Spheres packing of different sizes display a wide range of values of porosity (ε), pore size (d_e), particle size (d_av) and pore channel tortuosity (t) [1]. Tortuosity is associated with the flow and mass transfer characteristics such as permeability (k), diffusivity, thermal dispersion, effective thermal conductivity, etc. [2,3]. The glass spheres with two different diameters (d and D) were mixed using a water-glycerol solution as the binder between the different sized particles [1]. The mixture was transferred to a square acrylic transparent column (please see Fig. 1) and the column was tapped vertically until we got no variation on the packing thickness. After that, bed porosity (ε) was determined using gravimetry - packing height (L) varied between 10 and 15 cm. The pressure loss (ΔP) of the constructed binary packing beds was determined measuring the flow rate (Q) at a fixed height of water – the experimental setup being described in a previous investigation [3]. The cross-sectional area of the prismatic column and Q allowed the calculation of the Darcy velocity (U_D).

Using experiments at low velocities (creeping regime) and the Kozeny-Carman equation, tortuosity (t) was modelled using a power law function t=(1ε)ⁿ [3]. In the Kozeny-Carman equation a proportionality coefficient 1(36K₀t²) is often assumed as a constant. This assumption is acceptable in the packing porosity range 0.36-0.4. Beyond this range a dependence of the tortuosity on porosity must be taken in consideration and t must be considered as a variable. In Fig. 1 it can be observed that [...]