Technical term for water entering a semipermeable membrane?
This is not imbibition, as water molecules don't get absorbed in the semipermeable membranes commonly found in biological structures like Membrane around cells and cellular organelles (I took this example as you asked it in Biology forum). The water molecules pass through biological membranes via protein channels, that may be an active, secondarily active or passive process. Percolation and permeation are also inappropriate. 

If the membrane doesn't hinder a particular solvent it can be said to be permeable to that solvent (e.g. Permeable to water etc.). "Osmosis" is also applicable. As osmosis is only a type of diffusion, you can use the term 'diffusion', but it would be too broad or generalized.