{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T05:04:24Z","timestamp":1766466264581,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T00:00:00Z","timestamp":1648857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ESPOL","award":["FIMCP-CERA-05-2017"],"award-info":[{"award-number":["FIMCP-CERA-05-2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Geometric tortuosity is an essential characteristic to consider when studying a porous medium\u2019s morphology. Knowing the material\u2019s tortuosity allows us to understand and estimate the different diffusion transport properties of the analyzed material. Geometric tortuosity is useful to compute parameters, such as the effective diffusion coefficient, inertial factor, and diffusibility, which are commonly found in porous media materials. This study proposes an alternative method to estimate the geometric tortuosity of digitally created two-dimensional porous media. The porous microstructure is generated by using the PoreSpy library of Python and converted to a binary matrix for the computation of the parameters involved in this work. As a first step, porous media are digitally generated with porosity values from 0.5 to 0.9; then, the geometric tortuosity is determined using the A-star algorithm. This approach, commonly used in pathfinding problems, improves the use of computational resources and complies with the theory found in the literature. Based on the obtained results, the best geometric tortuosity\u2013porosity correlations are proposed. The selection of the best correlation considers the coefficient of determination value (99.7%) with a confidence interval of 95%.<\/jats:p>","DOI":"10.3390\/computation10040059","type":"journal-article","created":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T02:59:52Z","timestamp":1648954792000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Alternative Methodology to Compute the Geometric Tortuosity in 2D Porous Media Using the A-Star Pathfinding Algorithm"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7809-8659","authenticated-orcid":false,"given":"Mayken","family":"Espinoza-Andaluz","sequence":"first","affiliation":[{"name":"Escuela Superior Polit\u00e9cnica del Litoral, ESPOL, Facultad de Ingenier\u00eda Mec\u00e1nica y Ciencias de la Producci\u00f3n, Centro de Energ\u00edas Renovables y Alternativas, Campus Gustavo Galindo Km. 30.5 V\u00eda Perimetral, P.O. Box 09-01-5863, Guayaquil 090112, Ecuador"}]},{"given":"Javier","family":"Pagalo","sequence":"additional","affiliation":[{"name":"Escuela Superior Polit\u00e9cnica del Litoral, ESPOL, Facultad de Ingenier\u00eda Mec\u00e1nica y Ciencias de la Producci\u00f3n, Campus Gustavo Galindo Km. 30.5 V\u00eda Perimetral, P.O. Box 09-01-5863, Guayaquil 090112, Ecuador"}]},{"given":"Joseph","family":"\u00c1vila","sequence":"additional","affiliation":[{"name":"Escuela Superior Polit\u00e9cnica del Litoral, ESPOL, Facultad de Ingenier\u00eda en Electricidad y Computaci\u00f3n, Campus Gustavo Galindo Km. 30.5 V\u00eda Perimetral, P.O. Box 09-01-5863, Guayaquil 090112, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2732-979X","authenticated-orcid":false,"given":"Julio","family":"Barzola-Monteses","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, Escuela T\u00e9cnica Superior de Ingenier\u00edas Inform\u00e1tica y de Telecomunicaci\u00f3n, Universidad de Granada, 1807 Granada, Spain"},{"name":"Artificial Intelligence and Information Technology Research Group, University of Guayaquil, Guayaquil 090514, Ecuador"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.earscirev.2020.103439","article-title":"Tortuosity of porous media: Image analysis and physical simulation","volume":"212","author":"Fu","year":"2021","journal-title":"Earth-Sci. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11242-010-9613-9","article-title":"The Role of Tortuosity in Upscaling","volume":"88","author":"Porter","year":"2011","journal-title":"Transp. Porous Media"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1029\/98WR00939","article-title":"Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks","volume":"34","author":"Friedman","year":"1998","journal-title":"Water Resour. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.2136\/sssaj2012.0435","article-title":"Tortuosity in Porous Media: A Critical Review","volume":"77","author":"Ghanbarian","year":"2013","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1029\/95GL02230","article-title":"Direct simulation of electrical and hydraulic tortuosity in porous solids","volume":"22","author":"Zhang","year":"1995","journal-title":"Geophys. Res. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s11242-020-01387-z","article-title":"A Permeability\u2013Throat Diameter Correlation for a Medium Generated with Delaunay Tessellation and Voronoi Algorithm","volume":"132","author":"Encalada","year":"2020","journal-title":"Transp. Porous Media"},{"key":"ref_7","first-page":"951","article-title":"Arterial Tortuosity Novel Implications for an Old Phenotype","volume":"73","author":"Loeys","year":"2019","journal-title":"Australas. Phys. Eng. Sci. Med."