Mass transfer across a phase boundary

5 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 

If a gas is involved and the concentrations are expressed in partial pressures, then 

The theoretical treatment which has been developed in Sections 10.2-10.4 relates to mass transfer within a single phase in which no discontinuities exist. In many important applications of mass transfer, however, material is transferred across a phase boundary. Thus, in distillation a vapour and liquid are brought into contact in the fractionating column and the more volatile material is transferred from the liquid to the vapour while the less volatile constituent is transferred in the opposite direction this is an example of equimolecular counterdiffusion. In gas absorption, the soluble gas diffuses to the surface, dissolves in the liquid, and then passes into the bulk of the liquid, and the carrier gas is not transferred. In both of these examples, one phase is a liquid and the other a gas. In liquid -liquid extraction however, a solute is transferred from one liquid solvent to another across a phase boundary, and in the dissolution of a crystal the solute is transferred from a solid to a liquid. 

Each of these processes is characterised by a transference of material across an interface. Because no material accumulates there, the rate of transfer on each side of the interface must be the same, and therefore the concentration gradients automatically adjust themselves so that they are proportional to the resistance to transfer in the particular phase. In addition, if there is no resistance to transfer at the interface, the concentrations on each side will be related to each other by the phase equilibrium relationship. Whilst the existence or otherwise of a resistance to transfer at the phase boundary is the subject of conflicting views 8 , it appears likely that any resistance is not high, except in the case of crystallisation, and in the following discussion equilibrium between the phases will be assumed to exist at the interface. Interfacial resistance may occur, however, if a surfactant is present as it may accumulate at the interface (Section 10.5.5). 

In most irdustrial eqmpment, the flow pattern is so cornfflex that it is not capable of expression in matiiematical terms, and the interfacial area is not known precisely. 

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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... 

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. 

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. 

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