Turbulence on a small scale acts like increased viscosity on a large scale, because they're both forms of momentum diffusion. However, current doesn't have any momentum diffusion terms, the momentum is lost to the conductor.

AFAIK nothing stops an electron from existing in the same space as a proton or neutron - they don't have to go around. Indeed that's required for certain kinds of radioactive decay to occur. Not all electron orbitals overlap the nucleus, but some do.

TL;DR: the analogy is helpful at a high level, but has limitations when you look closely.

> Ok, it's different in that liquid flows through pipes and electrons flow through crystal lattices or whatever, so electrons go between and around the material while liquid is bounded by it.

This is not perfect, but it works at a high level.

The main difference with e.g. water flows is that what restricts electron flux is traps. Electrons are not limited by walls that prevents them from going outside channels, instead they are held in place by atoms’ nuclei.

In a conductor, the “force” holding them is effectively zero, so when an electron comes in on one side, another one comes out of the other.

In a semiconductor. An electron needs some energy to get out of its trap before it can move. Then, “freed” electrons hop from trap to trap and the current is the overall effect of this. Electrons do not have to move far to create a current, there just needs to be enough of them. There is no real macroscopic analogy for this.

In an insulator, electrons just don’t get out of their traps because the energy required is too large.

This ignores a lot of details and quantum effects, but it is still a useful way to think about this.

> It makes me speculate that electron flow through a metal is sort of like liquid flowing through a compressible boundary tube, whereas flow through a non-metal has rigid walls.

Not really. Electrons moving in a metal are slowed down by a lot of different phenomena but this cannot really be considered as a compressible fluid. The effect is more similar to viscosity than compressibility.

In non-metals, electrons just don’t move unless they are made available, for example by doping or with a source of energy.

> Non-metals reject the electrons, metals allow them to play Spiderman and hitch a temporary ride

The general model is that metals let electrons flow and non-metals hold on to them.

> If resistivity is determined by the equivalent of turbulence, though, I've no idea what the graph against temperature should be. Do electrons travel faster when there's less resistance?

The analogy kind of breaks down here. There are competing effects and conductivity as a function of time is often highly non-trivial. In general, the number of electrons available increases with temperature, but scattering by other electrons, vibrations and defects also increases. Overall, resistivity tends to increase with temperature in metals and decrease in semiconductors, but there are exceptions.

How should we visualize what pushes the electron goop forward? If it's like water pressure, that would make the hindmost goop bunch up with the foremost goop.

Presumably electricity has something to do with positive charge at the back of the 'pipe' and negative charge at the 'front' (or have I got those backward?), perhaps a better visualization would be that they're all rolling down an inclined plane together?

Current flows due to a difference in electric potential, which is called voltage. This is similar to the difference in gravitational potential that causes a ball to roll downhill. If imagining electricity like water, then voltage is lifting up one end of the pipe (or water going over a waterfall of a certain height).