  We consider the space-time scaling limit of the particle mass in zero-range
particle systems on a $1$D discrete torus $\mathbb{Z}/N\mathbb{Z}$ with a
finite number of defects. We focus on two classes of increasing jump rates $g$,
when $g(n)\sim n^\alpha$, for $0<\alpha\leq 1$, and when $g$ is a bounded
function. In such a model, a particle at a regular site $k$ jumps equally
likely to a neighbor with rate $g(n)$, depending only on the number of
particles $n$ at $k$. At a defect site $k_{j,N}$, however, the jump rate is
slowed down to $\lambda_j^{-1}N^{-\beta_j}g(n)$ when $g(n)\sim n^\alpha$, and
to $\lambda_j^{-1}g(n)$ when $g$ is bounded. Here, $N$ is a scaling parameter
where the grid spacing is seen as $1/N$ and time is speeded up by $N^2$.
  Starting from initial measures with $O(N)$ relative entropy with respect to
an invariant measure, we show the hydrodynamic limit and characterize boundary
behaviors at the macroscopic defect sites $x_j = \lim_{N\uparrow \infty} k_{j,
N}/N$, for all defect strengths. For rates $g(n)\sim n^\alpha$, at critical or
super-critical slow sites ($\beta_j=\alpha$ or $\beta_j>\alpha$), associated
Dirichlet boundary conditions arise as a result of interactions with evolving
atom masses or condensation at the defects. Differently, when $g$ is bounded,
at any slow site ($\lambda_j>1$), we find the hydrodynamic density must be
bounded above by a threshold value reflecting the strength of the defect.
Moreover, due to interactions with masses of atoms stored at the slow sites,
the associated boundary conditions bounce between being periodic and Dirichlet.
