## 3 Results
### Experimental Results
#### 3.1.1 Dispersant Effectiveness  
The effectiveness of dispersing WTCO while controlling paddle mixer rotational speed and dispersant formulation added with the oil phase at a ratio of 10 parts oil to 1 part dispersant on a volume basis is presented in Figure 2. This series of experiments was conducted in a 1000 mL baffled flask (see Figure 1), using a working volume of 360 mL. The greatest DE occurred with the confidential dispersant (DE = 66%) and the FFT100% dispersant (DE = 57%) at the 400 rpm speed. Significant DE (DE in the 30-70% range) occurred at the 400 and 600 rpm speeds, while only minimal DE (15% or less) occurred at the 200 rpm speed. The calculated energy dissipation values associated with these mixing speeds were 0.29 W/kg at 200 rpm 2.3 W/kg at 400 rpm, and 7.8 W/kg at 600 rpm. Very little dispersion (<10%) occurred when the energy dissipation was less than 1.0 (specifically 0.29), at the 200 rpm condition. A marine impeller was also tested in this series of experiments (data not shown), but was much less effective than the paddle impeller in the baffled flask. The effectiveness of dispersing WTCO (100 to 1000 \(\mu\)L oil with Petroclean as dispersant) at three different flask orbital shaking speeds is shown in Figure 3. These experiments were conducted in a in a 250 mL Erlenmeyer flask with side spout (see Figure 1), using a working volume of 120 mL. The mixing involved orbital shaking of the flask at speeds of 150, 200, or 250 rpm, rather than stirring with a mixer inside the vessel, as occurred in the previous set of experiments. All DE levels were lower than 10% in this particular experiment, which is believed to be due to the relatively low rotational speeds and the fact that the mixing was accomplished without blade mixing of any type. At the shaking speed of 150 rpm, the low DE levels (1% or less) decreased as the volume of the oil/dispersant applied to the system increased from 100 to 1000 \(\mu\)L. At the shaking speed of 250 rpm, the DE levels increased from 2% to 7% as the volume of the oil/dispersant applied to the system increased from 100 to 1000 \(\mu\)L. The DE levels at 200 rpm (approximately 2%) in this set of experiments were generally consistent with the DE results with Petroclean dispersant presented in Figure 2. The Design Expert software was used to develop an empirical equation (Equation (18)) for the mass of oil dispersed (directly related to DE%) using the results from the full fractional factorial set of experiments, based upon the independent parameters mixing speed (A), volume of oil plus dispersant added (B), type of dispersant (C), and ratio of oil to dispersant (D). The equation originally included four first-order terms, six second-order terms mixed parameter terms, and the second-order parameter squared terms for A and B. The ANOVA table that resulted from this analysis is included as Table S5 (Supplemental Materials). The significant terms (\(p<0.05\)) were \(A\), \(B\), \(C\), \(A^{*}B\), \(A^{*}D\), and \(B^{*}D\); all others were not significant since their \(p\)-values were greater than 0.05. \[\text{Mass of oil}=19.06+14.33^{*}A+16.86^{*}B+2.36^{*}C+15.98^{*}AB-3.38^{*}AD -3.55^{*}BD \tag{18}\]  
In the third series of dispersant effectiveness experiments, the duration of the mixing period was utilized as a control parameter, along with the rotational speed of mixing of two different types of  
Figure 3: Dispersant effectiveness for WTCO in 250-mL Erlenmeyer flask with orbital shaking and at a laboratory ambient temperature of approximately 25 \({}^{\circ}\)C (there is no 200 rpm bar in the “WTCO + Petroclean 500” category due to fractional factorial design of this experiment (see Table S1)). Figure 2: Dispersant effectiveness for WTCO in a 1000-mL baffled flask using 2.5-inch paddle impeller at laboratory ambient temperature (approximately 25 \({}^{\circ}\)C) and a 10:1 oil to dispersant ratio. impellers (paddle and helical ribbon).