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.camwa.2016.12.001","article-title":"Computational time and domain size analysis of porous media flows using the lattice Boltzmann method","volume":"74","author":"Andersson","year":"2017","journal-title":"Comput. Math. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Encalada-D\u00e1vila, \u00c1., Espinoza-Andaluz, M., Barzola-Monteses, J., Li, S., and Andersson, M. (2021). Transport Parameter Correlations for Digitally Created PEFC Gas Diffusion Layers Using OpenPNM. Processes, 9.","DOI":"10.3390\/pr9071141"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/978-3-642-02094-0_7","article-title":"Engineering route planning algorithms","volume":"Volume 5515 LNCS","author":"Delling","year":"2009","journal-title":"Algorithmics of Large and Complex Networks"},{"key":"ref_11","first-page":"236","article-title":"Contraction hierarchies on grid graphs","volume":"Volume 8077 LNAI","author":"Storandt","year":"2013","journal-title":"Annual Conference on Artificial Intelligence"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bast, H., Funke, S., Matijevic, D., Sanders, P., and Schultes, D. (2007, January 6). In transit to constant time shortest-path queries in road networks. Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX), New Orleans, LA, USA.","DOI":"10.1137\/1.9781611972870.5"},{"key":"ref_13","first-page":"253","article-title":"A survey and classification of A* based best-first heuristic search algorithms","volume":"Volume 6404 LNAI","author":"Rios","year":"2010","journal-title":"Brazilian Symposium on Artificial Intelligence"},{"key":"ref_14","unstructured":"Davis, E., Edwards, D.D., Forsyth, D., Hay, N.J., Malik, J.M., Mittal, V., Sahami, M., and Thrun, S. (2010). Artificial Intelligence: A Modern Approach, Pearson Education. [3rd ed.]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1834","DOI":"10.1002\/aic.15160","article-title":"Predicting Effective Conductivities Based on Geometric Microstructure Characteristics","volume":"62","author":"Stenzel","year":"2016","journal-title":"AIChE J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.actamat.2014.03.003","article-title":"X-ray micro-computed tomography and tortuosity calculations of percolating pore networks","volume":"71","author":"Shanti","year":"2014","journal-title":"Acta Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1111\/jmi.12389","article-title":"Comparison of three-dimensional analysis and stereological techniques for quantifying lithium-ion battery electrode microstructures","volume":"263","author":"Taiwo","year":"2016","journal-title":"J. Microsc."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zharbossyn, A., Berkinova, Z., Boribayeva, A., Yermukhambetova, A., and Golman, B. (2020). Analysis of tortuosity in compacts of ternary mixtures of spherical particles. Materials, 13.","DOI":"10.3390\/ma13204487"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1080\/09506608.2016.1249995","article-title":"Tortuosity in electrochemical devices: A review of calculation approaches","volume":"63","author":"Tjaden","year":"2018","journal-title":"Int. Mater. Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102252","DOI":"10.1016\/j.cis.2020.102252","article-title":"Pattern detection in colloidal assembly: A mosaic of analysis techniques","volume":"284","author":"Lotito","year":"2020","journal-title":"Adv. Colloid Interface Sci."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lotito, V., and Zambelli, T. (2019). A journey through the landscapes of small particles in binary colloidal assemblies: Unveiling structural transitions from isolated particles to clusters upon variation in composition. Nanomaterials, 9.","DOI":"10.3390\/nano9070921"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102538","DOI":"10.1016\/j.cis.2021.102538","article-title":"Playing with sizes and shapes of colloidal particles via dry etching methods","volume":"299","author":"Lotito","year":"2022","journal-title":"Adv. Colloid Interface Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lotito, V., Karlu\u0161i\u0107, M., Jak\u0161i\u0107, M., Luketi\u0107, K.T., M\u00fcller, U., Zambelli, T., and Fazini\u0107, S. (2020). Shape deformation in ion beam irradiated colloidal monolayers: An AFM investigation. Nanomaterials, 10.","DOI":"10.3390\/nano10030453"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s11242-019-01363-2","article-title":"Predicting Resistivity and Permeability of Porous Media Using Minkowski Functionals","volume":"131","author":"Slotte","year":"2020","journal-title":"Transp. Porous Media"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"104550","DOI":"10.1016\/j.cageo.2020.104550","article-title":"Inferring fracture forming processes by characterizing fracture network patterns with persistent homology","volume":"143","author":"Suzuki","year":"2020","journal-title":"Comput. Geosci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.21105\/joss.01296","article-title":"PoreSpy: A Python Toolkit for Quantitative Analysis of Porous Media Images","volume":"4","author":"Gostick","year":"2019","journal-title":"J. Open Source Softw."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2388","DOI":"10.1088\/1742-2140\/aac4c1","article-title":"A Study on Homogenization Equations of Fractal Porous Media","volume":"15","author":"Wu","year":"2018","journal-title":"J. Geophys. