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Let $\Lambda$ be a connected closed region with smooth boundary contained inthe $d$-dimensional continuous torus $\bb T^d$. In the discrete torus $N^{-1}\bb T^d_N$, we consider a nearest neighbor symmetric exclusion process whereoccupancies of neighboring sites are exchanged at rates depending on $\Lambda$in the following way: if both sites are in $\Lambda$ or $\Lambda^\complement$,the exchange rate is one; If one site is in $\Lambda$ and the other one is in$\Lambda^\complement$ and the direction of the bond connecting the sites is$e_j$, then the exchange rate is defined as $N^{-1}$ times the absolute valueof the inner product between $e_j$ and the normal exterior vector to$\p\Lambda$. We show that this exclusion type process has a non-trivialhydrodynamical behavior under diffusive scaling and, in the continuum limit,particles are not blocked or reflected by $\partial\Lambda$. Thus the modelrepresents a system of particles under hard core interaction in the presence ofa permeable membrane which slows down the passage of particles between twocomplementar regions.

Hydrodynamic Limit for a type of Exclusion Processes with slow bonds in dimension $\ge 2$