{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T09:28:31Z","timestamp":1768037311226,"version":"3.49.0"},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper reports the implementation of slip boundary conditions in the open-source computational library OpenFOAM. The linear and nonlinear Navier slip laws, which are newly implemented in this paper, can be used both for Newtonian and viscoelastic constitutive models. For the former case, the Couette flow assumption near the wall is employed, and for the latter, the cell-centered extra-stress tensor components are linearly extrapolated to the wall. The validation is performed by comparing the numerical results obtained for Newtonian and simplified Phan-Thien-Tanner constitutive model fluids in Couette and Poiseuille flows, with existing analytical solutions. The results obtained using different slip factors were shown to be in agreement with the analytical solutions, even for the most extreme cases where the slip factor is high enough to induce a plug flow pattern for the velocity field. The newly implemented boundary conditions are also used to study the influence of slip in polymer processing, namely in the production of an extruded profile. The results obtained show that the developed slip boundary conditions are able to deal with complex geometrical problems, and are an important tool to support the search of a balanced flow distribution in the design of profile extrusion dies.<\/jats:p>","DOI":"10.1515\/polyeng-2018-0343","type":"journal-article","created":{"date-parts":[[2019,2,28]],"date-time":"2019-02-28T09:05:03Z","timestamp":1551344703000},"page":"377-387","source":"Crossref","is-referenced-by-count":4,"title":["Implementation of partial slip boundary conditions in an open-source finite-volume-based computational library"],"prefix":"10.1515","volume":"39","author":[{"given":"C\u00e9lio","family":"Fernandes","sequence":"first","affiliation":[{"name":"Institute for Polymers and Composites\/i3N, University of Minho , Campus de Azur\u00e9m , 4800-058 Guimar\u00e3es , Portugal"}]},{"given":"Lu\u00eds Lima","family":"Ferr\u00e1s","sequence":"additional","affiliation":[{"name":"Institute for Polymers and Composites\/i3N, University of Minho , Campus de Azur\u00e9m , 4800-058 Guimar\u00e3es , Portugal"}]},{"given":"Florian","family":"Habla","sequence":"additional","affiliation":[{"name":"Catalysis Research Center and Chemistry Department , Technische Universit\u00e4t M\u00fcnchen , Lichtenbergstra\u03b2e 4, D-85748 Garching b. , M\u00fcnchen , Germany"}]},{"given":"Olga Sousa","family":"Carneiro","sequence":"additional","affiliation":[{"name":"Institute for Polymers and Composites\/i3N, University of Minho , Campus de Azur\u00e9m , 4800-058 Guimar\u00e3es , Portugal"}]},{"given":"Jo\u00e3o Miguel","family":"N\u00f3brega","sequence":"additional","affiliation":[{"name":"Institute for Polymers and Composites\/i3N, University of Minho , Campus de Azur\u00e9m , 4800-058 Guimar\u00e3es , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2019,2,28]]},"reference":[{"key":"2023040101025997601_j_polyeng-2018-0343_ref_001_w2aab3b7d185b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Mitsoulis E, Kazatchkov I, Hatzikiriakos SG. Rheol. Acta 2005, 44, 418\u2013426.","DOI":"10.1007\/s00397-004-0423-2"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_002_w2aab3b7d185b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"Reilly FJ, Price WL. SPE J. 1961, 17, 1097\u20131101.","DOI":"10.1177\/003591576105401209"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_003_w2aab3b7d185b1b6b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"Benbow J, Lamb P. Polym. Eng. Sci. 1963, 3, 7\u201317.","DOI":"10.1002\/pen.760030104"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_004_w2aab3b7d185b1b6b1ab2b1b4Aa","unstructured":"Archer LA, Eds., Polymer Processing Instabilities, Marcel Dekker, New York, 2005."},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_005_w2aab3b7d185b1b6b1ab2b1b5Aa","doi-asserted-by":"crossref","unstructured":"Hatzikiriakos SG. Prog. Polym. Sci. 2012, 37, 624\u2013643.","DOI":"10.1016\/j.progpolymsci.2011.09.004"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_006_w2aab3b7d185b1b6b1ab2b1b6Aa","unstructured":"Lauga E, Brenner MP, Stone HA, Eds., Handbook of Experimental Fluid Dynamics, Springer, New York, 2006."},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_007_w2aab3b7d185b1b6b1ab2b1b7Aa","doi-asserted-by":"crossref","unstructured":"Neto C, Evans DR, Bonaccurso E, Butt HJ, Craig VSJ. Rep. Prog. Phys. 2005, 68, 2859\u20132897.","DOI":"10.1088\/0034-4885\/68\/12\/R05"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_008_w2aab3b7d185b1b6b1ab2b1b8Aa","unstructured":"Navier CLMH. Mem. Acad. Sci. Inst. Fr. 1822, 6, 389\u2013440."