  The diffusive transport of biased Brownian particles in a two-dimensional
symmetric channel is investigated numerically considering both the no-flow and
the reflection boundary conditions at the channel boundaries. Here, the
geometrical confinement leads to entropic barriers which effectively control
the transport properties of the particles. We show that compared to no-flow
boundary conditions, the transport properties exhibit distinct features in a
channel with reflection boundary conditions. For example, the nonlinear
mobility exhibits a nonmonotonic behavior as a function of the scaling
parameter $f$, which is a ratio of the work done to the particles to available
thermal energy. Also, the effective diffusion exhibits a rapidly increasing
behavior at higher $f$. The nature of reflection, i.e., elastic or inelastic,
also influences the transport properties firmly. We find that inelastic
reflections increase both the mobility and the effective diffusion for smaller
$f$. In addition, by including the short range interaction force between the
Brownian particles, the mobility decreases and the effective diffusion
increases for various values of $f$. These findings, which are a signature of
the entropic nature of the system, can be useful to understand the transport of
small particles or molecules in systems such as microfluidic channels, membrane
pores, and molecular sieves.
