Water moves across a permeable membrane whenever two solutions separated by the membrane differ in total solute concentration. the process is called

This process is called osmosis.

It happens when there's a difference in water potential in two solutions separated by a semi permeable membrane. Water molecules will eventually flow from the region of higher water potential to a region of lower water potential. Down the water potential gradient.

Note that this is only applicable for water. Other fluids travel down the concentration gradient by a process called diffusion instead. This process doesn't require a semi permeable membrane though.