  Using the porous structures made up of homogeneously arranged solid
obstacles, we examine the effects of rarefaction on the hydraulic tortuosity in
the slip and early transition flow regimes via extended lattice Boltzmann
method. We observed that modification in either the obstacle's arrangement or
the porosity led to a power-law relation between the porosity-tortuosity. Along
with this, we also found that in the slip flow regime, the exponent of this
relation contains the effect of finite Knudsen number (Kn). In addition, we
observed that on properly scaling Kn with porosity and hydraulic tortuosity, a
generalized correlation can be obtained for apparent permeability.
