## 4 Discussion  
The dispersant effectiveness results in both shake flasks (mixing by orbital shaking) and in the baffled flask (mixing with paddle mixer) indicate a certain level of mixing energy is needed to effect good dispersion or breakup of NAPL into particles in the bulk phase (Figures 2-4). In these laboratory-scale environments, generally a mixing speed above 200 rpm is needed to achieve a desirable level of dispersion. At mixing speeds of 200 rpm or below, which corresponds with energy dissipation values of 1 or below at this scale, only low dispersant effectiveness results were obtained, specifically levels of 20% DE or lower. The dispersion tests performed at the pilot scale demonstrated improved NAPL breakup was achieved at lower mixing speeds (and lower energy dissipation levels), although it involved higher power input (Figure 8). The pilot scale results also indicated a significant difference in dispersion using the helical ribbon impeller versus the paddle impeller. The helical ribbon provided dispersion results comparable to the paddle impeller, but at energy dissipation levels that were roughly one order of magnitude lower (see Figure 8). Also at the pilot scale, dispersion was evaluated over 2 h. At the higher mixing speeds (150 and 275 rpm), high dispersion levels of 80 to 90% were achieved within 1 h, while at the lower mixing speeds in the range of 45 to 100 rpm, a slower and continually-increasing dispersion occurred out to 2 h. Similar results of increasing dispersion with time was observed in the work [PERSON] et al. [6]. The dispersant effectiveness test detailed from the Code of Federal Regulations [7] is described for only small lab-scale testing volumes and only one time period of mixing. In this work, the size of testing and duration of mixing have been expanded for the purposes of evaluating dispersion as a possible oily sludge treatment method. These changes present challenges, such as obtaining a dispersed-phase-only sample when used at a larger scale, and the size of the mixing element as compared to the container of testing, which need to be adequately addressed by careful experimental planning if similar methods are used for larger scale testing. Estimates of the energy dissipation that occurs in the open ocean environment were also provided by [PERSON] et al. in an experiment conducted in a lake in Ontario, where the mixing by wave action was estimated to represent an energy dissipation rate between \(10^{-3}\) and \(10^{-2}\) W/kg for the open water surface and between 1 and 10 W/kg for breaking waves [6]. The results depicted in Figures 6 and 8 suggest that a helical mixer operated at a low to medium rotational speed may be effective at a full scale to effectively disperse NAPL oil material over time so as to feed an aqueous phase biodegradation process. The comparison of the different dispersants used per the results presented in Figure 2 suggests that the confidential dispersant is the best and the Petroclean dispersant performed as least desirable. However, other results presented here suggest that the Petroclean can achieve high dispersant effectiveness results when the mixing time is extended beyond the originally prescribed 20 min (Figures 5 and 6). These comparable outcomes are also implied by the biodegradation results presented in Table 2. The polynomial equation derived from the fractional factorial design experiment indicated the C term (type of dispersant) was significant; however, review of the p-values in Table S5 indicates that the type of dispersant term is not as highly significant as the first two terms; that is, the mixing speed (A) and volume of oil added to the system (B). The biodegradation of dispersed oil in batch culture demonstrated oil removal, as measured by the difference from the dispersed oil remaining in the aqueous phase over a testing period of 21 to 28 days.