Stagnant gases, diffusion through

The gas-phase diffusivity of sodium in helium Dvl may then be evaluated from the experimental data by using Equation 15. A value of 1.96 cm.2/sec. was obtained, which compares favorably with 2.11 cm.2/ sec. estimated from an equation given by Hirschfelder, Curtiss, and Bird (8), using Lennard-Jones parameters given by Chapman (5). The close agreement obtained here seems to justify the assumption of a stagnant gas layer through which both sodium and cesium diffuse. 

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... 

General Situation. Both unidirectional diffusion through stagnant media and equimolar diffusion are idealizations that ate usually violated in real processes. In gas absorption, slight solvent evaporation may provide some counterdiffusion, and in distillation counterdiffusion may not be equimolar for a number of reasons. This is especially tme for multicomponent operation. 

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 steady-state transport of A through the stagnant gas film is by molecular diffusion, characterized by the molecular diffusivity DAg. The rate of transport, normalized to refer to unit area of interface, is given by Fick s law, equation 8.5-4, in the integrated form... 

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. 

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. 

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... 

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.

The diffusion coefficient for a gas can be experimentally measured in an Arnold diffusion cell. The device is shown in Figure 3.6 consisting of a narrow tube partially filled with pure liquid A. The system is maintained under constant pressure and gas B flows across the open end of the tube. Component A vaporizes and diffuses into the gas phase, hence the rate of vaporization can be physically measured. Develop a general steady-state expression to describe the diffusion of one gas through a second stagnant gas. Assume that the gas has negligible solubility in liquid A and is also chemically inert in A. 

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... 

Diffusion Through a Stagnant Gas. The diffusion of a solute A through a stagnant gas B often oeeurs in systems in which two phases are present. Evaporation and gas absorption are typical processes in which this type of diffusion ean be foimd. If gas B is stagnant, there is no net flux of B with respect to a fixed coordinate that is,... 

As explained in Section II,A, when a soluble gas is mixed with an insoluble gas, it must diffuse through the latter to reach the interface. It is usual to refer to a gas film resistance. This implies a stagnant film of gas across which the soluble gas is transferred by molecular diffusion from the bulk gas with partial pressure p to the interface where the partial pressure is p,. If the component B has negligible vapor pressure, the reaction will proceed only in the liquid phase. 

Consider multi-component diffusion of gases A and B through stagnant gas C (Gianakopulos, 1972 Cutlip and Shacham, 1999).[23] The governing equations for concentration of A and B are ... 

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