Phase boundary, mass transfer across

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. 

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... 

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. 

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 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... 

Now that we have established the importance of interfacial mass transfer in packed towers, let s talk about modelling mass transfer across a phase boundary. 

Consider, once again, mass transfer across the phase boundary in Figure 7.1. We must have continuity of the fluxes across the interface (Eq. 7.1.1). We may express these fluxes in terms of the driving forces for mass transfer on either side of the interface as... 

In writing down the equations that model the behavior of this nonequilibrium stage, the flow rates of vapor and liquid phases leaving the jth stage are denoted by Vj and Lj, respectively. The mole fractions in these streams are y j and x j. The yT-y are the rates of mass transfer of species i on stage j. The temperature of the vapor and liquid phases are not assumed to be equal and we must allow for heat transfer as well as mass transfer across the interface. The symbol represents the rate of energy transfer across the phase boundary. 

Several models have been proposed to represent the mechanics of mass transfer across the phases. In the two-film theory, the resistance to mass transfer is assumed to take place in a liquid film and a vapor film at the phase boundary interface, as shown schematically in Figure 15.3b. The coordinates X and Y in Figure 15.3a represent the mole fractions of a given component in the liquid and vapor, respectively. For simplicity, component subscripts are dropped and the discussions refer to one... 

All these phenomena are contributions to the surface loss angle in the strain-stress relationship. 3D-rheology deals with a closed system. There is no mass transfer across the limits of this system. In contrast, the so-called surface phase with an adsorption layers can exchange matter with the bulk phase depending on the boundary conditions, such as adsorption after formation of a fresh surface or periodic adsorption and desorption due to periodic changes of the surface area. 

---