component A through b, which is a measure of its diffusive mobility. Molar flux relative to stationary coordinate na is equal to dc N=(NA +NB -D Ab Di (6.2) Where C is total concentration of components a and B and nb is the molar flux of b relative to stationar coordinate. The first term of the right hand side of 1411 Eq (9.2)is the flux due to bulk flow, and the second term is due to the diffusion. For dilute solution of A NA≈JA (6.3)
component A through B, which is a measure of its diffusive mobility. Molar flux relative to stationary coordinate NA is equal to ( ) Z A A B A B A A D dC N N D C C N = + − (6.2) Where C is total concentration of components A and B and NB is the molar flux of B relative to stationary coordinate. The first term of the right hand side of Eq.(9.2) is the flux due to bulk flow, and the second term is due to the diffusion. For dilute solution of A, A A N J (6.3)
Diffusivity: The kinetic theory of ds 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,(or see 戚以政“bo647) D°,: 1.173×101(2MB)3T64) 1.1rr0.6 bA When the solvent is water. and the solute is small molecular substance, Do2 is about 0.52.0X10-5cm2/s Kelland(1974) recommends the use of the o pation developed by othmer and Thakar(1953)
Diffusivity: 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, ( or see 戚以政 ‘book 6-47) ( ) 1.1 0.6 1 6 0.5 1.173 10 b A B A B V M T D = − ξ (6.4) When the solvent is water, and the solute is small molecular substance , DO2 is about 0.5～2.0×10-5cm2/s. Skelland(1974) recommends the use of the correlation developed by Othmer and Thakar(1953)
112×10 13 AB 1.1r0.6 (6.5) bA 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: Dar diffusivity of A in B, in a very dilute solution, m?/s MB-molecular weight of component B, kg/kmol T-temperature K u=solution viscosity, kg/m s VbA - Solute molecular volume at normal boiling point, m3/kmol: 0.0256m/kmol for oxygen [See Perry and Chil
1.1 0.6 13 1.112 10 bA AB V D = − (6.5) 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: DAB =diffusivity of A in B, in a very dilute solution, m2 /s MB=molecular weight of component B, kg/kmol T=temperature, K μ=solution viscosity, kg/m s VbA=solute molecular volume at normal boiling point, m3 /kmol:0.0256m3 /kmol for oxygen [See Perry and Chil-
ton(p. 3-233, 1973 )for extensive table -association factor for the solvent, 2.26 for water. 1.9 for methanol,1.5 for ethanol, 1.0 for unassociated solvents Such as benzene and ethyl ether Example 6.1 Estimate the diffusivity for oxygen in water at 25C. Compare the predictions from the Wilke-Chang and Othmer- Thakar correlations with the experimental value of 2.5*10-9 m2/s(Perry and Chilton, p. 3-225, 1973) Convert the experimental value to that corresponding to a temperature of40℃ Solution Oxygen is designated as component A, and water
ton (p.3-233,1973)for extensive table] ξ=association factor for the solvent: 2.26 for water, 1.9 for methanol, 1.5 for ethanol, 1.0 for unassociated solvents, such as benzene and ethyl ether Example 6.1 Estimate the diffusivity for oxygen in water at 25℃.Compare the predictions from the Wilke-Chang and Othmer-Thakar correlations with the experimental value of 2.5*10-9 m2 /s (Perry and Chilton, p. 3-225,1973). Convert the experimental value to that corresponding to a temperature of 40℃. Solution: Oxygen is designated as component A, and water
component B The molecular volume of oxygen Vba is 0.0256 m3/kmol. The association factor for water 5 is 2.26 The viseosity of water at 25C is 8.904*10-kg/ms(CSC Handbook of chemistry and Physics, p. F-38, 1983).In Eq(64) AB 1173×101226(8)N5298=2.25×103m2/s 8.904×10-4(0.0256 0.6 In Eq (6.5) 1.112×0-13 AB =2.27×10-m?2/s 8904×10+)2(0256)06
component B. The molecular volume of oxygen VbA is 0.0256 m3 /kmol. The association factor for water ξis 2.26. The viscosity of water at 25℃ is 8.904*10-4kg/ms (CSC Handbook of chemistry and Physics,p. F-38, 1983). In Eq.(6.4) ( ) ( ) D m s A B 2.25 10 / 8.904 10 0.0256 1.173 10 2.26 18 298 9 2 4 0.6 1 6 0.5 − − − = = In Eq.(6.5) ( ) ( ) D m s A B 2.27 10 / 8.904 10 0.0256 1.112 10 9 2 4 1.1 0.6 1 3 − − − = =