We propose numerical methods for the estimation of the yield of reaction in laminar flows. The methods are based on backward tracking of tracer particles. In the case of fast reaction (high Damköhler number) the degree of mixing at a particular point can be calculated by a backward random-walk Monte Carlo simulation. This procedure is applicable for both chaotic and nonchaotic regions. In a chaotic flow the reaction-diffusion equation can be approximated by a one-dimensional equation in Lagrangian coordinates along the stable manifold of a fluid element. An adaptive tracking technique of the stable manifold allows the numerical quantification of the effect of the flow on a finite rate chemistry.
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