  In this paper we consider three classes of interacting particle systems on
$\mathbb Z$: independent random walks, the exclusion process, and the inclusion
process. We allow particles to switch their jump rate (the rate identifies the
type of particle) between $1$ (fast particles) and $\epsilon\in[0,1]$ (slow
particles). The switch between the two jump rates happens at rate
$\gamma\in(0,\infty)$. In the exclusion process, the interaction is such that
each site can be occupied by at most one particle of each type. In the
inclusion process, the interaction takes places between particles of the same
type at different sites and between particles of different type at the same
site. We derive the macroscopic limit equations for the three systems, obtained
after scaling space by $N^{-1}$, time by $N^2$, the switching rate by $N^{-2}$,
and letting $N\to\infty$. The limit equations for the macroscopic densities
associated to the fast and slow particles is the well-studied double
diffusivity model. This system of reaction-diffusion equations was introduced
to model polycrystal diffusion and dislocation pipe diffusion, with the goal to
overcome the limitations imposed by Fick's law. In order to investigate the
microscopic out-of-equilibrium properties, we analyse the system on
$[N]=\{1,\ldots,N\}$, adding boundary reservoirs at sites $1$ and $N$ of fast
and slow particles, respectively. Inside $[N]$ particles move as before, but
now particles are injected and absorbed at sites $1$ and $N$ with prescribed
rates that depend on the particle type. We compute the steady-state density
profile and the steady-state current. It turns out that uphill diffusion is
possible, i.e., the total flow can be in the direction of increasing total
density. This phenomenon, which cannot occur in a single-type particle system,
is a violation of Fick's law made possible by the switching between types.
