{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T16:18:27Z","timestamp":1782317907652,"version":"3.54.5"},"reference-count":65,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1409286,1319483,1453101"],"award-info":[{"award-number":["1409286,1319483,1453101"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-04360-2014"],"award-info":[{"award-number":["RGPIN-04360-2014"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Graduate Student Research Fellowship","award":["DGE-16-44869"],"award-info":[{"award-number":["DGE-16-44869"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2017,8,31]]},"abstract":"<jats:p>The diverse interactions between hair and liquid are complex and span multiple length scales, yet are central to the appearance of humans and animals in many situations. We therefore propose a novel multi-component simulation framework that treats many of the key physical mechanisms governing the dynamics of wet hair. The foundations of our approach are a discrete rod model for hair and a particle-in-cell model for fluids. To treat the thin layer of liquid that clings to the hair, we augment each hair strand with a height field representation. Our contribution is to develop the necessary physical and numerical models to evolve this new system and the interactions among its components. We develop a new reduced-dimensional liquid model to solve the motion of the liquid along the length of each hair, while accounting for its moving reference frame and influence on the hair dynamics. We derive a faithful model for surface tension-induced cohesion effects between adjacent hairs, based on the geometry of the liquid bridges that connect them. We adopt an empirically-validated drag model to treat the effects of coarse-scale interactions between hair and surrounding fluid, and propose new volume-conserving dripping and absorption strategies to transfer liquid between the reduced and particle-in-cell liquid representations. The synthesis of these techniques yields an effective wet hair simulator, which we use to animate hair flipping, an animal shaking itself dry, a spinning car wash roller brush dunked in liquid, and intricate hair coalescence effects, among several additional scenarios.<\/jats:p>","DOI":"10.1145\/3072959.3073630","type":"journal-article","created":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T12:24:07Z","timestamp":1500639847000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":57,"title":["A multi-scale model for simulating liquid-hair interactions"],"prefix":"10.1145","volume":"36","author":[{"given":"Yun (Raymond)","family":"Fei","sequence":"first","affiliation":[{"name":"Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Henrique Teles","family":"Maia","sequence":"additional","affiliation":[{"name":"Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher","family":"Batty","sequence":"additional","affiliation":[{"name":"University of Waterloo"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changxi","family":"Zheng","sequence":"additional","affiliation":[{"name":"Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eitan","family":"Grinspun","sequence":"additional","affiliation":[{"name":"Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2017,7,20]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2019406.2019408"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2786784.2786793"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tca.2012.11.001"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276502"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778853"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360662"},{"key":"e_1_2_2_7_1","unstructured":"Florence Bertails Basile Audoly Bernard Querleux Fr\u00e9d\u00e9ric Leroy Jean-Luc L\u00e9v\u00eaque and Marie-Paule Cani. 2005. Predicting natural hair shapes by solving the statics of flexible rods. In Eurographics short papers.  Florence Bertails Basile Audoly Bernard Querleux Fr\u00e9d\u00e9ric Leroy Jean-Luc L\u00e9v\u00eaque and Marie-Paule Cani. 2005. Predicting natural hair shapes by solving the statics of flexible rods. In Eurographics short papers."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1038\/432690a"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.03.040"},{"key":"e_1_2_2_10_1","volume-title":"Fluid simulation for computer graphics","author":"Bridson Robert","unstructured":"Robert Bridson . 2015. Fluid simulation for computer graphics , 2 nd edition. A. K. Peters, Ltd. Robert Bridson. 2015. Fluid simulation for computer graphics, 2nd edition. A. K. Peters, Ltd.","edition":"2"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601211"},{"key":"e_1_2_2_12_1","volume-title":"Adaptive Skinning for Interactive Hair-Solid Simulation","author":"Chai Menglei","year":"2016","unstructured":"Menglei Chai , Changxi Zheng , and Kun Zhou . 2016. Adaptive Skinning for Interactive Hair-Solid Simulation . IEEE transactions on visualization and computer graphics ( 2016 ). Menglei Chai, Changxi Zheng, and Kun Zhou. 2016. Adaptive Skinning for Interactive Hair-Solid Simulation. IEEE transactions on visualization and computer graphics (2016)."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112006008706"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2012.0429"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0301-9322(84)90079-X"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1038\/nature10779"},{"key":"e_1_2_2_17_1","first-page":"89","article-title":"Fluid flow through packed columns","volume":"48","author":"Ergun Sabri","year":"1952","unstructured":"Sabri Ergun . 