Stagnant film, diffusion through

Equimolar Counterdiffusion. Just as unidirectional diffusion through stagnant films represents the situation in an ideally simple gas absorption process, equimolar counterdiffusion prevails as another special case in ideal distillation columns. In this case, the total molar flows and are constant, and the mass balance is given by equation 35. As shown eadier, noj/g factors have to be included in the derivation and the height of the packing is... 

Xm are not. For unimolecular diffusion through stagnant gas = 1), and reduce to T and X and and reduce to and equation 64 then becomes equation 34. For equimolar counterdiffusion = 0, and the variables reduce tojy, x, G, and F, respectively, and equation 64 becomes equation 35. Using the film factor concept and rate equation 28, the tower height may be computed by... 

The two-film theory considering molecular diffusion through stagnant liquid and gas films is the traditional way of understanding mass transfer across the air-water boundary. As briefly described, other theories exist. However, the two-film theory gives an understanding of fundamental phenomena that may lead to simple empirical expressions for use in practice. 

There is diffusion of salt away from both the solid-liquid interface and the vapor-liquid interface, in each case toward the brine. Water moves counterflow to the salt. Heat must transfer from solid to liquid to gas through stagnant films at the solid surface and through the turbulent liquid. An additional resistance to the formation of ice exists at the ice surface, where water molecules must orient themselves and find positions of low energy before being incorporated into the crystal lattice. When inadequate ice surface or foreign particles exist in the freezer, nucleation may control or affect the rate of ice production. 

Using the same data as in Example 10.4-1, calculate the overall mass-transfer coefficient K y, the flux, and the percent resistance in the gas and liquid films. Do this for the case of A diffusing through stagnant B. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

There have been many modifications of this idealized model to account for variables such as the freezing rate and the degree of mix-ingin the liquid phase. For example, Burton et al. [J. Chem. Phy.s., 21, 1987 (1953)] reasoned that the solid rejects solute faster than it can diffuse into the bulk liquid. They proposed that the effect of the freezing rate and stirring could be explained hy the diffusion of solute through a stagnant film next to the solid interface. Their theoiy resulted in an expression for an effective distribution coefficient k f which could be used in Eq. (22-2) instead of k. 

The partial pressures in the rate equations are those in the vicinity of the catalyst surface. In the presence of diffusional resistance, in the steady state the rate of diffusion through the stagnant film equals the rate of chemical reaction. For the reaction A -1- B C -1-. . . , with rate of diffusion of A limited. 

Two-film theory (Lewis and Whitman, 1924) the theory is based on molecular diffusion through two stagnant films, a liquid and a gas film, at the air-water interface. 

External diffusion of products. The last step is the diffusion of product(s) through the stagnant film into the bulk gas under conditions similar to those in step 1. 

Mass transfer is usually limited by diffusion through the stagnant liquid film because of the low liquid diflusivities. 

Dilute A diffuses through a stagnant liquid film onto a plane surface consisting of B, reacts there to produce R which diffuses back into the mainstream. Develop the overall rate expression for the L/S reaction... 

Consider the steady state ideal-gas diffusion of A through a stagnant film of B surrounding a sphere of radius ri (as in the preceding example). The temperature is assumed to vary according to... 

Diffusion through a stagnant film, as in absorption or stripping processes involving the transfer of a single component between liquid and vapor phases. Since there is a concentration gradient... 

Figure 13.44. Factors in Eqs. (13.239) and (13.240) for HTUs of liquid and vapor films and slopes m and m" of the combining Eqs. (13.235) and (13.236) [Bolles and Fair, Inst. Chem. Eng. Symp. Ser. 56(2), 3.3/3.S, (1979)]. (a) Definitions of slopes m and m" in Eqs. (13.235) and (13.236) for combining liquid and gas film HTUs / = 1 for equimolal counter diffusion / = (jtB)mean for diffusion through a stagnant film, (b) Factor (j> of the liquid phase Eq. (13.239). (c) Factor C of the liquid phase, Eq. (13.239). (d) Factor ip of the gas phase, Eq. (13.240), for metal pall rings.

We wish to estimate the time it takes to evaporate a puddle of water. The depth of the puddle is 0.08 inches and covers a surface area of 2 ft2. Both the surr.ounding air (which is stagnant) and the water are at a constant temperature of 77°F. The absolute humidity is 0.001 lb water/lb dry air. Assume the evaporation to occur, through stagnant gas film that is 0.28 inches thick. The gas diffusion coefficient of water vapor at these conditions is 0.259 cm2/sec. 

The diffusion through the stagnant gas film surrounding the particles as well as the diffusion through the pores can play an important role in limiting the overall rate of reaction [1], In the case of heterogeneous reactions, in which a fluid contacts a solid... 

A heterogeneous reaction A -> 2B with nth order kinetics. /rA = k( A (n > 0) takes place on a catalyst surface. The component A with initial concentration CA0 diffusses through a stagnant film on the catalyst surface at isothermal and isobaric conditions. Assume one-dimensional diffusion, and determine the concentration profile of component A within the film of thickness 8 if the k is constant. 

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