Mixing enhancement in enzymatic chemical reactions by optimal tuning of flows

We consider the problem of mixing enhancement in enzymatic chemical reactions in moving fluids, which are modeled by a reaction–convection–diffusion equation. The problem is formulated as an optimal control problem using the flow field as a control variable. By variational principles, we prove the existence of an optimal flow and derive an optimality system that consists of nonlinear reaction–convection–diffusion equations and Laplace’s equations. The uniqueness of the optimal flow is left open.