The Fluid Mechanics of Chemical Reaction

The ability for reactive constituents to mix is often the key limiting factor for the completion of reactions across a huge range of scales in a variety of media. In flowing systems, deformation and shear enhance mixing by bringing constituents into closer proximity, thus increasing reaction potential. Accurately quantifying this enhanced mixing is key to predicting reactions, and typically is done by observing or simulating scalar transport. To eliminate this computationally expensive step, we use a Lagrangian stochastic framework to derive the enhancement to reaction potential by calculating the collocation probability of particle pairs in a heterogeneous flow field accounting for deformations. We relate the enhanced reaction potential to three well-known flow topology metrics (Okubo-Weiss, finite-time Lyapunov exponent, and right Cauchy-Green tensor) and demonstrate that it is best correlated to the largest eigenvalue of the right Cauchy-Green tensor. The reason is that this eigenvalue reflects compression and shear but ignores rotation, which does not enhance mixing. We demonstrate that regions of high shear and/or compression do indeed have higher rates of reaction in particle-tracking reaction simulations, but this is not necessarily seen in traditional Eulerian simulations due to numerical (artificial) mixing and the amplification of these errors by non-linear reactions.