3.MASS-TRANSFER THEORIES (1)Mass Transfer Coefficient For steady-state mass transfer through a stagnant layer of fluid , mass transfer rate can be predicted by following equations: (1)Equimolal diffusion or

(2)One-component mass transfer (one-way diffusion) More common used type of equations: Analogous to heat transfer, Heat transfer rate=(Heat transfer coefficient)  (Heat transfer driving force) Mass transfer rate=(Mass transfer coefficient)  (Mass transfer driving force)

Definition of mass transfer coefficient: The rate of mass transfer per unit area per unit concentration difference, usually based on equal molal flows. Other forms of mass transfer equations:

Therefore, =mass transfer coefficient based on molal concentration driving force =gas phase mass transfer coefficient based on the partial pressure driving force

=gas phase mass transfer coefficient based on the mole fraction differences =liquid phase mass transfer coefficient based on the mole fraction differences

Relations between mass transfer coefficients: Similarly, in liquid phase,

Here, =density of liquid, kg/m3 =average molecular weight of liquid Significance of kc: from

For steady-state equimolal diffusion in a stagnant film, mass transfer coefficient kc is the molecular diffusivity divided by the thickness of the stagnant layer（BT）. When we are dealing with unsteady-state diffusion or diffusion in flowing streams（对流）, Eq.(17.42) can still be used to give an effective film thickness BT from known values of kc and Dv.对于对流传质，（17.42）式有效, BT为有效膜厚度

(2)Film Theory Analogous to convective heat transfer, Heat transfer rate q:

Illustrational diagram of wetted wall tower BT The basic concept of the film theory is that the resistance to diffusion can be considered equivalent to（相等于） that in a stagnant film of a certain thickness Then, 膜理论基本概念是传质阻力相等于 停滞膜厚度 Illustrational diagram of wetted wall tower BT

The implication is that the coefficient kc varies with the first power of Dv, which is rarely true, but this does not detract from the value of the theory in many applications. The film theory is often used as a basis for complex problems of multi-component diffusion（多组分扩散） or diffusion plus chemical reaction. The value of BT depends on the diffusivity Dv and not just on flow parameters, such as Reynolds number. The concept of an effective film thickness is useful, but values of BT must not be confused with the actual thickness of the laminar layer（层流底层）.

Effect of one-way diffusion When only one component A is diffusing through a stagnant film, the rate of mass transfer for a given concentration difference is greater than if component B is diffusing in the opposite direction. Where, =molal flux of one-way diffusion =molal flux of equimolal diffusion

Some times the mass transfer coefficient for one-way transfer is denoted by kc’ or ky’, then Because the correction is small compared to the uncertainty in the diffusivity and the mass-transfer coefficient.

(3)Boundary Layer Theory When diffusion through a stagnant fluid film , When diffusion takes place in a thin boundary layer near a surface where the fluid is in laminar flow, For boundary layer flows, no matter what the shape of the velocity profile or value of the physical properties, the transfer rate cannot increase with the 1.0 power of the diffusivity, as implied by the film theory.

(4)Penetration Theory（渗透理论） and Surface Renewal Theory表面更新理论 When the boundary layer becomes turbulent or separation occurs, penetration theory and surface renewal theory apply, and

(5) Two-Film Theory Basic viewpoints: 1)On two sides of the interface, there exist two effective films of certain thickness, component A passes through these two film by molecular diffusion. 2)At the interface, the gas is in equilibrium with liquid. 3)The concentration gradients in the two bulk phases equal to zero. （1） 接触的两相流体间存在相界面，界面两侧各有一个很薄的停滞层，组分A以分子扩散方式通过此两膜层。（2） 相界面处，气、液两相达到平衡（界面上不存在阻力）。 （3）两滞流膜外的气液相主体中，流体充分湍动，物质浓度均匀。

[xAi is in equilibrium with yAi]

In the two-film theory, the rate of mass transfer to the interface is set equal to the rate of the transfer from the interface:

Let =overall mass transfer coefficient in gas phase =overall mass transfer driving force

To get Ky in terms of kx and ky,

=overall resistance to mass transfer = resistance to mass transfer in the gas film =resistance to mass transfer in the liquid film

Similarly, let =overall mass transfer coefficient in liquid phase =overall mass transfer driving force Where We can get

=overall resistance to mass transfer = resistance to mass transfer in the liquid film =resistance to mass transfer in the gas film

Gas film “controls” and Liquid film “controls” When When