## 2 Materials and Methods
### Oil Spill Behavior and Calculation Principles
#### 2.2.2 Weathering Process  
Weathering of oil particles involves processes such as evaporation, dissolution, and emulsion formation, during which the composition of oil particles changes, but the horizontal position of the oil particles does not change [19]. Evaporation: Oil film evaporation is affected by oil content, air temperature, water temperature, oil spill area, wind speed, solar radiation, and oil film thickness. It is assumed that the diffusion in the oil film is unlimited, the temperature is higher than 0 \({}^{\circ}\)C, the thickness of the oil film is less than 5-10 cm, the oil film is completely mixed, and the partial pressures of some atmospheric components are negligible compared to the vapor pressure. The evaporation rate can be expressed by the following equation:  
\[\mathrm{N}_{\mathrm{i}}^{\mathrm{e}}=\mathrm{k}_{\mathrm{ei}}\cdot\mathrm{P}_ {\mathrm{i}}^{\mathrm{SAT}}/\mathrm{RT}\cdot\frac{\mathrm{M}_{\mathrm{i}}}{ \rho_{\mathrm{i}}}\cdot\mathrm{X}\cdot\left[\mathrm{m}^{3}/\mathrm{m}^{2} \mathrm{s}\right] \tag{4}\]  
where N is the evaporation rate; \(\mathrm{k}_{\mathrm{e}}\) is the material transport coefficient; \(\mathrm{P}^{\mathrm{SAT}}\) is the vapor pressure; R is the gas constant; T is the temperature; M is the molecular weight; \(\rho\) is the oil component density; and i is the oil component of interest. \(\mathrm{K}_{\mathrm{ei}}\) is estimated from the following equation:  
\[\mathrm{k}_{\mathrm{ei}}=\mathrm{k}\cdot\mathrm{A}_{\mathrm{oil}}^{0.045}\cdot \mathrm{S}_{\mathrm{ci}}^{-2/3}\cdot\mathrm{U}_{\mathrm{w}}^{0.78} \tag{5}\]  
where k is the evaporation coefficient and \(\mathrm{S}_{\mathrm{ci}}\) is the Schmidt number for the vapor of component i.  
Emulsification: Emulsification of oil spills refers to the process of mixing oil and seawater to form oil-water emulsions during weathering. Emulsification begins within hours of an oil spill. It depends on factors such as the thickness of the oil film, the density and viscosity of the spill itself, and the size of the wind waves [20]. Formation Process of Oil-In-Water Emulsions  
The mechanisms driving oil into water include dissolution, diffusion, precipitation, etc., among which diffusion is the most important during the first few weeks after an oil spill. Diffusion is a mechanical process in which turbulent energy in the stream tears the oil film into oil droplets, forming an oil-in-water emulsion. These emulsions can be stabilized by surfactants that prevent the oil droplets from returning to the oil film. In bad weather, the dominant diffusion force comes from wave breaking, while in calm weather it comes from the stretching and compression of the oil film. The calculation of oil loss from oil film diffusion to the water body is as follows:  
\[D=\mathrm{D_{a}}\cdot\mathrm{D_{b}} \tag{6}\]  
where \(\mathrm{D_{a}}\) is the component entering the water body and \(\mathrm{D_{b}}\) is the component that does not return after entering the water body:  
\[\mathrm{D_{a}}=\frac{0.11(1+\mathrm{U_{w}})^{2}}{3600} \tag{7}\]  
\[\mathrm{D_{b}}=\frac{1}{1+50\mu_{oil}\cdot\mathrm{h_{s}}\cdot\mathrm{Y_{ow}}} \tag{8}\]  
where \(\mu_{oil}\) is the viscosity of the oil and \(\mathrm{Y_{ow}}\) is the oil-water interfacial tension.