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Things tend to be more classical the bigger they are, so I guess the area where the Drude model (the one that explains resistivity with classical scattering) would work best is when the charge carriers are big. One example of that is ionic compounds dissolved in liquids. There, the charge carriers are whole atoms, plus solvation shells made out of several water molecules. Dissolved ions are far more localized than electrons are in metals.

One prediction of Drude theory is that conductivity is linear in electron (or charge carrier) density. This appears to be a pretty solid law for solution conductivity (see this chart for one example) which is an encouraging sign.

Is it true that Drude theory works better for solutions than it does for metals? If so, which questions can it answer more accurately for solutions than it can for metals? (An implied sub-question to this question is, "what are the failings of Drude theory in metals?")

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    $\begingroup$ Although it doesn't discuss solutions at all, Ashcroft & Mermin's Solid State Physics has a good list of shortcomings of the Drude model in solids. $\endgroup$
    – Puk
    Jun 27, 2020 at 3:43

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