Determining the limits of geometrical tortuosity from seepage flow calculations in porous media

Recent investigations have found a distinct correlation of effective properties of porous media to sigmoidal functions, where one axis is the Reynolds number Re and the other is the effective property dependent of Re, Θ = S (Re) -- One of these properties is tortuosity -- At very low Re (seepage flow), there is a characteristic value of tortuosity, and it is the upper horizontal asymptote of the sigmoidal function -- With higher values of Re (transient flow) the tortuosity value decreases, until a lower asymptote is reached (turbulent flow) -- Estimations of this parameter have been limited to the low Reynolds regime in the study of porous media -- The current state of the art presents different numerical measurements of tortuosity, such as skeletization, centroid binding, and arc length of streamlines -- These are solutions for the low Re regime. So far, for high Re, only the arc length of stream lines has been used to calculate tortuosity -- The present approach involves the simulation of fluid flow in large domains and high Re, which requires numerous resources, and often presents convergence problems -- In response to this, we propose a geometrical method to estimate the limit of tortuosity of porous media at Re → ∞, from the streamlines calculated at low Re limit -- We test our method by calculating the tortuosity limits in a fibrous porous media, and comparing the estimated values with numerical benchmark results -- Ongoing work includes the geometric estimation of different intrinsic properties of porous medi