{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T22:22:35Z","timestamp":1778624555053,"version":"3.51.4"},"reference-count":29,"publisher":"The Royal Society","issue":"2143","license":[{"start":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T00:00:00Z","timestamp":1551657600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"name":"University of Greenwich Vice Chancellor postgraduate grant scheme"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Phil. Trans. R. Soc. A."],"published-print":{"date-parts":[[2019,4,22]]},"abstract":"<jats:p>The fundamental mechanisms governing macroscopic freckle defect formation during directional solidification are studied experimentally in a Hele\u2013Shaw cell for a low-melting point Ga-25\u2009wt.% In alloy and modelled numerically in three dimensions using a microscopic parallelized Cellular Automata Lattice Boltzmann Method. The size and distribution of freckles (long solute channels, or chimneys) are shown to be strongly dependent on the thermal profile of the casting, with flat, concave and convex isotherms being considered. For the flat isotherm case, no large-scale freckles form, while for concave or convex isotherms, large freckles appear but in different locations. The freckle formation mechanism is as expected buoyancy-driven, but the chimney stability, its long-term endurance and its location are shown to depend critically on the detailed convective transport through the inter-dendritic region. Flow is generated by curved isopleths of solute concentration. As solute density is different from that of the bulk fluid, gravity causes \u2018uphill\u2019 or \u2018downhill\u2019 lateral flow from the sample centre to the edges through the mush, feeding the freckle. An excellent agreement is obtained between the numerical model and real-time X-ray observations of a solidifying sample under strictly controlled temperature conditions.<\/jats:p>\n                  <jats:p>This article is part of the theme issue \u2018Heterogeneous materials: metastable and non-ergodic internal structures\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2018.0206","type":"journal-article","created":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T03:05:55Z","timestamp":1551668755000},"page":"20180206","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":22,"title":["Thermal dependence of large-scale freckle defect formation"],"prefix":"10.1098","volume":"377","author":[{"given":"A.","family":"Kao","sequence":"first","affiliation":[{"name":"Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE109LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"Shevchenko","sequence":"additional","affiliation":[{"name":"Helmholtz-Zentrum Dresden-Rossendorf, Institute of Fluid Dynamics, Bautzner Landstrasse 400, 01328 Dresden, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Alexandrakis","sequence":"additional","affiliation":[{"name":"Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE109LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"Krastins","sequence":"additional","affiliation":[{"name":"Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE109LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Eckert","sequence":"additional","affiliation":[{"name":"Helmholtz-Zentrum Dresden-Rossendorf, Institute of Fluid Dynamics, Bautzner Landstrasse 400, 01328 Dresden, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Pericleous","sequence":"additional","affiliation":[{"name":"Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE109LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2019,3,4]]},"reference":[{"key":"e_1_3_5_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.actamat.2009.08.018"},{"key":"e_1_3_5_3_2","volume-title":"Investigation of solidification defect formation by three-dimensional reconstruction of dendritic structures","author":"Madison JD","year":"2010"},{"key":"e_1_3_5_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11663-000-0117-9"},{"key":"e_1_3_5_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11661-000-0199-7"},{"key":"e_1_3_5_6_2","doi-asserted-by":"publisher","DOI":"10.2355\/isijinternational.53.935"},{"key":"e_1_3_5_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0363(199801)27:1\/4<207::AID-FLD660>3.0.CO;2-X"},{"key":"e_1_3_5_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-6454(03)00110-1"},{"key":"e_1_3_5_9_2","doi-asserted-by":"publisher","DOI":"10.1088\/0965-0393\/18\/5\/055008"},{"key":"e_1_3_5_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.actamat.2012.04.043"},{"key":"e_1_3_5_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.actamat.2014.07.002"},{"key":"e_1_3_5_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0921-5093(01)01700-2"},{"key":"e_1_3_5_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11661-015-2963-8"},{"key":"e_1_3_5_14_2","doi-asserted-by":"crossref","unstructured":"Shimokawabe T Aoki T Takaki T Endo T Yamanaka A Maruyama N Nukada A Matsuoka S. 2011 Peta-scale phase-field simulation for dendritic solidification on the TSUBAME 2.0 supercomputer. 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