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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2019-10-3-235-242</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-548</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Effect of periodic permeability of lung airways on the flow dynamics of viscous fluid</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Kori</surname><given-names>J.</given-names></name></name-alternatives><bio xml:lang="en"><p>Roorkee-247667, Uttarakhand</p></bio><email xlink:type="simple">jyotikorii@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Pratibha</surname><given-names>.</given-names></name></name-alternatives><bio xml:lang="en"><p>Roorkee-247667, Uttarakhand</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="en">Department of Mathematics, Indian Institute of Technology Roorkee<country>India</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>07</day><month>08</month><year>2025</year></pub-date><volume>10</volume><issue>3</issue><fpage>235</fpage><lpage>242</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Kori J., Pratibha .., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Kori J., Pratibha ..</copyright-holder><copyright-holder xml:lang="en">Kori J., Pratibha ..</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/548">https://nanojournal.ifmo.ru/jour/article/view/548</self-uri><abstract><p>In this study, we aimed to find the effect of periodic permeability on the flow dynamics of an incompressible, Newtonian, viscous and pulsatile flow of air flowing through airway generations 5–10. To solve this problem, we used a generalized Navier Stokes equation by including the Darcy law of a porous media with periodic permeability for the flow of air and Newton equation of motion for the flow of nanoparticles. The finite difference explicit numerical scheme has been carried out to solve the governing nonlinear equations and then computational work is done on MATLAB R2016 by user defined code. After performing numerical computation we found by varying mean permeability of porous media velocity of air and particle increased gradually with axial and radial distance respectively.</p></abstract><kwd-group xml:lang="en"><kwd>lung generation</kwd><kwd>deposition</kwd><kwd>periodic permeability</kwd><kwd>pulsatile flow</kwd><kwd>nanoparticle</kwd></kwd-group><funding-group xml:lang="en"><funding-statement>One of the authors, Jyoti Kori, is thankful to Ministry of Human Resource Development India (Grant Code:- MHR-02-23-200-44) for providing fund and support while writing this manuscript.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Heyder J. Deposition of Inhaled Particles in the Human Respiratory Tract and Consequences for Regional Targeting in Respiratory Drug Delivery. Proc Am Thorac Soc., 2004, P. 315-320.</mixed-citation><mixed-citation xml:lang="en">Heyder J. Deposition of Inhaled Particles in the Human Respiratory Tract and Consequences for Regional Targeting in Respiratory Drug Delivery. Proc Am Thorac Soc., 2004, P. 315-320.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Kori J., Pratibha. Numerical Simulation of Dusty Air Flow and Particle Deposition Inside Permeable Alveolar Duct. Int. J. Appl. Comput. Math, 2019, 5, P. 1–13.</mixed-citation><mixed-citation xml:lang="en">Kori J., Pratibha. Numerical Simulation of Dusty Air Flow and Particle Deposition Inside Permeable Alveolar Duct. Int. J. Appl. Comput. Math, 2019, 5, P. 1–13.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Tian L., Shang Y., Chen R., Bai R., Chen C., Inthavong K., Tu1 J. A combined experimental and numerical study on upper airway dosimetry of inhaled nanoparticles from an electrical discharge machine shop. Particle and Fibre Toxicology, 2017, 14, P. 24.</mixed-citation><mixed-citation xml:lang="en">Tian L., Shang Y., Chen R., Bai R., Chen C., Inthavong K., Tu1 J. A combined experimental and numerical study on upper airway dosimetry of inhaled nanoparticles from an electrical discharge machine shop. Particle and Fibre Toxicology, 2017, 14, P. 24.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Li D., Xu Q., Liu Y., Libao Y., Jun J. Numerical Simulation of Particles Deposition in a Human Upper Airway. Advances in Mechanical Engineering, 2014.</mixed-citation><mixed-citation xml:lang="en">Li D., Xu Q., Liu Y., Libao Y., Jun J. Numerical Simulation of Particles Deposition in a Human Upper Airway. Advances in Mechanical Engineering, 2014.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Sturm R. Theoretical deposition of carcinogenic particle aggregates in the upper respiratory tract. Ann Transl Med., 2013, 1, P. 25.