In various aspects, methods and apparatuses for liquid-liquid extraction are provided. In certain aspects, an emulsion can be formed by combining a feed stream, an extractant, and a surfactant. The feed stream comprises a plurality of distinct components including a first component to be removed therefrom. The feed stream may be selected from a group consisting of: a hydrocarbon feed stream and an azeotrope. Then, a portion of the first component is extracted from the feed stream (or emulsion) by contact with a superoleophobic and hygroscopic membrane filter that facilitates passage of the first component and extractant through the superoleophobic and hygroscopic membrane filter. A purified product is collected having the portion of the first component removed. Such methods are particularly useful for refining fuels and oils and separating azeotropes and other miscible component systems. Energy-efficient, continuous single unit operation apparatuses for conducting such separation techniques are also provided.
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