Unidirectional diffusion. ...

Applying the same derivation as for unidirectional diffusion through a stagnant medium, the results turn out to be... 

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. 

For the special case of steady-state unidirectional diffusion of a component through an inert-gas film in an ideal-gas system, the rate of mass transfer is derived as... 

According to this analysis one can see that for gas-absorption problems, which often exhibit unidirectional diffusion, the most appropriate driving-force expression is of the form y — y tyBM,. ud the most appropriate mass-transfer coefficient is therefore kc- This concept is to he found in all the key equations for the design of mass-transfer equipment. 

Derive the partial differential equation for uosieady-slate unidirectional diffusion accompanied by an /Uli-order chemical reaction irate constant k) ... 

Unicracking process, 16 842—843 Unidendate ligands, 7 575, 13 443 Unidirectional diffusion, 1 40-41 Unidirectional fiber composites fabrication of, 26 766—767 Unidirectional lamina... 

C. Robinson. Diffusion and swelling of high polymers. II. The orientation of polymer molecules which accompanies unidirectional diffusion. Trans. Faraday Soc., 42B 12-17, 1946. 

The differential equation for unidirectional diffusion (diffusion by sample edges neglected) may be written as... 

The unidirectional diffusion of solute is a function of cross-sectional area (A) and time along a concentration gradient (dct/dx) ... 

The figure legend reads Model of the unidirectional diffusion of dye between coupled oligodendrocytes and astrocytes, based on differences in connection pore diameter. Like a fish in a fish trap, dye molecules (black circles) can pass from an astrocyte to an oligodendrocyte (A) but not back in the other direction (B). ... 

Tn most applications of zeolites, it is necessary for molecules to be able to diffuse into or out of their fine pore structure, and in many of these applications, particularly catalysis, the counterdiffusion of at least 2 different kinds of molecules occurs. The rates of these diffusion processes can have a profound effect upon the apparent activity and selectivity of zeolitic catalysts (21) and upon such characteristics as dispersion and sharpness of separation in the use of zeolites in separation and purification processes. The state of knowledge of intracrystalline diffusion in zeolites is reviewed by Barrer in a paper for this symposium (4). Little is known about unidirectional diffusion in zeolites of substances of indus-... 

For unidirectional diffusion in the z-direction, Pick s two laws reduce to... 

Equation (15-58) is written for steady-state unidirectional diffusion in a quiescent liquid, assuming that the net transfer of component B is negligible. For transfer of component A across an interface or film between two liquids, it may be rewritten in the form... 

Steady-State Equimolal Counterdiffusion and Unimolal Unidirectional Diffusion... 

Equation (7.1-16) reduces to two special cases of molecalar difiiision which are customarily considered. In equimolal counterdiffusion, component A diffuses through component B, which is diffusing at the same molal rate as A relative to stetionaiy coordinates, but in die opposite direction. This process is often approximated in the distillation of a binary system. In unimolol unidirectional diffusion, only one molecalar species—component A—diffuses through component B, which is motionless relative to stationary coordinates. This type of transfer is approximated frequently in the operations of gas absorption, liquid-liquid extraction, and adsorption. 

Steady-State Unimolal Unidirectional Diffusion in Gases... 

Equation (7.1-21) demonstrates that (he partial-pressure distribution is nonlinear in the case of steady-state unidirectional diffusion. 

For unimola unidirectional diffusion, the liquid-phase analog of Eq. (7,1-22) is... 

In the important case of tmimolal unidirectional diffusion, Eqs. (7.1-25) and (7.1-43) show the following relationship ... 

Approximatj Expressions for NTU in Unimoial Unidirectional Diffusion In many cases the evalueiion of the integrals in Eq. (7.3-30) is facilitated by the use of the arithmetic mean in place of ihe logarithmic mean (1 — yA)LM or (1 — xA)LM. jocaning only a small error.5 Thus, in the case of (NTU)c,... 

The integrals in Eqs. (7.3-30) and (7.3-33)-(7-3-36) are usually evaluated numerically, for example, by graphical integration. Information for (his procedure is obtained from the equilibrium onrve-opetruing line plot on (jrA, yA) coordinates, as sketched in Fig. 7.3-14 for unimotai unidirectional diffusion (liquid extraction). 

In the case of unimolal unidirectional diffusion, the HTU expressions in Eq. (7.3-30) may he reenanged to give... 

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