Diffusion-controlled reaction in a vortex field

Finite-rate diffusion-controlled reaction in a vortex:

“…In Section 3 the case of infinite-rate chemistry is reconsidered and an asymptotic solution for large Schmidt number (small species diffusion) is presented. This solution is new and much simpler than that previously presented [8]. Transformations of the independent variables make analysis of the problem more tractable.…”

“…In the present paper, the authors extend the analysis presented in [8] to consider the effects of finite-rate chemistry. In Section 2 we formulate the problem and give its mathematical description when there is a time scale associated with the combustion chemistry.…”

“…This activity has occurred because both theoretical progress has been made in the understanding of the governing processes and because of the great technological importance of turbulent combustion. In earlier papers [4], [8] [4] is to analyze each of these three scales separately at first, and then to couple them through their dynamical interactions subsequently.…”

“…The analytical method utilized by Marble and students to attack this problem is based on a technique developed earlier by Carrier, Fendell and Marble [1] in which the flame front is analyzed locally, assuming that the front is sharp, and summing over this flame front to obtain global dependences of consumption rates upon the governing parameters. While important scaling results are obtained, the mathematical limitations of the analyses are not clear from the presentations [3], [5], [6] and [7], a fact pointed out by Rehm et al [8] and addressed in their analysis.…”

“…In Section 4 this analysis is applied to with initial conditions Z = 1 for tt/2 < 0 < 3n/2 and Z = 0 for -7t/2 < 0 < 7t/2. This equation determines the solution to the infinite-rate or Same-sheet problem and was solved in [8].…”