  We introduce a discrete time microscopic single particle model for kinetic
transport. The kinetics is modeled by a two-state Markov chain, the transport
by deterministic advection plus a random space step. The position of the
particle after $n$ time steps is given by a random sum of space steps, where
the size of the sum is given by a Markov binomial distribution (MBD). We prove
that by letting the length of the time steps and the intensity of the switching
between states tend to zero linearly, we obtain a random variable $S(t)$, which
is closely connected to a well known (deterministic) PDE reactive transport
model from the civil engineering literature. Our model explains (via bimodality
of the MBD) the double peaking behavior of the concentration of the free part
of solutes in the PDE model. Moreover, we show for instantaneous injection of
the solute that the partial densities of the free and adsorbed part of the
solute at time $t$ do exist, and satisfy the partial differential equations.
