundary or interface can be expressed by N=K. A (AQm... 

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

A homogeneous open system consists of a single phase and allows mass transfer across its boundaries. The thermodynamic functions depend not only on temperature and pressure but also on the variables necessary to describe the size of the system and its composition. The Gibbs energy of the system is therefore a function of T, p and the number of moles of the chemical components i, tif. 

The two-film theory considering molecular diffusion through stagnant liquid and gas films is the traditional way of understanding mass transfer across the air-water boundary. As briefly described, other theories exist. However, the two-film theory gives an understanding of fundamental phenomena that may lead to simple empirical expressions for use in practice. 

Although mass transfer across the water-air interface is difficult in terms of its application in a sewer system, it is important to understand the concept theoretically. The resistance to the transport of mass is mainly expected to reside in the thin water and gas layers located at the interface, i.e., the two films where the gradients are indicated (Figure 4.3). The resistance to the mass transfer in the interface itself is assumed to be negligible. From a theoretical point of view, equilibrium conditions exist at the interface. Because of this conceptual understanding of the transport across the air-water boundary, the theory for the mass transport is often referred to as the two-film theory (Lewis and Whitman, 1924). 

Equation (4.20) expresses that the total resistance to mass transfer across the air-water boundary is equal to the sum of the resistances across the liquid film and the gas film. The importance of the magnitude of Henry s constant is, in this respect, evident. For high values of HA, e.g., exemplified by 02, the resistance mainly exists in the water film, and turbulence in a sewer will, therefore, enhance the water-air transfer process. The importance of turbulence in the water phase is reduced for odorous components with a relatively low HA value, and turbulence in the air phase will correspondingly increase the release rate (Table 4.1). As seen from Equations (4.20) and (4.21), these facts also depend on the k1A/k2A ratio that varies according to system characteristics. 

The process of mass transfer across a phase boundary is discussed in Volume 1, Chapter 10. A resistance to mass transfer exists within the fluid on each side of the interface, and the overall transfer rate of a component in a mixture depends on the sum of these resistances and the total driving force. 

MASS TRANSFER ACROSS A PHASE BOUNDARY 6.5.1 Introduction... 

There are several theories concerned with mass transfer across a phase boundary. One of the most widely used is Whitman s two-film theory in which the resistance to transfer in each phase is regarded as being located in two thin films, one on each side of the interface. The concentration gradients are assumed to be linear in each of these layers and zero elsewhere while at the interface itself, equilibrium conditions exist (Fig. 5). Other important theories are Higbie s penetration theory and the theory of surface renewal due to Danckwerts. All lead to the conclusion that, in... 

The mechanism of transport of GPG using SLM has been studied at the authors laboratory [56]. GPG could be permeated from alkaUne feed of carbonate buffer into an acidic stripping solution of acetate buffer across the membrane comprising Aliquat-336 in -butyl acetate immobiUzed in a polypropylene (Gelgard 2400) support. The transport mechanism is a case of counter transport exhibiting overall rate dependence on solute diffusion in the membrane phase as well as the mass transfer across the aqueous boundary films. 

The permeability class boundary is based indirectly on the extent of absorption (fraction of dose absorbed, not systemic BA) of a drug substance in humans and directly on measurements of the rate of mass transfer across human intestinal membrane. Alternatively, nonhuman systems capable of predicting the extent of drug absorption in humans can be used (e.g., in vitro epithelial cell culture methods). In the absence of evidence suggesting instability in the gastrointestinal tract, a drug substance is considered to be highly permeable when the extent of absorption in humans is determined to be 90% or more of an administered dose based on a mass balance determination or in comparison to an intravenous reference dose. 

With respect to the physical processes, boundaries can be subdivided into just three classes. The distinction will be made according to the nature of the resistance to mass transfer across the boundary. We must recognize that this transfer is usually mediated by random motions. Thus, the resistance is like the inverse of a generalized diffusivity or transfer velocity, since both these quantities have the function of a conductivity (of mass, heat, momentum, etc.). For simplicity, the following discussion will be focused on the diffusion model (Eq. 18-6), although everything which will be said can also be adapted to the transfer model (Eq. 18-4). 

Mass transfer across the boundary at the surface of the catalyst pellet... 

As is shown in Figure 2, in the two-phase model the fluid bed reactor is assumed to be divided into two phases with mass transfer across the phase boundary. The mass transfer between the two phases and the subsequent reaction in the suspension phase are described in analogy to gas/liquid reactors, i.e. as an absorption of the reactants from the bubble phase with pseudo-homogeneous reaction in the suspension phase. Mass transfer from the bubble surface into the bulk of the suspension phase is described by the film theory with 6 being the thickness of the film. D is the diffusion coefficient of the gas and a denotes the mass transfer coefficient based on unit of transfer area between the two phases. 6 is given by 6 = D/a. 

The inclusion in the model of the mass and energy transport equations introduces the mole fractions and temperature at the interface. It is common in almost all treatments of mass transfer across a phase boundary to assume that the mole fractions in the vapor and liquid phases at the interface are in equilibrium with each other. We may, therefore, use the very famihar equations from phase equilibrium thermodynamics to relate the interface mole fractions... 

A system of fixed mass is called a closed system and a system that involves mass transfer across its boundaries j.s called an open system or control volume. The first law of therrtiody-nnmics or the energy balance for any system undergoing any process can be expressed as... 

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