article: mathematical model of osmosis

(“The movement of ionic solutions is an essential part of biology and technology.”)
Here is the link.
keywords:
[gradients of concentration]
[chemical and electrical potential]
[hydrostatic pressure]
[a classical osmotic cell]
[using a sharp interface method]
[volume change with concentration] [flexible membranes]
[inflexible membranes]
[macro, micro, and nano scales]
[semi-permeable membrane]
[interactions]