Diffusing with Stefan and Maxwell

In most chemical engineering problems, diffusion is treated as an add-on to forced advection, and the boundary conditions are the Danckwerts conditions in order to maintain conservation. If we treat problems in which there is no applied advection or chemical reaction for a steady-state situation and with an ideal gas, it is an equi-molar process. Because it is considered the natural movement of molecules moving down a concentration gradient, this requires the Stefan-Maxwell equations. In the standard I-D two-component boundary value problem, analogous to the Dirichlet problem, the solution is direct and is probably the only one there is. In a ternary system, the solution is already not direct and can only be obtained by numerical means, which is not severe. In a quaternary system, it does not appear feasible to obtain a simple procedure like that obtained for the ternary system. A different numerical scheme developed is robust with rapid convergence and works well with an arbitrary number of components, 60 having been used in one problem. As the number of components increases, the solution profiles tend to become linear and the dependence on particular diffusivities is less important. This manifests itself when using diffusivities from a random collection. The problem using a continuous distribution of components is solved, and computationally and theoretically the profiles are probably linear and with a single pairwise diffusion coefficient.