Multi-chamber contact tanks have been extensively used in industry for water treatment to provide potable water to communities, which is essential for human health. To evaluate the efficiency of this treatment process, flow and tracer transport analysis have been used in the literature using Reynolds averaged Navier-Stokes (RANS) and large-eddy simulations (LES). The purpose of this study is two-fold. First a unifying analysis of the flow field is presented and similarities and differences in the numerical results that were reported in the literature are discussed. Second, the vorticity field is identified as the key parameter to use in separating the mean flow (jet zone) and the recirculating zones. Based on the concepts of vorticity gradient and flexion product, it is demonstrated that the separation of the recirculation zone and the jet zone, fluid-fluid flow separation, is possible. The separation of the recirculation zones and vortex core lines are characterized using the definition of the Lamb vector. The separated regions are used to characterize the mixing efficiency in the chambers of the contact tank. This analysis indicates that the recirculation zone and jet zone formation are three-dimensional and require simulations over a long period of time to reach stability. It is recognized that the characteristics of the jet zones and the recirculation zones are distinct for each chamber and they follow a particular pattern and symmetry between the alternating chambers. Hydraulic efficiency coefficients calculated for each chamber show that the chambers having an inlet adjacent to the free surface may be designed to have larger volumes than the chambers having wall bounded inlets to improve the efficiency of the contact tank. This is a simple design alternative that would increase the efficiency of the system. Other observations made through the chamber analysis are also informative in redefining the characteristics of the efficiency of the contact tank system.