{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T06:52:01Z","timestamp":1778223121314,"version":"3.51.4"},"reference-count":0,"publisher":"Wiley","issue":"46","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>The creeping flow through a swarm of spherical particles that\nmove with constant velocity in an arbitrary direction and rotate\nwith an arbitrary constant angular velocity in a quiescent\nNewtonian fluid is analyzed with a 3D sphere\u2010in\u2010cell model. The\nmathematical treatment is based on the two\u2010concentric\u2010spheres\nmodel. The inner sphere comprises one of the particles in the\nswarm and the outer sphere consists of a fluid envelope. The\nappropriate boundary conditions of this non\u2010axisymmetric\nformulation are similar to those of the 2D sphere\u2010in\u2010cell Happel\nmodel, namely, nonslip flow condition on the surface of the solid\nsphere and nil normal velocity component and shear stress on the\nexternal spherical surface. The boundary value problem is solved\nwith the aim of the complete Papkovich\u2010Neuber differential\nrepresentation of the solutions for Stokes flow, which is valid\nin non\u2010axisymmetric geometries and provides us with the velocity\nand total pressure fields in terms of harmonic spherical\neigenfunctions. The solution of this 3D model, which is\nself\u2010sufficient in mechanical energy, is obtained in closed form\nand analytical expressions for the velocity, the total pressure,\nthe angular velocity, and the stress tensor fields are provided.<\/jats:p>","DOI":"10.1155\/s0161171204312445","type":"journal-article","created":{"date-parts":[[2004,9,22]],"date-time":"2004-09-22T15:41:23Z","timestamp":1095867683000},"page":"2429-2441","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["The 3D Happel model for complete isotropic Stokes flow"],"prefix":"10.1155","volume":"2004","author":[{"given":"George","family":"Dassios","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panayiotis","family":"Vafeas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,9,22]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/493272.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204312445","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T21:08:18Z","timestamp":1723064898000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204312445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"46","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204312445"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204312445","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-12-04","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-09-22","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}