## 4 Demulsification of Crude Oil-in-Water Emulsions for Enhanced Membrane Separation  
Demulsifiers reduce the cohesion and electrostatic repulsion between oil droplets in oil-in-water emulsions, thereby enhancing membrane separation performance. This study investigated the effects of adding the divalent salt calcium chloride (CaCl\({}_{2}\)) as a demulsifier to crude oil-in-water emulsions, evaluating zeta potential, particle size distribution, and separation performance. CaCl\({}_{2}\) was added at concentrations of 0.1, 0.5, and 1.0 g per 100 mL of emulsion at 60 \({}^{\circ}\)C. The zeta potential was measured using Brookhaven Instruments with an accuracy of \(\pm\)2%. Figure 13a shows that the zeta potential of the emulsion increased with the addition of CaCl\({}_{2}\), approaching 0 mV from \(-\)16.14 mV in the absence of CaCl\({}_{2}\). Increasing the zeta potential reduces electrostatic repulsion between oil droplets, promoting emulsion instability [73]. This led to droplet clustering and coalescence, as evidenced by increased oil droplet sizes (1.64 \(\upmu\)m, 13.77 \(\upmu\)m, 33.74 \(\upmu\)m, and 48.94 \(\upmu\)m at CaCl\({}_{2}\) concentrations of 0.0, 0.1, 0.5, and 1 mg/100 mL, respectively). Microscopic images display this behavior in Figure 14, where oil droplets aggregate to form flocs, which subsequently coalesce into larger droplets. Higher CaCl\({}_{2}\) concentrations enhance the flocculation rate, correlating with increased coalescence. The separation performance of the emulsion using 1.0 g/100 mL CaCl\({}_{2}\) was tested after 2 h of gravity separation and oil skimming, then fed to the filtration system. The influence of various electrolytes (CaCl\({}_{2}\), MgCl\({}_{2}\):6H\({}_{2}\)O, and NaCl) on the separation efficiency of crude oil-in-water emulsions was systematically evaluated under consistent experimental conditions. Figure 13b compares their impact on the permeate flux of a saline crude oil-in-water emulsion at neutral pH using an AM-NaA/PVDF membrane. The addition of CaCl\({}_{2}\) to the oil-in-water emulsion significantly raised the permeate flux  
Figure 13: (**a**) Effect of CaCl\({}_{2}\) concentration on the zeta potential and particle size distribution of crude oil-in-water emulsions. (**b**) The permeate flux of a saline crude oil-in-water emulsion containing different salts (NaCl, MgCl\({}_{2}\):6H\({}_{2}\)O, and CaCl\({}_{2}\)). to 14,818 L/m\({}^{2}\)-h. This represents a significant increase compared to the permeate fluxes observed with MgCl\({}_{2}\cdot\)6H\({}_{2}\)O (11,748 L/m\({}^{2}\cdot\)h) and NaCl (11,823 L/m\({}^{2}\cdot\)h) while maintaining >99% separation efficiency. According to the Debye-Huckel theory [74], divalent Ca\({}^{2+}\) ions more effectively screen surface charges, compressing the electrical double layer and promoting droplet coalescence, thus enhancing flux. The double-layer thickness (\(k^{-1}\)) decreases inversely with the square root of the ionic strength. Table 3 presents the calculated \(k^{-1}\) in water at 25 \({}^{\circ}\)C as a function of electrolyte concentration. At 1.0 g/100 mL, CaCl\({}_{2}\) exhibits the highest ionic strength (270.3 mol/m\({}^{3}\)), resulting in the smallest double-layer thickness (\(k^{-1}=5.85\times 10^{-10}\) m), which explains its superior flux enhancement due to greater compression of the double layer compared to MgCl\({}_{2}\cdot\)6H\({}_{2}\)O and NaCl.