{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:24:16Z","timestamp":1767911056917,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["24-21-00356"],"award-info":[{"award-number":["24-21-00356"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Numerical modeling was conducted to study the capture of particles diffusing in porous media with traps. The pores are cylindrical in shape, and the traps are randomly distributed along the cylindrical surfaces of the pores. The dynamics of particle capture by the traps, as well as the filling of the traps, were investigated. In general, the decrease in the number of particles follows an exponential trend, with a characteristic time determined by the trap concentration. However, at longer times, extended plateaus emerge in the particle distribution function. Additionally, the dynamics of the interface boundary corresponding to the median trap filling (M = 0.5) were examined. This interface separates regions where traps are filled with a probability greater than 0.5 from regions where traps are filled with a probability less than 0.5. The motion of the interface over time was found to follow a logarithmic dependence. The influence of the radius of the pore on the capture on traps, which are placed on the internal surface of the cylinders, was investigated. The different dependencies of the extinction time on the number of traps were found at different radii of pores the first time.<\/jats:p>","DOI":"10.3390\/computation13040082","type":"journal-article","created":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T10:53:54Z","timestamp":1742900034000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Simulation of Capture of Diffusing Particles in Porous Media"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3468-0414","authenticated-orcid":false,"given":"Valeriy E.","family":"Arkhincheev","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Physics and Computer Sciences, Buryat State University, Ulan-Ude 670000, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7272-6810","authenticated-orcid":false,"given":"Bair V.","family":"Khabituev","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Physics and Computer Sciences, Buryat State University, Ulan-Ude 670000, Russia"}]},{"given":"Stanislav P.","family":"Maltsev","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Physics and Computer Sciences, Buryat State University, Ulan-Ude 670000, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1063\/1.1704269","article-title":"Random Walks on Lattices","volume":"6","author":"Montrol","year":"1965","journal-title":"J. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1016\/0032-3950(70)90173-5","article-title":"Diffusion control in reactions between macromolecules","volume":"12","author":"Kozlov","year":"1970","journal-title":"Polym. Sci. U.S.S.R."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/BF01090731","article-title":"Random walks on a flat lattice with traps","volume":"10","author":"Ryazanov","year":"1972","journal-title":"Theor. Math. Phys."},{"key":"ref_4","first-page":"1600","article-title":"Theory of diffuse phase transitions","volume":"65","author":"Balagurov","year":"1973","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_5","first-page":"1939","article-title":"Random walks of particles on lattices with traps","volume":"65","author":"Balagurov","year":"1973","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1007\/BF01049606","article-title":"Diffusion and Reaction Among Traps: Some Theoretical and Simulation Results","volume":"65","author":"Torquato","year":"1991","journal-title":"J. Stat. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"118857","DOI":"10.1016\/j.actamat.2023.118857","article-title":"Simulated diffusion spreadability for characterizing the structure and transport properties of two-phase materials","volume":"250","author":"Skolnick","year":"2023","journal-title":"Acta Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1002\/cpa.3160280406","article-title":"Asymptotics for the Wiener sausage","volume":"28","author":"Donsker","year":"1975","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"100601","DOI":"10.1103\/PhysRevLett.117.100601","article-title":"Langevin Equations for Reaction-Diffusion Processes","volume":"117","author":"Benitez","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s00220-012-1492-1","article-title":"Self-Attractive Random Walks: The Case of Critical Drifts","volume":"313","author":"Ioffe","year":"2012","journal-title":"Commun. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"063027","DOI":"10.1088\/1367-2630\/14\/6\/063027","article-title":"The true reinforced random walk with bias","volume":"14","author":"Agliari","year":"2012","journal-title":"New J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1134\/S1063776117010022","article-title":"Effect of drift on the temporal asymptotic form of the particle survival probability in media with absorbing traps","volume":"124","author":"Arkhincheev","year":"2017","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8793","DOI":"10.1063\/1.1567460","article-title":"Low Dielectric Constant Materials for Micro Electronics","volume":"93","author":"Maex","year":"2003","journal-title":"J. Appl. