Plume stretching in the trapped region of a reoriented potential mixer

The reoriented potential mixer (RPM) can enhance mixing and reaction during in situ remediation of contaminated groundwater, in which a chemical or biological amendment is introduced into a contaminant plume to react with and degrade the contaminant. Each step of the RPM consists of dipole flow between a pair of wells-one for injection and one for extraction-that is active for a dimensionless time τ. Subsequently, a different pair of wells is activated at a reorientation angle Θ. Certain {τ,Θ} pairs lead to chaotic advection, with elliptic islands embedded in a chaotic sea. Importantly, a central elliptic island encompasses a "trapped" region containing fluid that does not reach an extraction well during typical groundwater remediation timescales. Indeed for groundwater remediation, the RPM must be designed so that the contaminant remains within such a trapped region, eliminating the possibility of degrading previously uncontaminated regions of the aquifer. In our model, this trapped region consists of two parts: an inner region surrounding an elliptic fixed point within which the fluid is minimally mixed by weak shear, and an outer region with stronger shear that can produce substantial stretching of the interface between the contaminant and amendment plumes. An RPM designed to contain the contaminant and amendment plumes within the trapped region has the potential to enhance reaction during in situ remediation of contaminated groundwater, while preventing the spread of contaminated groundwater into previously uncontaminated regions of the aquifer.