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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">10.17586/2220-8054-2026-17-4-442-451</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-1906</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>Theoretical investigation of the effects of viscosity variation, couple stress, and slip velocity on squeeze film lubrication of porous conical bearings</article-title><trans-title-group xml:lang="ru"><trans-title>Теоретическое исследование влияния изменения вязкости, моментного напряжения и скорости скольжения на пленочную смазку пористых конических подшипников</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бирадар</surname><given-names>Кашинат</given-names></name><name name-style="western" xml:lang="en"><surname>Biradar (Rtd.)</surname><given-names>Kashinath</given-names></name></name-alternatives><bio xml:lang="en"><p>Kashinath Biradar (Rtd.)  – Department of Mathematics</p><p>Sedam, Karnataka</p></bio><email xlink:type="simple">kbbiradar@yahoo.co.in</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8433-2891</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Упадхья</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Upadhya</surname><given-names>Adinatha C.</given-names></name></name-alternatives><bio xml:lang="en"><p>Adinatha C. Upadhya – Department of Mathematics</p><p>Belagavi, Ka nataka</p></bio><email xlink:type="simple">adinatha06@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Government First Grade College</institution><country>India</country></aff><aff xml:lang="en" id="aff-2"><institution>Sangolli Rayanna First Grade Constituent College</institution><country>India</country></aff><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>31</day><month>08</month><year>2026</year></pub-date><volume>17</volume><issue>4</issue><fpage>442</fpage><lpage>451</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Biradar (Rtd.) K., Upadhya A.C., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Бирадар К., Упадхья А.С.</copyright-holder><copyright-holder xml:lang="en">Biradar (Rtd.) K., Upadhya A.C.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" 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/1906">https://nanojournal.ifmo.ru/jour/article/view/1906</self-uri><abstract><p>This study examines the effects of viscosity variation and velocity slip on the performance of porous conical bearings lubricated with a couple stress fluid. Darcy’s law is used to describe fluid flow through the porous medium, while Stokes’ couple stress theory accounts for the microstructure of the lubricant. A modified Reynolds equation is developed by incorporating viscosity variation and slip effects. Numerical results illus- trate the influence of couple stress, slip velocity, permeability, and viscosity variation on pressure distribution, load-carrying capacity, and squeeze film time. It is observed that an increase in the couple stress parameter enhances the pressure and load capacity, while higher permeability tends to reduce the supporting ability of the bearing. The presence of slip at the boundary modifies the flow behaviour and contributes to improved lubrica- tion characteristics. The combined effects of porous structure and slip lead to better aggregate performance, and the use of couple stress fluids significantly improves lubrication efficiency and operational reliability.</p></abstract><trans-abstract xml:lang="ru"><p>В данном исследовании изучается влияние изменения вязкости и скольжения скорости на характеристики пористых конических подшипников, смазываемых жидкостью с учетом моментных напряжений. Закон Дарси используется для описания течения жидкости через пористую среду, а теория моментных напряжений Стокса учитывает микроструктуру смазки. Разработано модифицированное уравнение Рейнольдса с учетом изменения вязкости и эффектов скольжения. Численные результаты иллюстрируют влияние моментных напряжений, скорости скольжения, проницаемости и изменения вязкости на распределение давления, несущую способность и время сжатой пленки. Наблюдается, что увеличение параметра моментных напряжений повышает давление и несущую способность, в то время как более высокая проницаемость, как правило, снижает несущую способность подшипника. Наличие скольжения на границе изменяет поведение потока и способствует улучшению характеристик смазки. Совместное воздействие пористой структуры и скольжения приводит к улучшению общих характеристик, а использование жидкостей с учетом моментных напряжений значительно повышает эффективность смазки и эксплуатационную надежность.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>жидкость с учетом парных напряжений</kwd><kwd>изменение вязкости</kwd><kwd>проскальзывание скорости</kwd><kwd>пористый конический подшипник</kwd></kwd-group><kwd-group xml:lang="en"><kwd>couple stress fluid</kwd><kwd>viscosity variation</kwd><kwd>velocity slip</kwd><kwd>porous conical bearing</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Stokes V.K. Couple stresses in fluids. Physics of Fluids, 1966, 9(9), P. 1709–1715.</mixed-citation><mixed-citation xml:lang="en">Stokes V.K. Couple stresses in fluids. 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