Is it permissible to transfer water by rubbing from a place on the face that the water reached to another place that it did not reach?

If water flows over an ablutioned limb but does not separate from it, it is not considered used water. So, if water is moved by hand from the middle of the face to its side, and it flows over an area that was not directly touched by water, that suffices as a washing. However, merely wiping with a wet hand without water flowing is not considered a washing.