  Using analytical techniques and Langevin dynamics simulations, we investigate
the dynamics of polymer translocation into a narrow channel of width $R$
embedded in two dimensions, driven by a force proportional to the number of
monomers in the channel. Such a setup mimics typical experimental situations in
nano/micro-fluidics. During the the translocation process if the monomers in
the channel can sufficiently quickly assume steady state motion, we observe the
scaling $\tau\sim N/F$ of the translocation time $\tau$ with the driving force
$F$ per bead and the number $N$ of monomers per chain. With smaller channel
width $R$, steady state motion cannot be achieved, effecting a non-universal
dependence of $\tau$ on $N$ and $F$. From the simulations we also deduce the
waiting time distributions under various conditions for the single segment
passage through the channel entrance. For different chain lengths but the same
driving force, the curves of the waiting time as a function of the
translocation coordinate $s$ feature a maximum located at identical
$s_{\mathrm{max}}$, while with increasing the driving force or the channel
width the value of $s_{\mathrm{max}}$ decreases.
