Calculating the effective diffusion coefficients in a laminar dissociated multicomponent boundary layer: PMM vol. 33, no. 1, 1969, pp. 180–192

Abstract

We derive expressions for the effective diffusion coefficients D i ( i = 1, …, N) defined in [1,2] in terms of the ratios of the mass diffusion fluxes for an arbitrary N-component mixture in a boundary layer. Sufficient conditions for the identity of theconcentrations, diffusion fluxes, and generalized Schmidt numbers S i = μ/( ϱD i ) across the “frozen” boundary layer are obtained. Using a generalization of the analogy between mass transfer coefficients based on the analytical and numerical solutions of the diffusion equations in the “frozen” boundary layer, we reduce the determination of the coefficients D i for an arbitrary N-component medium at the wall to the solution of algebraic equations with and without blow-in. We solve this system approximately and obtain explicit expressions for D iw for typical mixtures which appear in the boundary layer (at the surface) of thermoplastics based on phenol-formaldehyde resin, which decompose in a dissociated air stream in planetary atmospheres. Using the asymptotic form of solution of the boundary layer equations at the outer edge of the layer, we derive exact analytic formulas for the effective diffusion coefficients D i∞ in an arbitrary N-component system. The behavior of the corresponding generalized Schmidt numbers S i is described qualitatively and their approximate (exact at the boundaries) values across the boundary layer are given. These results simplify appreciably the numercial and analytical solution of the equations for an arbitrary multicomponent dissociated boundary layer at the surface of a heat-insulating coating which disintegrates under the action of heat [3]. This in turn enables us to automatically extend various solutions, in particular the correlation formulas for the heat and mass transfer coefficients obtained in the “binary” boundary layer approximation, to a multicomponent layer. We can accomplish this simply by introducing the appropriate effective diffusion coefficients into these solutions [4]. Diffusion in specific multicomponent mixtures is also dealt with in an approximate manner in [5].