Chaos, Mixing, and Restart - Fluid-solid reaction enhancement under pore-scale chaotic advection

Biogeochemical reactions at the interface between fluid and solid phases are of central importance to a broad range of natural and engineered processes in porous media. As dissolved reactants are transported through a porous medium, advection and diffusion act to homogenize their concentrations, in competition with reactive depletion at the solid interface. Transport limitations can limit reactant availability, leading to reduced reaction efficiency when compared to well-mixed conditions. Chaotic advection has been recently established to occur spontaneously in steady, three-dimensional flows through porous media. In this work, we explore and quantify its role in mitigating transport limitations and correspondingly increasing reaction efficiency. We employ the continuous time random walk framework to connect reaction delays due to transport limitations to the statistics of solute excursion times to the interface. Chaotic advection is associated with a rapid loss of memory of initial conditions and efficient exploration of the bulk of the pore space. We model the corresponding effect on excursion times through a stochastic restart process, such that reactant positions are randomly restarted homogeneously across the domain over a characteristic time scale that depends on flow and geometry. Processes that restart under some condition have received much attention in the context of search strategies, where it is known that they can increase the efficiency of the underlying process. Here, we find a corresponding effect on excursion times, and a consequent increase of reaction efficiency with Péclet number. As chaotic advection leads to efficient bulk exploration, low velocities near the interface due to no-slip boundary conditions become the limiting factor on mixing and thus control the restart rate. This has the surprising consequence that, while chaotic advection sets the stage for enhanced reaction efficiency, the increase is insensitive to the "strength" of chaos as quantified by the Lyapunov exponent, and is instead controlled by flow shear at the interface. The theoretical predictions are in excellent agreement with numerical simulations of reactive decay at solid surfaces in a crystalline porous medium, over a broad range of Péclet and Damköhler numbers.