The Development of Travelling Waves in Quadratic and Cubic Autocatalysis with Unequal Diffusion Rates. II. An Initial-Value Problem with an Immobilized or Nearly Immobilized Autocatalyst
We study the isothermal autocatalytic reaction schemes, A + B --> 2B (quadratic autocatalysis), and A + 2B --> 3B (cubic autocatalysis), where A is a reactant and B is an autocatalyst. We consider the situation when a quantity of B is introduced locally into a uniform expanse of A, in one-dimensional slab geometry. In addition, we allow the chemical species A and B to have unequal diffusion rates DA and DB, respectively, and study the two closely related cases, (DB/DA) = 0 and 0 < (DB/DA) << 1. When (DB/DA) = 0 a spike forms in the concentration of B, which grows indefinitely, and we can obtain both large and small time asymptotic solutions. For 0 < (DB/DA) << 1 there is a long induction period during which a large spike forms in the concentration of B, before a minimum speed travelling wave is generated. We can relate the results for case (DB/DA) = 0 to the solution when 0 < (DB/DA) << 1 to obtain detailed information about its behaviour.
Philosophical Transactions of the Royal Society of London Series A
- Pub Date:
- September 1991