</mixed-citation><mixed-citation xml:lang="en">Sturm R. Theoretical deposition of carcinogenic particle aggregates in the upper respiratory tract. Ann Transl Med., 2013, 1, P. 25.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Sturm R. A computer model for the simulation of nanoparticle deposition in the alveolar structures of the human lungs. Ann Transl Med., 2015, 3, P. 281.</mixed-citation><mixed-citation xml:lang="en">Sturm R. A computer model for the simulation of nanoparticle deposition in the alveolar structures of the human lungs. Ann Transl Med., 2015, 3, P. 281.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Saini A., Katiyar V.K., Pratibha. Two-dimensional model of nanoparticle deposition in the alveolar ducts of the human lung. Applications &amp; Applied Mathematics, 2017, 12, P. 305–318.</mixed-citation><mixed-citation xml:lang="en">Saini A., Katiyar V.K., Pratibha. Two-dimensional model of nanoparticle deposition in the alveolar ducts of the human lung. Applications &amp; Applied Mathematics, 2017, 12, P. 305–318.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Haber S., Yitzhak D., Tsuda A. Gravitational deposition in a rhythmically expanding and contracting alveolus. J. Appl. Physiol., 2013, 95, P. 657–671.</mixed-citation><mixed-citation xml:lang="en">Haber S., Yitzhak D., Tsuda A. Gravitational deposition in a rhythmically expanding and contracting alveolus. J. Appl. Physiol., 2013, 95, P. 657–671.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">DeGroot C.T., Straatman A.G. A porous media model of alveolar duct flow in the human lung. Journal of Porous Media, 2018.</mixed-citation><mixed-citation xml:lang="en">DeGroot C.T., Straatman A.G. A porous media model of alveolar duct flow in the human lung. Journal of Porous Media, 2018.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Khanafer K., Cook K., Marafie A. The Role of Porous Media in Modeling Fluid Flow Within Hollow Fiber Membranes of The Total Artificial Lung. J. Porous Media, 2012, 15, P. 113–122.</mixed-citation><mixed-citation xml:lang="en">Khanafer K., Cook K., Marafie A. The Role of Porous Media in Modeling Fluid Flow Within Hollow Fiber Membranes of The Total Artificial Lung. J. Porous Media, 2012, 15, P. 113–122.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Cheng P. Heat Transfer in Geothermal Systems. Advances in Heat Transfer, 1979, 14, P. 1–105.</mixed-citation><mixed-citation xml:lang="en">Cheng P. Heat Transfer in Geothermal Systems. Advances in Heat Transfer, 1979, 14, P. 1–105.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Vafai K., Tien C.L. Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media. Int. J. Heat Mass Transfer, 1981, 24, P. 195–203.</mixed-citation><mixed-citation xml:lang="en">Vafai K., Tien C.L. Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media. Int. J. Heat Mass Transfer, 1981, 24, P. 195–203.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Kuwahara F., Sano Y., Liu J., Nakayama A. A Porous Media Approach for Bifurcating Flow and Mass Transfer in a Human Lung. J. Heat Transfer, 2009, 131, P. 101013-5.</mixed-citation><mixed-citation xml:lang="en">Kuwahara F., Sano Y., Liu J., Nakayama A. A Porous Media Approach for Bifurcating Flow and Mass Transfer in a Human Lung. J. Heat Transfer, 2009, 131, P. 101013-5.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Saini A., Katiyar V.K., Pratibha. Numerical simulation of gas flow through a biofilter in lung tissues. World Journal of Modelling and Simulation, 2015, 11, P. 33–42.</mixed-citation><mixed-citation xml:lang="en">Saini A., Katiyar V.K., Pratibha. Numerical simulation of gas flow through a biofilter in lung tissues. World Journal of Modelling and Simulation, 2015, 11, P. 33–42.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Balashazy I., Hofmann W., Farkas A.,, Madas B.G. Three-dimensional model for aerosol transport and deposition in expanding and contracting alveoli. Inhalation Toxicology, 2008, 20, P. 611–621.</mixed-citation><mixed-citation xml:lang="en">Balashazy I., Hofmann W., Farkas A.,, Madas B.G. Three-dimensional model for aerosol transport and deposition in expanding and contracting alveoli. Inhalation Toxicology, 2008, 20, P. 611–621.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Sturm R., Hofmann W. A theoretical approach to the deposition and clearance of fibers with variable size in the human respiratory tract. J. of Hazardous Materials, 2009, 170, P. 210–218.</mixed-citation><mixed-citation xml:lang="en">Sturm R., Hofmann W. A theoretical approach to the deposition and clearance of fibers with variable size in the human respiratory tract. J. of Hazardous Materials, 2009, 170, P. 210–218.