## 2 Materials and Methods  
### Experimental Methods  
The dispersant effectiveness (DE) test was implemented using the USEPA protocol developed for the assessment of dispersant formulations for oil spill cleanup/treatment [7]. This DE procedure was implemented with dichloromethane (DCM) as the extraction solvent and concentration of residual oil determined by spectrophotometric absorbance of extracted oil, measured at wavelengths of 340, 370, and 400 nanometers, as specified in the protocol. The DE is determined by direct measurement of the concentration of oil dispersed in the continuous phase after dispersant addition and completion of the mixing protocol, as determined using absorbance versus concentration calibration curves established for each oil and dispersant mixture, and for each of the three spectrophotometer wavelengths. The oil concentrations calculated based upon each separate wavelength measurement are averaged to give the final estimated dispersed oil concentration in the continuous phase. This test was extended to different size containers and different means of mixing (orbital shaking of flask, stirring with paddle mixer or helical ribbon mixer (see Figure 1)) to evaluate the dispersion of oil by different means and at different scales (250-mL Erlenmeyer flask, 1000-mL baffled jar flask, or a 30-L plastic container with no baffles). The amount of oil added and the ratio of oil to dispersant were also altered in this work. In particular, one set of experiments for dispersant effectiveness was conducted using a fraction factorial design (see Table S1 in the Supplementary Materials), with mixing speed, dispersed phase volume, dispersant type, and dispersant to oil ratio as the independent variables. Aside from the paddle mixer, the helical ribbon mixer was selected for testing because this type of impeller is used in commercial wastewater pond mixing equipment (Solarbee and Gridbee, Medora Corporation, Dickinson, ND, USA). The oil material used for testing in the entirety of this work was West Texas Crude Oil (WTCO), sold as West Texas blend from ONTA Corp. The dispersants tested included a confidential dispersant (commercially available product), Petroclean (Alabaster Corporation, Pasadena, TX, USA) and FFT (FFT Technologies, Charleston, SC, USA). The calculation of the oil droplet average size was based upon oil fluid properties and the energy dissipation. Equation (1) below is based on the Weber number theory to predict the average equilibrium droplet size (Equation (1)), as presented by [PERSON] et al. [6]. This method is based on a semi-empirical theory, the Sauter mean droplet diameter, \(D_{32}\), at equilibrium, as previously developed by [PERSON] [8], [PERSON] et al. [9], [PERSON] and [PERSON] [10], and [PERSON] [11]. \[\frac{D_{32}}{D}=A\bigg{(}\rho_{c}(\varepsilon D)^{\frac{2}{3}}D/\sigma\bigg{)} ^{-3/5}\bigg{[}1+B\bigg{(}\frac{\rho_{c}}{\rho_{d}}\bigg{)}^{\frac{1}{2}}\mu_ {d}\varepsilon^{\frac{1}{3}}D_{32}^{\frac{1}{3}}/\sigma\bigg{]}^{3/5} \tag{1}\]  
In Equation (1), \(D\) is the diameter of the vessel (m), \(\sigma\) is the oil-water interfacial tension (N/m), \(\varepsilon\) is the average energy dissipation rate (W/kg), \(\rho_{d}\) is the density of the dispersed phase (kg/m\({}^{3}\)), \(\rho_{c}\) is the density of continuous phase (kg/m\({}^{3}\)), \(\mu_{d}\) is the viscosity of the dispersed phase (N/m), and \(A\) and \(B\) are system-dependent constants based on geometry and impeller. [PERSON] et al. found that the constants \(A\) and \(B\) for \(\mu_{d}<500\) cP are 0.054 and 4.08, respectively [12]. The fluid properties used in this instance to calculate the droplet size are listed in Table 1. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Symbol** & **Value** \\ \hline Bulk phase density & \(\rho_{c}\) & 998 kg/m\({}^{3}\) \\ Disperse phase density & \(\rho_{d}\) & 821 kg/m\({}^{3}\) \\ Dispersed phase viscosity & \(\mu_{d}\) & 0.005 Pa-sec \\ Interfacial tension & \(\sigma\) & 0.03 N/meters \\ \hline \end{tabular}
\end{table}