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The essential property of insoluble bilayers is that they optimise their area at fixed surfactant number.
I have emphasized experiments more than theory. Of course, we need some theory when thinking of soft matter.
Surfactants allow us to protect a water surface and to generate these beautiful soap bubbles, which are the delight of our children.
What do we mean by soft matter? Americans prefer to call it 'complex fluids.' This is a rather ugly name, which tends to discourage the young students.
Usually a fiber, after being dipped in a liquid, shows a string of droplets, and thus, for some time, people thought that most common fibers were non-wettable.
Benjamin Franklin performed a beautiful experiment using surfactants: on a pond at Clapham Common, he poured a small amount of oleic acid, a natural surfactant which tends to form a dense film at the water-air interface.