  We investigate nanoflows through dilute disordered media by means of joint
lattice Boltzmann (LB) and molecular dynamics (MD) simulations -- when the size
of the obstacles is comparable to the size of the flowing particles -- for
randomly located spheres and for a correlated particle-gel. In both cases at
sufficiently low solid fraction, $\Phi<0.01$, LB and MD provide similar values
of the permeability. However, for $\Phi > 0.01$, MD shows that molecular size
effects lead to a decrease of the permeability, as compared to the
Navier-Stokes predictions. For gels, the simulations highlights a surplus of
permeability, which can be accommodated within a rescaling of the effective
radius of the gel monomers.
