Theories of Mass Transfer

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Presentation transcript:

Theories of Mass Transfer

Theories of Mass Transfer Film Theory Penetration Theory Boundary-layer Theory Surface-renewal Theories Combination Film–Surface-renewal Theory Two Film Theory (very important)

1. Film Theory (or Film Model)

The Film Theory

The Film Theory

2. Penetration Theory (Higpie,1935) Basic assumptions:

2. Penetration Theory (Higpie,1935) Time of exposure ‘’ is too short and constant for all the eddies; No possibility of formation of concentration gradient; Liquid particle is subjected to unsteady state diffusion; hence,

2. Penetration Theory (Higpie,1935) The conditions are CA = CA0 at t = 0 for all Z; CA = CAi at Z = 0 t  0; CA = CA0 at Z =  for all t Solving the equation kL,av is proportional to (DAB)0.5 for different solutes under the same circumstances. The range of exponents on D varies from 0 to 0.8 or 0.9

Surface Renewal Theory( Danckwerts, 1951) In reality, all eddies are exposed for varying lengths of time. If ‘S’ is the fractional rate of replacement of the elements, then ‘kL is proportional to (DAB)0.5 Combination of Film – Surface renewal Theory (Dobbins, 1956,1964) If ‘Zb’ is of finite length, then the B.C becomes CA = CA0 at Z = Zb for all  Case i) For rapid penetration & rate of surface renewal is small, ‘k’ follows Film Theory Case ii) For slow penetration & rapid surface renewal, k’ follows surface renewal Theory

Slope m Gas film resistance Over all resistance Liquid film resistance

Slope = -kx/ky Slope M Slope m Liquid film resistance Gas film resistance Over all resistance

Slope = -kx/ky Slope M

Slope = -kx/ky Slope M Slope m

Example 1 In the dilute concentration region, equilibrium data for SO2 distributed between Air and water can be approximated by Where the partial pressure of SO2 in the vapor is expressed in atmosphere. For An absorption column operating at 10 atm, the bulk vapor and liquid concentrations at one point in the column are yA1 = 0.01 and xA1 = 0.0 The mass transfer coefficient for this process are: Find the overall mass transfer? And vapor and liquid mole fraction at the interface

m =2.5

Slope = -kx/ky

=0.0067

Example 2 KG= Ky