Fig. 4 Photographs for the demulsification process (a was the image of demulsification, the insert ofa1 and a2 were the embossment of edge before and after demulsification.b ~d were the representative coalescence modes of emulsion, and e exhibited the moment of cracking for the coalesced emulsion drop)
The fast fusion for emulsion drops during the demulsification process can be explained by the amphipathicity of MIL-100(Fe). The hydrophilic domain of MIL-100(Fe) ensured the contact with the interface film of emulsion, so that it was beneficial for MIL-100(Fe) to adhere on the emulsion drops. Meanwhile, the lipophilicity domain of MIL-100(Fe) can enhance the fusion of emulsion drops by the hydrophobic interaction, which was supported by the facts that the oleic acid drop permeated into the waterwetted MIL-100(Fe) quickly (Fig. S6 ).
The model for oleic acid permeates horizontally on the water wetted MIL-100(Fe) was presented in Fig. 5 . The\(f_{\mathrm{\text{Attraction}}}\), which stands for apparent affinity of oleic acid on the waterwetted MIL-100(Fe), can be expressed as theEq. 2 . In this study, the oleic acid is newton liquid, which has a constant viscosity at a certain temperature. That is the inner resistance to oleic acid (\(f_{\mathrm{\text{Viscosity}}}\)) against motion is constant and equal to the viscosity. The outer resistance against motion for the permeation is from hydrophobicity (\(f_{\mathrm{\text{Hydrophobicity}}}\)) because of the layer of hydration covered on MIL-100(Fe). It was difficult to record permeation in situ. Herein, we instead the accelerated speed of\(a\) (Eq. 3 ) with average accelerated speed of\(\overline{a}\) (Eq. 4 ) along with a change of\(F_{\mathrm{\text{Attraction}}}\) by\({\overline{F}}_{\mathrm{\text{Attraction}}}\) (average apparent affinity). Giving a hypothesis of unit volume \(V\) for oleic acid, there are \(m=0.89V\), where 0.89 (kg·m-3) is the density of oleic acid at 20 ℃. Then, the\({\overline{F}}_{\mathrm{\text{Attraction}}}\) is\((1.78V\frac{L}{t^{2}}+\mathrm{35.3}\times\mathrm{1}\mathrm{0}^{-3}\mathrm{\text{\ N}}+f_{\mathrm{\text{Hydrophobicity}}})\), where the items of \(1.78V\frac{L}{t^{2}}\) and\(f_{\mathrm{\text{Hydrophobicity}}}\) are positive. Therefore, the\({\overline{F}}_{\mathrm{\text{Attraction}}}\) is more than the surface tension of oleic acid (\(33.8\times 10^{-3}\mathrm{\text{\ N}}\)). This indicated the oleic acid can access to the MIL-100(Fe) without inhibiting of hydration even in water, which caused the fast fusion of emulsion drops as shown in Fig. 4 . This conclusion is in good agreement with the stable demulsification performance against the pH and salinity (Fig. 3b and Fig. 3c ).
\(F_{\mathrm{\text{Attraction}}}-f_{\mathrm{\text{Viscosity}}}-f_{\mathrm{\text{Hydrophobicity}}}=m\cdot a\)Eq. (2)
\(a=\nabla^{2}\frac{\partial L}{\partial t}\)Eq. (3)
\(\overline{a}=\frac{2L}{t^{2}}\)Eq. (4)
Where, the \(F_{\mathrm{\text{Attraction}}}\) is the apparent affinity for oleic acid on thewater wetted MIL-100(Fe), \(m\) is the mass of oleic acid, \(f_{\mathrm{\text{Viscosity}}}\) is the resistance because of viscosity (the viscosity of oleic acid is 35.3×10-3N·s·m-1 at 20℃40),\(f_{\mathrm{\text{Hydrophobicity}}}\)is the force originated from hydrophobicity, \(a\) is the accelerated speed of motion for permeation, \(L\) is the distance for permeation,\(t\) is the time for permeation, \(\overline{a}\) is the average accelerated speed of motion for permeation.