Electrons diffuse very slowly in a wire, typically no more then millimeters per second depending on the current and the size of the wire. They move in a direction opposite to the current in the wire because of their negative charge.
Ma'Mon Abu Hammad I think you are trying to visualise the flow of electrons in a metal wire?
When you look at the Wikipedia description of electric current they talk about free electrons being able to move along the wire in an electrical circuit.
I think of the electron not as a point particle but as a looped wave associated at any time with the outer shell of an atom of the metal substance of the wire.
With no electric potential and no electric current the electrons would all be in some atomic shell. Then when there is an electric potential there is a tendency for the outer electrons to be detached from their host atom and move to an adjacent atom where there is an empty spot in the shell.
So this would imply no free electrons, just the ability of electrons to move from one atom to another.
This is how I would visualise the current based on the Space Time Wave theory: