Determining the limits of geometrical tortuosity from seepage flow calculations in porous media. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Uribe, David; Osorno, Maria; Sivanesapillai, Rakulan; Steeb, Holger; Ruiz, Oscar
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 453
• Page End: 454
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410214
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>Recent investigations have found a distinct correlation of effective properties of porous media to sigmoidal functions, where one axis is the Reynolds number <italic>Re</italic> and the other is the effective property dependent of <italic>Re</italic>, Θ<sub><italic>i</italic></sub>=<italic>S<sub>i</sub>(Re)</italic>. One of these properties is tortuosity. At very low <italic>Re</italic> (seepage flow), there is a characteristic value of tortuosity, and it is the upper horizontal asymptote of the sigmoidal function. With higher values of <italic>Re</italic> (transient flow) the tortuosity value decreases, until a lower asymptote is reached (turbulent flow).</p> <p>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 <italic>Re</italic> regime. So far, for high <italic>Re</italic>, 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 <italic>Re</italic>, 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 <italic>Re</italic> → ∞, from the streamlines calculated at low <italic>Re</italic> 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 media. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)</p> </abstract>