The Number of Solutions of an Equation from Catalysis.
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In the production of chemicals, catalysts are often required to convert gaseous reactants into useful products. Frequently the catalyst is in the form of a porous pellet and the gas must diffuse into the interior of the pellet so that the catalyst there is fully utilized. Depending upon the relative rates of diffusion and reaction, temperature and concentration gradients are set up across the pellet, and their determination is essential for the calculation of the over-all rate of conversion. The modelling of these processes within the pellet leads to a set of parabolic partial differential equations, and a first step in the study of these is to determine whether there exist steady-state solutions, and, if so, how many of these there are. The present paper works at a particular one-dimensional steady-state equation which nonetheless seems to be typical of more general situations, and it is shown rigorously that if the activation energy is sufficiently high, then the number of solutions must be essentially either one or three depending upon the other parameters in the problem. Author
- Physical Chemistry
- Numerical Mathematics