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Darcy H. Les Fontaines Publiques de la Ville de Dijon. Dalmont, Paris, 1856.</mixed-citation><mixed-citation xml:lang="en">Darcy H. Les Fontaines Publiques de la Ville de Dijon. Dalmont, Paris, 1856.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Singh K.D., Verma G.N. Three-Dimensional Oscillatory Flow through a Porous Medium with Periodic Permeability. Z. Angew. Math. Mech., 1995, 75, P. 599–604.</mixed-citation><mixed-citation xml:lang="en">Singh K.D., Verma G.N. Three-Dimensional Oscillatory Flow through a Porous Medium with Periodic Permeability. Z. Angew. Math. Mech., 1995, 75, P. 599–604.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Kori J., Pratibha. Numerical Simulation of Mucus Clearance inside Lung Airways. Journal of Applied Fluid Mechanics, 2018, 11, P. 1163– 1171.</mixed-citation><mixed-citation xml:lang="en">Kori J., Pratibha. Numerical Simulation of Mucus Clearance inside Lung Airways. Journal of Applied Fluid Mechanics, 2018, 11, P. 1163– 1171.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Kori J., Pratibha. Simulation and Modeling for Aging and Particle Shape Effect on Airflow Dynamics and Filtration Efficiency of Human Lung, Journal of Applied Fluid Mechanics, 2019, 12, P. 1273–1285.</mixed-citation><mixed-citation xml:lang="en">Kori J., Pratibha. Simulation and Modeling for Aging and Particle Shape Effect on Airflow Dynamics and Filtration Efficiency of Human Lung, Journal of Applied Fluid Mechanics, 2019, 12, P. 1273–1285.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Smith S., Cheng U.S., Yeh H.C. Deposition of ultrafine particles in human tracheobronchial airways of adults and children. Aerosol Sci. Tech., 2010, 35, P. 697–709.</mixed-citation><mixed-citation xml:lang="en">Smith S., Cheng U.S., Yeh H.C. Deposition of ultrafine particles in human tracheobronchial airways of adults and children. Aerosol Sci. Tech., 2010, 35, P. 697–709.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Seraa T., Uesugib K., Yagib N., Yokotac H. Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model. Computer Methods in Biomechanics and Biomedical Engineering, 2013, 18, P. 1427-1435.</mixed-citation><mixed-citation xml:lang="en">Seraa T., Uesugib K., Yagib N., Yokotac H. Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model. Computer Methods in Biomechanics and Biomedical Engineering, 2013, 18, P. 1427-1435.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Koullapis P.G., Kassinos S.C., Bivolarova M.P., Melikov A.K. Particle deposition in a realistic geometry of the human conducting airways: Effects of inlet velocity profile, inhalation flowrate and electrostatic charge. J Biomech., 2016, 49(11), P. 2201–2212.</mixed-citation><mixed-citation xml:lang="en">Koullapis P.G., Kassinos S.C., Bivolarova M.P., Melikov A.K. Particle deposition in a realistic geometry of the human conducting airways: Effects of inlet velocity profile, inhalation flowrate and electrostatic charge. J Biomech., 2016, 49(11), P. 2201–2212.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Ismail Z., Abdullah I., Mustapha N., Amin N. A power-law model of blood flow through a tapered overlapping stenosed artery. Appl. Math. Comput., 2007, 195, P. 669–680.</mixed-citation><mixed-citation xml:lang="en">Ismail Z., Abdullah I., Mustapha N., Amin N. A power-law model of blood flow through a tapered overlapping stenosed artery. Appl. Math. Comput., 2007, 195, P. 669–680.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Kapur J.N. Mathematical Models in Biology and Medicine. East-West Press, Pvt. Ltd., New Delhi, 1985.</mixed-citation><mixed-citation xml:lang="en">Kapur J.N. Mathematical Models in Biology and Medicine. East-West Press, Pvt. Ltd., New Delhi, 1985.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Mandal P.K. An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis. Int. J. Non-Linear Mech., 2005, 40, P. 151–164.</mixed-citation><mixed-citation xml:lang="en">Mandal P.K. An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis. Int. J. Non-Linear Mech., 2005, 40, P. 151–164.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Singh P., Misra J.K., Narayan K.A. Free convection along a vertical wall in a porous medium with periodic permeability variation. Int. J. Numer. Anal. Methods Geomech., 1989, 13.</mixed-citation><mixed-citation xml:lang="en">Singh P., Misra J.K., Narayan K.A. Free convection along a vertical wall in a porous medium with periodic permeability variation. Int. J. Numer. Anal. Methods Geomech., 1989, 13.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
