Consider the domain $Z_{ϵ}=\{x\in {ℝ}^n;dist(x,ϵ{\mathbb{Z}}^n)>{ϵ}^{\gamma }\}$ and let the free path length be defined as ${\tau }_{ϵ}(x,v)=inf\{t>0;x-tv\in Z_{ϵ}\}.$ In the Boltzmann-Grad scaling corresponding to $\gamma =\frac{n}{n-1}$, it is shown that the limiting distribution ${\phi }_{ϵ}$ of ${\tau }_{ϵ}$ is bounded from below by an expression of the form , for some . A numerical study seems to indicate that asymptotically for large , ${\phi }_{ϵ}\sim C/t$. This is an extension of a previous work [J. Bourgain , (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate...