  We define a new disordered asymmetric simple exclusion process (ASEP) with
two species of particles, first-class particles labelled $\bullet$ and
second-class particles labelled ${\scriptstyle \Box}$, on a two-dimensional
toroidal lattice. The dynamics is controlled by particles labelled $\bullet$,
which only move horizontally, with forward and backward hopping rates $p_i$ and
$q_i$ respectively if the $\bullet$ is on row $i$. The motion of particles
labelled ${\scriptstyle \Box}$ depends on the relative position of these with
respect to $\bullet$'s, and can be both horizontal and vertical. We show that
the stationary weight of any configuration is proportional to a monomial in the
$p_i$'s and $q_i$'s. Our process projects to the disordered ASEP on a ring, and
so explains combinatorially the stationary distribution of the latter first
derived by Evans (Europhysics Letters, 1996). We compute the partition
function, as well as densities and currents of $\bullet$'s and ${\scriptstyle
\Box}$'s in the stationary state. We observe a novel mechanism we call the
Scott Russell phenomenon: the current of ${\scriptstyle \Box}$'s in the
vertical direction is the same as that of $\bullet$'s in the horizontal
direction.
