## 2 Methodology  
This study employed a multiscale simulation framework to investigate the formation and stabilization of water-in-oil HIPEs. The approach integrates quantum-level, atomistic, and mesoscale modeling tools to capture the behavior of emulsifiers and oil molecules across different length and time scales. Each scale contributes unique physical insights, which are translated into parameters for the next stage of simulation, enabling a seamless transition from molecular properties to emulsion morphology prediction.  
The overall strategy, illustrated in Figure 1, begins with the definition of the research objective: to simulate the formation of water-in-oil HIPEs and understand the influence of emulsifier properties on system stability. The methodology is driven by a structured sequence of tasks starting with molecular setup, where an emulsifier, oil type, and water-to-oil ratio are selected. This is followed by property calculations using density functional theory (DFT) to obtain dipole moments and electronic descriptors. A decision checkpoint is incorporated into the workflow, where emulsifiers with dipole moments between 4-7 Debye are prioritized, as this range was preliminarily identified as optimal for interfacial stabilization.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** & **Application/Method** & **Key Finding** & **Limitation** \\ \hline
[25] & DPD of asphaltenes and sodium & Oxygenated asphaltenes form & Focused only on binary mixtures \\  & naphtenates & more stable interfacial films & without complex multicomponent \\  & & & emulsions \\
[27] & Superhydrophobic foam for & Graphene/polystyrene foams & Experimental only; no \\  & emulsion separation & effectively separate W/O & molecular-level understanding \\  & & emulsions & \\
[28] & DPD + experimental on Gemini & Gemini surfactants stabilize & Concentration effect overlaps \\  & surfactants & emulsions more effectively & structural interpretation \\  & DPD of copolymer-crude & Longer co-polymer chains & Emulsion system limited to single \\  & oil–water emulsions & improve coalescence control & polymer–oil configuration \\  & & Surfactants and crude & No discussion of performance \\  & & components compete for & under varying water contents \\  & & interfacial adsorption & \\  & & PBO-based demulsifiers enhance & Mechanism valid only for \\  & & coalescence via network & ultra-heavy crude and certain \\  & & formation & polymer types \\  & & Mixed surfactants reduce IFT & Spacer group effect needs more \\  & surfactants & (interfacial tension) and enhance & systematic quantification \\  & & emulsion stability & \\  & & Salinity and temperature & Radius of gyration and \(\chi\) \\  & salt/surfactant effects & influence IFT and interfacial & parameter treated in ideal \\  & & structure & conditions \\  & & Shorter spacers yield better & Aging behavior not fully \\  & variable spacers & interfacial activity and lower & validated experimentally \\  & & sedimentation & \\  & & & \\  & & \\  & & & \\  & & & \\  & & \\  & & & \\  & & \\  & & & \\ \end{tabular}
\end{table}
Table 1: State-of-the-art literature on the study topic.  
Once the electronic properties are determined, the simulation proceeds with mapped input parameters into the DPD environment. A full simulation process is carried out using mesoscale coarse-grained models under NVT (number of particles, volume, and temperature) ensemble conditions. Afterward, post-simulation analysis evaluates the resulting structures to classify whether a high internal phase emulsion has successfully formed. The results are then used to establish correlations between emulsifier molecular descriptors and emulsion performance.