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.mee.2010.07.014","article-title":"Integrated diffusion\u2013recombination model for describing the logarithmic time dependence of plasma damage in porous low-k materials","volume":"88","author":"Kunnen","year":"2011","journal-title":"Microelectron. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Rasadujjaman, M., Wang, X., Wang, Y., Zhang, J., Arkhincheev, V.E., and Baklanov, M.R. (2021). Analytical Study of Porous Organosilicate Glass Films Prepared from Mixtures of 1,3,5- and 1,3-Alkoxysilylbenzenes. Materials, 14.","DOI":"10.3390\/ma14081881"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"050802","DOI":"10.1116\/6.0002793","article-title":"Challenges in porosity characterization of thin films:cross-evaluation of different techniques","volume":"41","author":"Baklanov","year":"2021","journal-title":"J. Vac. Sci. Technol. A Vac. Surf. Film."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1088\/0034-4885\/64\/7\/202","article-title":"Diffusion and Related Transport Mechanisms in Brain Tissue","volume":"64","author":"Nicholson","year":"2001","journal-title":"Rep. Prog. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1080\/21681163.2021.1956370","article-title":"3D FEM Model to Simulate Brownian Motion inside Trabecular Tissue from Human Femoral Head","volume":"10","author":"Bini","year":"2022","journal-title":"Comput. Methods Biomech. Biomed. Eng. Imaging Vis."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bini, F., Pica, A., Marinozzi, A., and Marinozzi, F. (2021). 3D random walk model of diffusion in human Hypo- and Hyper- mineralized collagen fibrils. J. Biomech., 125.","DOI":"10.1016\/j.jbiomech.2021.110586"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bini, F., Pica, A., Marinozzi, A., and Marinozzi, F. (2019). A 3D model of the effect of tortuosity and constrictivity on the diffusion in mineralized collagen fibril. Sci. Rep., 9.","DOI":"10.1038\/s41598-019-39297-w"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s00249-010-0629-4","article-title":"Diffusion tensor of water in articular cartilage","volume":"40","author":"Momot","year":"2011","journal-title":"Eur. Biophys. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1529\/biophysj.108.131466","article-title":"Random-Walk model of diffusion in three dimensions in brain extracellular space: Comparison with microfiberoptic photobleaching measurements","volume":"95","author":"Jin","year":"2008","journal-title":"Biophys. J."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Maghsoudi-Ganjeh, M., Wang, X., and Zeng, X. (2020). Computational investigation of the effect of water on the nanomechanical behavior of bone. J. Mech. Behav. Biomed. Mater. V, 101.","DOI":"10.1016\/j.jmbbm.2019.103454"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Vilinski-Mazur, K., Kirillov, B., Rogozin, O., and Kolomenskiy, D. (2025). Numerical modeling of oxygen diffusion in tissue spheroids undergoing fusion using function representation and finite volumes. Sci. Rep., 15.","DOI":"10.1038\/s41598-025-86805-2"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"245320","DOI":"10.1103\/PhysRevB.83.245320","article-title":"Saturation of front propagation in a reaction-diffusion process describing plasma damage in porous low-k materials","volume":"83","author":"Safaverdi","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_26","first-page":"686","article-title":"Active species in porous media: Random walk and capture in traps","volume":"88","author":"Arkhincheev","year":"2011","journal-title":"J. Microelectron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1016\/j.apsusc.2019.01.078","article-title":"Influence of porosity and pore size on sputtering of nanoporous structures by low-energy Ar ions: Molecular dynamics study","volume":"475","author":"Sycheva","year":"2019","journal-title":"Appl. Surf. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1134\/S1027451019060521","article-title":"Analysis of results of silicon sputtering simulation with various Ar\u2013Si potentials","volume":"13","author":"Sycheva","year":"2019","journal-title":"J. Surf. Investig. X-Ray Synchrotron Neutron Tech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"101161","DOI":"10.1016\/j.bonr.2021.101161","article-title":"Bone Hydration: How We Can Evaluate It, What Can It Tell Us, and Is It an Effective Therapeutic Target?","volume":"16","author":"Surowiec","year":"2022","journal-title":"Bone Rep."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1038\/nmat3787","article-title":"Water-Mediated Structuring of Bone Apatite","volume":"12","author":"Wang","year":"2013","journal-title":"Nat. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"14219","DOI":"10.1021\/jp2025768","article-title":"Dehydration-Induced Structural Changes in the Collagen-Hydroxyapatite Interface in Bone by High-Resolution Solid-State NMR Spectroscopy","volume":"115","author":"Rai","year":"2011","journal-title":"J. Phys. Chem. C"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/4\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:58:24Z","timestamp":1760029104000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/4\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,22]]},"references-count":31,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["computation13040082"],"URL":"https:\/\/doi.org\/10.3390\/computation13040082","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,22]]}}}