The theory considers that the resistance to mass transfer in a given turbulent fluid phase is present in a thin layer adjacent to the interface that is called a film ( Seader et al., 2011 ). Transfer of mass to the bulk flow of the second phase The theory has 2 main principles of assumptions: Rate of mass transfer between the two phases is controlled by the rate of diffusion through the phases on each side of the interface.

x-direction.

Penetration theory was first proposed by R. Higbie in 1935 and the theory is called Higbie’s penetration theory.

Equation (9.1. Instead, we will use a simplified TWO-FILM THEORY as a basis for analysis as well as development of various correlations of mass transfer phenomena. A theory of the transfer of material or heat across a phase boundary, where one or both of the phases are flowing fluids, the main controlling factor being resistance to heat conduction or mass diffusion through a relatively stagnant film of the fluid next to the surface. The common denominator in mass transfer processes is that species fluxes occur within a phase when there are compositionvariations within that phase.

A. Two-Resistance Theory Interphase mass transfer involves three transfer steps. The transfer of oxygen across the interface.

The analysis is the same as before leading to 2 1 2 1 z 1 z z dz d c 0 A j j ' D but the boundary conditions differ: " 1 1" 1 10 z , c Hc z 0, c Hc 9-10.

Two-Film Theory of Mass Transfer. Other mass transfer operations include distillation, humidification, liquid-liquid extraction, adsorption and ion exchange, and so on.

Binary Mass Transfer in Stagnant Systems and in Laminar Flow 5.1 Equimolar Counterdiffusion 5.2 Diffusion Through Stagnant Gas Film 5.3 Gas Absorption into a Falling Liquid Film 5.4 Mass Transfer and Chemical Reaction inside a Porous Catalyst Pellet 6.

Assumptions: • Same as in “Film-theory” but the film is VERY thick • Diffusion is important in . 9.Concept of Mass Transfer Coefficient; 10.Dimensionless Groups and Co-relations for Convective; 11.Mass Transfer co-efficient in Laminar Flow Condition; 12.Boundary Layer Theory and Film Theory in Mass Transfer; 13.Mass Transfer Coefficients in Terbulant Flow I; 14.Interphase Mass Transfer and Mass Transfer Theories


Transfer of mass across interface into the second phase 3.

The film theory has been extensively applied to describe the mass transfer in systems in which fluid phases are present. The transfer of oxygen from the bulk air to the surface of the water.

Film Concept in Mass Transfer As previously noted, gas absorption operation involves mass transfer from the gas phase to the liquid phase.

5.
z-direction • Convection is important in . 2. Penetration theory is one of the mass transfer theories among Film Theory, Surface Renewal Theory, and Boundary Layer Theory. Once again consider the interface between the gas phase and the liquid phase, now simplified as shown in the figure below.

2. Mass transfer may take place in a single phase or over phase boundaries in multiphase systems.

For the specific example of oxygen transporting from air to water, these three steps are: 1. Such phenomena are difficult to analyze. •Mass transfer theory of crystal growth based on equilibrium at the crystal solution interface [Noyes and Whitney, 1897] dmdt kAc c= -c s( ) dm/dt: rate of mass deposited on the crystal surface kc: mass-transfer coefficient A: surface area of the crystal c: mass … Mass Transfer –Diffusion in Dilute Solutions_ Fick‘sLaws 2-8 Example 2.1.2: Membrane diffusion Derive the concentration profile and the flux for a single solute diffusing across a thin membrane. Mass Transfer – Basic Theories for Mass Transfer Coefficients. 3. kG = gas film mass transfer coefficient = DO 2 G ... 4.3 Penetration Theory We assume a non-steady-state film, which at the moment of film formation, curtains the bulk concentrations in both the gas and liquid phases.

N k(c c ) 1 1i 1 = −-1): The solution to … Multicomponent Diffusion 6.1 The Generalized Fick’s Law 6.2 The Maxwell – Stefan Relations That means the gas molecules must diffuse from the main body of the gas phase to the gas-liquid interface , then cross this interface into the liquid side, and finally diffuses from the interface into the main body of the liquid. Mass transfer describes the transport of mass from one point to another and is one of the main pillars in the subject of Transport Phenomena.


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