Wiktionary
n. (context chemistry English) A separation process in which a solution is permeated through a membrane and subsequently extracted with a solvent
Wikipedia
Perstraction is a typical perstraction includes two liquid phases but only other phase includes an extractant. Perstraction can be more gentle, faster and cheaper than the traditional biphase extraction. There many potential applications. Perstraction has been applied to oil refining, decontamination of drinking water and improving the downstream process in biorefineries (source?).
Perstraction is about 30-year-old technique. It is analogous to pervaporation. The technique is used commercially (source?). There are many good ideas and potential applications but they have met problems. Membranes can not be done in the cheap way. Usually many compounds can not be extracted concurrently.