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.