Multicomponent gas diffusion in nonuniform tubes

Abstract

In many technical processes gas multicomponent diffusion takes place in confinements that are rarely uniform in direction of their long axis (e.g., catalysts pores). Here we show that in conical tubes multicomponent diffusion is hindered. This effect increases with ratio of inlet to outlet cone radius Λ, indifferent of the orientation of the tube. Based on the Maxwell-Stefan equations we developed a predictive analytical solution for ideal multicomponent diffusion in slightly tapered ducts. (1962) were reproduced. Comparison of model and experiment shows that the solution presented here provides a reliable quantitative prediction of the temporal change of H 2 , N 2 , and CO 2 -concentration for both tube geometries, uniform and slightly conical. In the demonstrated case (Λ = 3.16) mass diffusion is 68 % delayed. Thus, for gaseous diffusion in "real", typically tapered pores the transport limitation is more serious than considered so far. In Two Bulb Diffusion Experiments on a uniform tube the results of Duncan and Toor

Applicability of the linearized theory of the Maxwell–Stefan equations

“…Afterwards, the molar fraction decreased again to the initial condition (which was also the equilibrium state). Recently, Veltzke et al 23 conducted the experiment with a conical tube and made similar observations. Apart from providing experimental data for uniform and tapered tubes, Veltzke et al 23 also developed an analytical model whose basic form they attributed to Duncan and Toor.…”

“…Recently, Veltzke et al 23 conducted the experiment with a conical tube and made similar observations. Apart from providing experimental data for uniform and tapered tubes, Veltzke et al 23 also developed an analytical model whose basic form they attributed to Duncan and Toor. 4 The model predicts the evolution of the molar fractions in the bulbs and is based on the linearized theory, using the equilibrium conditions as reference state.…”

“…For the considered case the bulb volumes are much larger than the tube volumes, implying a timescale separation and allowing for a quasi-stationary treatment of the connecting tube. 23 Using the definition of the fluxes (13), the stationary part of (23) can be written as…”

“…For a conical tube the concentration can be computed as shown in Ref. 23. Expressing the cross sectional area as…”

“…19 Taylor and Webb 20 and especially Smith and Taylor 21 verified the theory's accuracy by a huge amount of numerical computations. Krishna et al 22 reproduced experimental results from liquid-liquid extraction cells, and Veltzke et al 23 developed a predictive model for the two-bulb diffusion cell. All studies assert the validity of the linearized theory and recommend its use.…”