Simple model that explain the flow of electrons in metals I am not quite clear about how electrons (negative electric charges in general) flow through a metal.
I imagine the metal as a lattice of small positive charges $+q$ that can not move and the - and + of the battery (source) as two strong charges $-Q$ and $+Q$. The current will be a negative charge $-e$ that is somehow initially placed close to $-Q$. Under the strong attraction of  $+Q$ and repulsion of "-Q" the $-e$ charge will start to move. However it appears it will get stuck in the network of positive charges (even if the collisions are considered elastic) finally sticking to one of them.
Am I missing something. Can this model be improved to work. Can the $-e$ charge reach $+Q$?
Note: I do not want to involve in the model the Quantum Mechanics or other concepts excepting the law of Coulomb and Newton's laws.

 A: You can't really explain the conductivity in metals without basic quantum mechanics.
Metals as made up of lattices of metal atoms, packed at very close distances. The outermost and least tightly bound (to the nucleus) electrons, the valence electrons, occupy atomic orbitals  of the least energy.
Due to the close vicinity of the atoms and the similarity in energy of the valence electron orbitals, the latter show enough overlap to form a conduction band. This is illustrated in the figure below:

Source, p. 142
Here the atomic orbitals $2s^1$ of the lithium atoms fuse together into a 'mega molecular orbital', called the conduction band. In this conduction band the electrons can move more or less freely.
A: Actually, the metal is totally filled with positive nuclei and negative electrons,
but the outer electrons are quite able to move about from one atom to another,
because of the way all the atoms are packed in a lattice.
That's why metals conduct heat so well.
The electrons are like a gas filling the metal, and they can easily carry momentum.
They can't get out of the metal of course, because the positive charges hold them back.
And if there is any sort of electric field, they can easily follow it.
Sometimes they bounce off the atoms, and that's what electrical resistance is.
