Design criteria of a chemical reactor based on a chaotic flow

Abstract

We consider the design criteria of a chemical mixing device based on a chaotic flow, with an emphasis on the steady-state devices. The merit of a reactor, defined as the $Q$-factor, is related to the physical dimension of the device and the molecular diffusivity of the reactants through the local Lyapunov exponents of the flow. The local Lyapunov exponent can be calculated for any given flow field and it can also be measured in experimental situations. Easy-to-compute formulae are provided to estimate the $Q$-factor given either the exact spatial dependence of the local Lyapunov exponent or its probability distribution function. The requirements for optimization are made precise in the context of local Lyapunov exponents.