A COMPARISON OF EULERIAN AND LAGRANGIAN SIMULATIONS OF BIMOLECULAR REACTION AT THE PORE-SCALE

One problem with Eulerian models of transport and chemical reaction is that the reactions are forced to be well-mixed at the grid scale: One cannot differentiate concentration heterogeneity within a single numerical block. This means that the effects of poor mixing are either ignored in Eulerian models (hence the solutions depend on discretization) or are handled in an ad-hoc manner via pseudo-kinetic expressions. The influence of discretization on reaction rate is demonstrated by finite-difference simulations of a bimolecular reaction in a single pore of 1mm radius. The primary result is that the discretization must be smaller than the typical initial size of concentration perturbations, which may severely restrict the proper use of Eulerian methods. We apply a Lagrangian (particle tracking and reaction) simulation, in which all parameters are physically derived, to the same problem and find that accurate solutions are given without any discretization concerns.