},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_009_w2aab3b7d185b1b6b1ab2b1b9Aa","doi-asserted-by":"crossref","unstructured":"Schowalter W. J. Non-Newtonian Fluid Mech. 1988, 29, 25\u201336.","DOI":"10.1016\/0377-0257(88)85048-1"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_010_w2aab3b7d185b1b6b1ab2b1c10Aa","doi-asserted-by":"crossref","unstructured":"Brochard F, de Gennes PG. Langmuir 1992, 8, 3033\u20133037.","DOI":"10.1021\/la00048a030"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_011_w2aab3b7d185b1b6b1ab2b1c11Aa","doi-asserted-by":"crossref","unstructured":"Denn MM. Annu. Rev. Fluid Mech. 2001, 33, 265\u2013287.","DOI":"10.1146\/annurev.fluid.33.1.265"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_012_w2aab3b7d185b1b6b1ab2b1c12Aa","doi-asserted-by":"crossref","unstructured":"Hatzikiriakos SG, Dealy JM. J. Rheol. 1991, 35, 497\u2013523.","DOI":"10.1122\/1.550178"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_013_w2aab3b7d185b1b6b1ab2b1c13Aa","doi-asserted-by":"crossref","unstructured":"Hatzikiriakos SG, Dealy JM. J. Rheol. 1992, 36, 703\u2013741.","DOI":"10.1122\/1.550313"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_014_w2aab3b7d185b1b6b1ab2b1c14Aa","doi-asserted-by":"crossref","unstructured":"Hatzikiriakos SG, Dealy JM. Int. Polym. Process. 1993, 8, 36\u201343.","DOI":"10.3139\/217.930036"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_015_w2aab3b7d185b1b6b1ab2b1c15Aa","doi-asserted-by":"crossref","unstructured":"Kountouriotis Z, Georgiou GC, Mitsoulis E. Comput. Fluids 2013, 71, 297\u2013305.","DOI":"10.1016\/j.compfluid.2012.09.026"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_016_w2aab3b7d185b1b6b1ab2b1c16Aa","doi-asserted-by":"crossref","unstructured":"Phan-Thien N, Tanner RI. J. Non-Newtonian Fluid Mech. 1977, 2, 353\u2013365.","DOI":"10.1016\/0377-0257(77)80021-9"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_017_w2aab3b7d185b1b6b1ab2b1c17Aa","doi-asserted-by":"crossref","unstructured":"Fernandes C, Ara\u00fajo MSB, Ferr\u00e1s LL, N\u00f3brega JM. J. Non-Newtonian Fluid Mech. 2017, 249, 63\u201378.","DOI":"10.1016\/j.jnnfm.2017.09.008"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_018_w2aab3b7d185b1b6b1ab2b1c18Aa","doi-asserted-by":"crossref","unstructured":"Ferr\u00e1s LL, Pinho FT, N\u00f3brega JM. J. Non-Newtonian Fluid Mech. 2012, 175176, 76\u201388.","DOI":"10.1016\/j.jnnfm.2012.03.004"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_019_w2aab3b7d185b1b6b1ab2b1c19Aa","doi-asserted-by":"crossref","unstructured":"Ferr\u00e1s LL, N\u00f3brega JM, Pinho FT. J. Non-Newtonian Fluid Mech. 2012, 171172, 97\u2013105.","DOI":"10.1016\/j.jnnfm.2012.01.009"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_020_w2aab3b7d185b1b6b1ab2b1c20Aa","doi-asserted-by":"crossref","unstructured":"N\u00f3brega JM, Carneiro OS, Oliveira PJ, Pinho FT. Int. Polym. Process. 2003, 18, 298\u2013306.","DOI":"10.3139\/217.1745"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_021_w2aab3b7d185b1b6b1ab2b1c21Aa","unstructured":"Carneiro OS, N\u00f3brega JM, Eds., Design of Extrusion Forming Tools, Smithers Rapra Technology: Shrewsbury\/UK, 2012."},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_022_w2aab3b7d185b1b6b1ab2b1c22Aa","doi-asserted-by":"crossref","unstructured":"Gon\u00e7alves ND, Pereira SP, Ferr\u00e1s LL, N\u00f3brega JM, Carneiro OS. Int. Polym. Process. 2015, 30, 442\u2013450.","DOI":"10.3139\/217.2957"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_023_w2aab3b7d185b1b6b1ab2b1c23Aa","doi-asserted-by":"crossref","unstructured":"Rajkumar A, Ferr\u00e1s LL, Fernandes C, Carneiro OS, Sacramento A, N\u00f3brega JM. Int. Polym. Process. 2018, 33, 276\u2013285.","DOI":"10.3139\/217.3514"},{"key":"2023040101025997601_j_polyeng-2018-0343_ref_024_w2aab3b7d185b1b6b1ab2b1c24Aa","doi-asserted-by":"crossref","unstructured":"Carneiro OS, N\u00f3brega JM, Oliveira PJ, Pinho FT. Int. Polym. Process. 2003, 18, 307\u2013312.","DOI":"10.3139\/217.1746"}],"container-title":["Journal of Polymer Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/polyeng.2019.39.issue-4\/polyeng-2018-0343\/polyeng-2018-0343.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/polyeng-2018-0343\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/polyeng-2018-0343\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T17:41:22Z","timestamp":1680370882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/polyeng-2018-0343\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,28]]},"references-count":24,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,2,28]]},"published-print":{"date-parts":[[2019,3,26]]}},"alternative-id":["10.1515\/polyeng-2018-0343"],"URL":"https:\/\/doi.org\/10.1515\/polyeng-2018-0343","relation":{},"ISSN":["2191-0340","0334-6447"],"issn-type":[{"value":"2191-0340","type":"electronic"},{"value":"0334-6447","type":"print"}],"subject":[],"published":{"date-parts":[[2019,2,28]]}}}