{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:51:32Z","timestamp":1768344692492,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,3]],"date-time":"2020-04-03T00:00:00Z","timestamp":1585872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study deals with the mass transport phenomena on the particle-fluid motion through an annulus. The non-Newtonian fluid propagates through a ciliated annulus in the presence of two phenomenon, namely (i) endoscopy, and (ii) blood clot. The outer tube is ciliated. To examine the flow behavior we consider the bi-viscosity fluid model. The mathematical modeling has been formulated for small Reynolds number to examine the inertia free flow. The purpose of this assumption is that wavelength-to-diameter is maximal, and the pressure could be considerably uniform throughout the entire cross-section. The resulting equations are analytically solved, and exact solutions are given for particle- and fluid-phase profiles. Computational software Mathematica has been used to evaluate both the closed-form and numerical results. The graphical behavior across each parameter has been discussed in detail and presented with graphs. The trapping mechanism is also shown across each parameter. It is noticed clearly that particle volume fraction and the blood clot reveal converse behavior on fluid velocity; however, the velocity of the fluid reduced significantly when the fluid behaves as a Newtonian fluid. Schmidt and Soret numbers enhance the concentration mechanism. Furthermore, more pressure is required to pass the fluid when the blood clot appears.<\/jats:p>","DOI":"10.3390\/sym12040532","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T03:40:19Z","timestamp":1586403619000},"page":"532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3219-7579","authenticated-orcid":false,"given":"Muhammad Mubashir","family":"Bhatti","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"}]},{"given":"Asmaa F.","family":"Elelamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Ain Shams University, El Makrizy Street, Roxy, Heliopolis, 11566 Cairo, Egypt"}]},{"given":"Sadiq","family":"M. Sait","sequence":"additional","affiliation":[{"name":"Center for Communications and IT Research, Research Institute, King Fahd University of Petroleum &amp; Minerals, Dhahran 31261, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7805-8259","authenticated-orcid":false,"given":"Rahmat","family":"Ellahi","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, FBAS, IIUI, Islamabad 44000, Pakistan"},{"name":"Fulbright Fellow Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA"},{"name":"Center for Modeling &amp; Computer Simulation, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02476445","article-title":"Cilia transport","volume":"34","author":"Lardner","year":"1972","journal-title":"Bull. Math. 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