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Tham khảo tài liệu 'a heat transfer textbook - third edition episode 3 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 614 An introduction to mass transfer 11.4 11.4 Transport properties of mixtures6 Direct measurements of mixture transport properties are not always available for the temperature pressure or composition of interest. Thus we must often rely upon theoretical predictions or experimental correlations for estimating mixture properties. In this section we discuss methods for computing Dim k and p in gas mixtures using equations from kinetic theory particularly the Chapman-Enskog theory 11.2 11.8 11.9 . We also consider some methods for computing D12 in dilute liquid solutions. The diffusion coefficient for binary gas mixtures As a starting point we return to our simple model for the self-diffusion coefficient of a dilute gas eqn. 11.32 . We can approximate the average molecular speed C by Maxwell s equilibrium formula see e.g. 11.9 - 8kBNAT 1 2 I nM J 11.37 where kB R NA is Boltzmann s constant. If we assume the molecules to be rigid and spherical then the mean free path turns out to be n V2N d2 n JBd2p 11.38 where d is the effective molecular diameter. Substituting these values of C and in eqn. 11.32 and applying a kinetic theory calculation that shows 2pa 1 2 we find Daa 2pa Cf kB n 3 2 d2 Nay 2 T3 2 MJ p 11.39 The diffusion coefficient varies as p 1 and T3 2 based on the simple model for self-diffusion. To get a more accurate result we must take account of the fact that molecules are not really hard spheres. We also have to allow for differences in the molecular sizes of different species and for nonuniformities 6This section may be omitted without loss of continuity. The property predictions of this section are used only in Examples 11.11 11.14 and 11.16 and in some of the end-of-chapter problems. 11.4 Transport properties of mixtures 615 Figure 11.6 The Lennard-Jones potential. in the bulk properties of the gas. The Chapman-Enskog kinetic theory takes all these factors into account 11.8 resulting in the following formula for Dab D _ 1.8583 X 10-7 T3 2 I 1 1 AB p DB T