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Gunathilake, T.M.S.U., Ching, Y.C., Ching, K.Y., Chuah, C.H., and Abdullah, L.C. (2017). Biomedical and microbiological applications of bio-based porous materials: A review. Polymers, 9.","DOI":"10.3390\/polym9050160"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1002\/fuce.201700239","article-title":"Microstructure Reconstruction and Characterization of the Porous GDLs for PEMFC Based on Fibers Orientation Distribution","volume":"18","author":"Simaafrookhteh","year":"2018","journal-title":"Fuel Cells"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1149\/06501.0059ecst","article-title":"Analysis of Porosity and Tortuosity in a 2D Selected Region of Solid Oxide Fuel Cell Cathode Using the Lattice Boltzmann Method","volume":"65","author":"Espinoza","year":"2015","journal-title":"ECS Trans."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.matcom.2019.09.017","article-title":"On hydraulic tortuosity variations due to morphological considerations in 2D porous media by using the Lattice Boltzmann method","volume":"169","year":"2020","journal-title":"Math. Comput. Simul."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s11242-017-0835-y","article-title":"Pore-Scale Numerical Investigation of Pressure Drop Behaviour Across Open-Cell Metal Foams","volume":"117","author":"Morvan","year":"2017","journal-title":"Transp. Porous Media"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Grigoriev, M., Khafizov, A., Kokhan, V., and Asadchikov, V. (2020, January 2\u20136). Robust technique for representative volume element identification in noisy microtomography images of porous materials based on pores morphology and their spatial distribution. Proceedings of the Thirteenth International Conference on Machine Vision. International Society for Optics and Photonics, Rome, Italy.","DOI":"10.1117\/12.2586785"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s11242-020-01502-0","article-title":"A Novel Method for Streamline-Based Tortuosity Calculation and Investigation of Obstacles Shape Effect on Tortuosity in Porous Media with Random Elliptical Obstacles Using Lattice Boltzmann Method","volume":"136","author":"Ezzatabadipour","year":"2021","journal-title":"Transp. Porous Media"},{"key":"ref_35","unstructured":"Ferguson, D., Likhachev, M., and Stentz, A. (2005, January 5\u201310). A guide to heuristic-based path planning. Proceedings of the International Workshop on Planning under Uncertainty for Autonomous Systems, International Conference on Automated Planning and Scheduling (ICAPS), Monterey, CA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, C., Mao, Q., Chu, X., and Xie, S. (2019). An Improved A-star algorithm considering water current, traffic separation and berthing for vessel path planning. Appl. Sci., 9.","DOI":"10.3390\/app9061057"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2785","DOI":"10.1149\/07801.2785ecst","article-title":"Pore-Scale Analysis of Diffusion Transport Parameters in Digitally Reconstructed SOFC Anodes with Gradient Porosity in the Main Flow Direction","volume":"78","author":"Espinoza","year":"2017","journal-title":"ECS Trans."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Mohamad, A.A. (2019). Lattice Boltzmann Method, Springer. [2nd ed.].","DOI":"10.1007\/978-1-4471-7423-3"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.1149\/05701.2671ecst","article-title":"Microstructural Analysis of an LSCF Cathode Using In Situ Tomography and Simulation","volume":"57","author":"Cooper","year":"2013","journal-title":"ECS Trans."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3748","DOI":"10.1016\/j.ces.2007.03.041","article-title":"Critical review of the impact of tortuosity on diffusion","volume":"62","author":"Shen","year":"2007","journal-title":"Chem. Eng. Sci."},{"key":"ref_41","first-page":"406","article-title":"Tortuous flow in porous media","volume":"54","author":"Koponen","year":"1996","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1088\/0256-307X\/21\/8\/044","article-title":"A geometry model for tortuosity of flow path in porous media","volume":"21","author":"Yu","year":"2004","journal-title":"Chin. Phys. Lett."},{"key":"ref_43","first-page":"3","article-title":"Tortuosity of flow paths through a Sierpinski carpet","volume":"28","author":"Li","year":"2011","journal-title":"Chin. Phys. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Ritter, F.E., Schoelles, M.J., Quigley, K.S., and Klein, L.C. (2011). Determining the Number of Simulation Runs: Treating Simulations as Theories by Not Sampling Their Behavior. Human-in-the-Loop Simulations Methods Pract, Springer.","DOI":"10.1007\/978-0-85729-883-6_5"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/4\/59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:48:52Z","timestamp":1760136532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/4\/59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,2]]},"references-count":44,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["computation10040059"],"URL":"https:\/\/doi.org\/10.3390\/computation10040059","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2022,4,2]]}}}