Molecular diffusion in liquids

Diffusion of solutes in liquids is very important in many industrial processes, especially in such separation operations as liquid-liquid extraction or solvent extraction, gas absorption, and distillation. Diffusion in liquids also occurs in many situations in nature, such as oxygenation of rivers and lakes by the air and diffusion of salts in blood. 

Since the molecules in a liquid are packed together much more closely than in gases, the density and the resistance to diffusion in a liquid are much greater. Also, because of this closer spacing of the molecules, the attractive forces between molecules play an important role in diffusion. Since the kinetic theory of liquids is only partially developed, we write the equations for diffusion in liquids similar to those for gases. 

In diffusion in liquids an important difference from diffusion in gases is that the diffusivities are often quite dependent on the concentration of the diffusing components. 

Equimolar counterdiffusion. Starting with the general equation (6.2-14), we can obtain for equimolal counterdiffusion where = —Ng, an equation similar to Eq. (6.1-11) for gases at steady state. 

Equation (6 3-1) uses the average value of D g, which may vary some with concentration and the average value of c, which also may vary with concentration. Usually, the linear average of c is used as in Eq. (6.3-2). The case of equimolar counterdiffusion in Eq. (6.3-1) occurs only very infrequently in liquids. 

Oiffusivity The kinetic theory of liquids is much less advanced than that of gases. Therefore, the correlation for diffusivities in liquids is not as reliable as that for gases. Among several correlations reported, the Wilke-Chang correlation (Wilke and Chang, 1955) is the most widely used for dilute solutions of nonelectrolytes, 

When the solvent is water, Skelland (1974) recommends the use of the correlation developed by Othmer and Thakar (1953). 

The preceding two correlations are not dimensionally consistent therefore, the equations are for use with the units of each term as SI unit as follows  

VbA solute molecular volume at normal boiling point, m3/kmol 0.0256 m3/kmol for oxygen [See Perry and Chilton (p.3 -233,1973) for extensive table] 

Estimate the diffusivity for oxygen in water at 25°C. Compare the predictions from the Wilke-Chang and Othmer-Thakar correlations with the experimental value of 2.5 x 10 9 m2/s (Perry and Chilton, p. 3 - 225,1973). Convert the experimental value to that corresponding to a temperature of 40°C. 

Equation (24-70) is used to calculate three gas-phase mole fractions (j = benzene, chlorobenzene, and HCl). The fourth mole fraction (i.e., chlorine) is obtained from the condition that 

7 Summary of Equations That Describe the Two-Phase CSTR Performance 

The two-phase CSTR problem has been reduced to the solution of the following nine nonlinear algebraic equations for S, xj, and yj, where j = B,C1,M,H, 

Gas-phase mass balances j = B,M,H Gas-phase mole fraction of chlorine  

The final task is to identify and calculate some important parameters that are needed to evaluate the time constant ratios X/ j and the interfacial equilibrium 

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Flayduk, W. and Minhas, B.S. (1982) Correlations for prediction of molecular diffusivities in liquids. Can.]. Chem. 

Equations describing molecular diffusion in liquids are similar to those applied to gases. The rate of diffusion of material A in a liquid is given by Eq. (40). 

Hayduk, W., Correlations for Molecular Diffusivities in Liquids, Encyclopedia of Fluid Mechanics, Cheremisinoff, N. P. (Ed.), Gulf Publishing Corp., Houston, TX, Vol. I, pp. 48-72, 1986. 

Wong, C. F. and Hayduk, W., Correlations for Prediction of Molecular Diffusivities in Liquids at... 

For R —> 0 ( point particles), theories of particle and molecular diffusion are equivalent. Schmidt numbers for particle diffusion are much larger than unity, often of the same order of magnitude as for molecular diffusion in liquids. The principle of dimensional similitude tells us that the results of diflusion experiments with liquids can be used to predict rates of diffusion of point particles in gases, at the same Reynolds number. 

The integration of equation (1-70) to put it in the form of equation (1-77) requires the assumption that DAB and c are constant. This is satisfactory for gas mixtures but not in the case of liquids, where both may vary considerably with concentration. Nevertheless, it is customary to use equation (1-77) to predict molecular diffusion in liquids with an average c, and the best average value of DAB available. Equation (1-77) is conveniently written for dilute solutions as... 

Example 1.19 Steady-State Molecular Diffusion in Liquids... 

Molecular diffusion in liquid phases, such as aqueous phase, is rather complicated because of possible dissociation of diffusing molecules or interaction between diffusing molecules and surrounding molecules, e.g. hydration. 

In many cases of liquid phase adsorption by adsorbents of small particle size in a vessel, fluid-to>particle mass transfer becomes an important rate controlling step. This is mainly because molecular diffusivities in liquid phase are small and the relative importance of fluid-to-particle contact efficiency may be more pronounced. 

This equation was derived by comparison of the elution curve approximated by the normal distribution and the equation derived from the plate theory The similarity of Eqs (10-11) and (10-12) is not surprising Eq (10-11) can be considered to be a more generalized form Eq (10-11) is further simplified in the cases of liquid phase chromatography since the contribution of the first term of R H S becomes negligible since molecular diffusion in liquid phase is small... 

So far, the exposition has focused on molecular diffusion in a gaseous mixture of species A and B. Almost identical results may also be used for molecular diffusion in liquids. In gaseous systems, AP = 0 implied that Qg was constant along the diffusion path. In a liquid mixture of solute i in solvent s, AP may be zero, but the molar solution density Cti generally varies substantially along the diffusion path. Further, the diffusion coefficient also varies with the solute concentration. The governing diffusion equation for species i in an i-s system is obtained from equations (3.1.87) and (3.1.89) for diffusion in the z-direction and Uiz = 0 as... 

An ideal gas has by definition no intermolecular structure. Also, real gases at ordinary pressure conditions have little to do with intermolecular interactions. In the gaseous state, molecules are to a good approximation isolated entities traveling in space at high speed with sparse and near elastic collisions. At the other extreme, a perfect crystal has a periodic and symmetric intermolecular structure, as shown in Section 5.1. The structure is dictated by intermolecular forces, and molecules can only perform small oscillations around their equilibrium positions. As discussed in Chapter 13, in between these two extremes matter has many more ways of aggregation the present chapter deals with proper liquids, defined here as bodies whose molecules are in permanent but dynamic contact, with extensive freedom of conformational rearrangement and of rotational and translational diffusion. This relatively unrestricted molecular motion has a macroscopic counterpart in viscous flow, a typical property of liquids. Molecular diffusion in liquids occurs approximately on the timescale of nanoseconds (10 to 10 s), to be compared with the timescale of molecular or lattice vibrations, to 10 s. 

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