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
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
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不等扩散速率的二次和三次自催化中行波的发展。
DOI：
10.1098/rsta.1991.0098
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
F. Smith
中科院分区：
文献类型：
--
作者：
J. Billingham;D. Needham;F. Smith
本文研究了等温自催化反应方案：A + B -> 2 B（二次自催化）和A +2 B → 3 B（三次自催化），其中A为反应物，B为自催化剂。我们考虑的情况时，量B局部引入到一个均匀的扩张的A，在一维板几何。此外，我们允许化学物种A和B分别具有不相等的扩散速率DA和DB，并研究了两种密切相关的情况，（DB/ DA）= 0和0 <（DB/ DA）< 1。当（D B/Da）= 0时，在B的浓度中形成一个尖峰，它无限增长，我们可以得到大时间和小时间的渐近解。对于0 <（DB/ DA）< 1，在产生最小速度行波之前，存在长的诱导期，在该诱导期期间，在B的浓度中形成大的尖峰。我们可以将情况（DB/DA）= 0的结果与0 <（DB/ DA）< 1时的解联系起来，以获得有关其行为的详细信息。
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.