Development of an effective advection-dispersion-reaction equation involving chemical mixing

Abstract:

Mixing in the subsurface is an important process for many kinds of remediation. Mixing, however, is a complex and poorly understood process. In this work, we focus on the process of microscale mixing and the development of a local volume-averaged advection-dispersion-reaction equation, where the microscale configuration of a reacting mixture (where two components must mix to create reaction) is an important quantity for predicting the effective rate of reaction. Although such a system is simple from the transport perspective, it has a sufficiently rich structure that the mixing and reaction dynamics are still reasonably complex. It also provides a model structure where the influence of microscale configuration can be understood in detail.

In this work, we focus on (1) development of the upscaled advection-dispersion-reaction equation (via volume averaging) for a system in which two chemical components must mix to react, and (2) an explicit representation of how the initial configuration influences the scalar dissipation and the effective reaction rate. In particular, we provide some perspective on a modified scalar dissipation rate as a local average over a finite volume of the domain. Some examples from the case of pure diffusive mixing will also be discussed in order to provide an example from a particularly simple system to help further understanding of the basic physics. By providing an explicit closure for the advection-dispersion-reaction problem, additional physical content is provided about how the scalar dissipation relates to the effective rate of reaction due to mixing.