Mass Transfer and Diffusion - Wiley

1 Chapter3 mass Transfer and Diffusionbarriers, such as membranes, differing species mass -transferrates through the membrane govern equipment a binary mixture, molecular Diffusion of componentAwith respect to B occurs because of different potentialsor driving forces, which include differences (gradients)of concentration (ordinary Diffusion ), pressure (pressurediffusion), temperature (thermal Diffusion ), and external forcefields (forced Diffusion ) that act unequally on the differentchemical species present. Pressure Diffusion requires a largepressure gradient, which is achieved for gas mixtures with acentrifuge.

2 Thermal Diffusion columns or cascades can beemployed to separate liquid and gas mixtures by establishingatemperature gradient. More widely applied is forceddiffusion in an electrical field, to cause ions of differentcharges to move in different directions at different this chapter, only molecular Diffusion caused byconcentration gradients is considered, because this is themost common type of molecular Diffusion in separationprocesses. Furthermore, emphasis is on binary systems, forwhich molecular- Diffusion theory is relatively simple andapplications are relatively straightforward.

3 Multicomponentmolecular Diffusion , which is important in many applica-tions, is considered briefly in Chapter 12. Diffusion in multi-component systems is much more complex than Diffusion inbinary systems, and is a more appropriate topic for advancedstudy using a text such as Taylor and Krishna [1].Molecular Diffusion occurs in solids and in fluids that arestagnant or in laminar or turbulent motion. Eddy diffusionoccurs in fluids in turbulent motion. When both moleculardiffusion and eddy Diffusion occur, they take place inparallel and are additive. Furthermore, they take placebecause of the same concentration difference (gradient).

4 When mass Transfer occurs under turbulent-flow conditions,but across an interface or to a solid surface, conditions maybe laminar or nearly stagnant near the interface or solidsurface. Thus, even though eddy Diffusion may be thedominant mechanism in the bulk of the fluid, the overall rateof mass Transfer may be controlled by molecular diffusionbecause the eddy- Diffusion mechanism is damped or eveneliminated as the interface or solid surface is Transfer of one or more species results in a total netrate of bulk flow or flux in one direction relative to a fixed66 mass transferis the net movement of a component in amixture from one location to another where the componentexists at a different concentration.

5 In many separationoperations, the Transfer takes place between two phasesacross an interface. Thus, the absorption by a solvent liquidof a solute from a carrier gas involves mass Transfer of thesolute through the gas to the gas liquid interface, across theinterface, and into the liquid. mass - Transfer models describethis and other processes such as passage of a species througha gas to the outer surface of a porous, adsorbent particle andinto the adsorbent pores, where the species is adsorbed onthe porous surface. mass Transfer also governs selectivepermeation through a nonporous, polymeric material of acomponent of a gas mixture.

6 mass Transfer , as used here,does not refer to the flow of a fluid through a pipe. However, mass Transfer might be superimposed on that flow. Masstransfer is not the flow of solids on a conveyor Transfer occurs by two basic mechanisms:(1)molecular diffusionby random and spontaneous micro-scopic movement of individual molecules in a gas, liquid, orsolid as a result of thermal motion; and (2) eddy(turbulent)diffusionby random, macroscopic fluid motion. Bothmolecular and/or eddy Diffusion frequently involve themovement of different species in opposing directions.

7 Whena net flow occurs in one of these directions, the total rate ofmass Transfer of individual species is increased or decreasedby this bulk flow or convection effect,which may beconsidered a third mechanism of mass Transfer . Moleculardiffusion is extremely slow, whereas eddy Diffusion is ordersof magnitude more rapid. Therefore, if industrial separationprocesses are to be conducted in equipment of reasonablesize, fluids must be agitated and interfacial areas mass Transfer in solids is involved, using small particles todecrease the distance in the direction of Diffusion willincrease the separations involve two or more phases, the extentof the separation is limited by phase equilibrium, because,with time, the phases in contact tend to equilibrate by masstransfer between phases.

8 When mass Transfer is rapid,equilibration is approached in seconds or minutes, anddesign of separation equipment may be based on phaseequilibrium, not mass Transfer . For separations , Ordinary Molecular Diffusion67plane or stationary coordinate system. When a net fluxoccurs, it carries all species present. Thus, the molar flux ofan individual species is the sum of all three mechanisms. IfNiis the molar flux of species iwith mole fraction xi, and Nis the total molar flux, with both fluxes in moles per unit timeper unit area in a direction perpendicular to a stationaryplane across which mass Transfer occurs, thenNi=xiN+molecular Diffusion flux ofi+eddy Diffusion flux ofi(3-1)where xiNis the bulk-flow flux.

9 Each term in (3-1) is positiveor negative depending on the direction of the flux relative tothe direction selected as positive. When the molecular andeddy- Diffusion fluxes are in one direction and Nis in theopposite direction, even though a concentration differenceor gradient of iexists, the net mass - Transfer flux, Ni, of icanbe this chapter, the subject of mass Transfer and diffusionis divided into seven areas: (1) steady-state Diffusion instagnant media, (2) estimation of Diffusion coefficients,(3) unsteady-state Diffusion in stagnant media, (4) masstransfer in laminar flow, (5) mass Transfer in turbulent flow,(6) mass Transfer at fluid fluid interfaces, and (7) masstransfer across fluid fluid INSTRUCTIONAL OBJECTIVESA fter completing this chapter, you should be able to: Explain the relationship between mass Transfer and phase equilibrium.

10 Explain why separation models for mass Transfer and phase equilibrium are useful. Discuss mechanisms of mass Transfer , including the effect of bulk flow. State, in detail, Fick s law of Diffusion for a binary mixture and discuss its analogy to Fourier s law of heatconduction in one dimension. Modify Fick s law of Diffusion to include the bulk flow effect. Calculate mass - Transfer rates and composition gradients under conditions of equimolar, countercurrent diffusionand unimolecular Diffusion . Estimate, in the absence of data, diffusivities ( Diffusion coefficients) in gas and liquid mixtures, and know of somesources of data for Diffusion in solids.