1952 . Fluid flow through packed columns . Chem. Eng. Prog. 48 (1952), 89 -- 94 . Sabri Ergun. 1952. Fluid flow through packed columns. Chem. Eng. Prog. 48 (1952), 89--94.","journal-title":"Chem. Eng. Prog."},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2791261.2791271"},{"key":"e_1_2_2_19_1","unstructured":"Ga\u00ebl Guennebaud Beno\u00eet Jacob and others. 2010. Eigen v3. http:\/\/eigen.tuxfamily.org. (2010).  Ga\u00ebl Guennebaud Beno\u00eet Jacob and others. 2010. Eigen v3. http:\/\/eigen.tuxfamily.org. (2010)."},{"key":"e_1_2_2_20_1","doi-asserted-by":"crossref","unstructured":"Sunil Hadap Marie-Paule Cani Florence Bertails Ming Lin Kelly Ward Stephen Marschner Tae-Yong Kim and Zoran Kacic-Alesic. 2007. Strands and hair - Modeling simulation and rendering. In SIGGRAPH Courses. 1--150.  Sunil Hadap Marie-Paule Cani Florence Bertails Ming Lin Kelly Ward Stephen Marschner Tae-Yong Kim and Zoran Kacic-Alesic. 2007. Strands and hair - Modeling simulation and rendering. In SIGGRAPH Courses. 1--150.","DOI":"10.1145\/1281500.1281689"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00525"},{"key":"e_1_2_2_22_1","volume-title":"Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation. The Eurographics Association.","author":"Han Dongsoo","year":"2013","unstructured":"Dongsoo Han and Takahiro Harada . 2013 . Tridiagonal matrix formulation for inextensible hair strand simulation . In Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation. The Eurographics Association. Dongsoo Han and Takahiro Harada. 2013. Tridiagonal matrix formulation for inextensible hair strand simulation. In Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation. The Eurographics Association."},{"key":"e_1_2_2_23_1","first-page":"129","article-title":"Flow through porous media at moderate Reynolds number","volume":"2","author":"Hellstr\u00f6m JGI","year":"2006","unstructured":"JGI Hellstr\u00f6m and TS Lundstr\u00f6m . 2006 . Flow through porous media at moderate Reynolds number . In International Scientific Colloquium: Modelling for Material Processing , Vol. 2. 129 -- 134 . JGI Hellstr\u00f6m and TS Lundstr\u00f6m. 2006. Flow through porous media at moderate Reynolds number. In International Scientific Colloquium: Modelling for Material Processing, Vol. 2. 129--134.","journal-title":"International Scientific Colloquium: Modelling for Material Processing"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2485895.2485913"},{"key":"e_1_2_2_25_1","unstructured":"Markus Ihmsen Jens Orthmann Barbara Solenthaler Andreas Kolb and Matthias Teschner. 2014. SPH fluids in computer graphics. In Eurographics State of the Art Reports.  Markus Ihmsen Jens Orthmann Barbara Solenthaler Andreas Kolb and Matthias Teschner. 2014. SPH fluids in computer graphics. In Eurographics State of the Art Reports."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjce.5450640302"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766996"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/97880.97884"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601100"},{"key":"e_1_2_2_30_1","volume-title":"Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation. Eurographics Association, 169--178","author":"Kugelstadt Tassilo","year":"2016","unstructured":"Tassilo Kugelstadt and Elmar Sch\u00f6mer . 2016 . Position and orientation based Cosserat rods . In Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation. Eurographics Association, 169--178 . Tassilo Kugelstadt and Elmar Sch\u00f6mer. 2016. Position and orientation based Cosserat rods. In Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation. Eurographics Association, 169--178."},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360648"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcis.1993.1452"},{"key":"e_1_2_2_33_1","volume-title":"Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation.","author":"Lin Wei-Chin","year":"2014","unstructured":"Wei-Chin Lin . 2014 . Coupling hair with smoothed particle hydrodynamics fluids . In Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation. Wei-Chin Lin. 2014. Coupling hair with smoothed particle hydrodynamics fluids. In Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation."},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2015.06.005"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1088\/0022-3727\/40\/16\/038"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcis.2004.06.054"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531368"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211208500115X"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.37.061903.175743"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1034"},{"key":"e_1_2_2_41_1","volume-title":"Symposium on Computer Animation. 154--159","author":"M\u00fcller Matthias","year":"2003","unstructured":"Matthias M\u00fcller , David Charypar , and Markus Gross . 2003 . Particle-based fluid simulation for interactive applications . In Symposium on Computer Animation. 154--159 . Matthias M\u00fcller, David Charypar, and Markus Gross. 2003. Particle-based fluid simulation for interactive applications. In Symposium on Computer Animation. 154--159."},{"key":"e_1_2_2_42_1","volume-title":"Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation","volume":"12","author":"M\u00fcller Matthias","year":"2012","unstructured":"Matthias M\u00fcller , Tae-Yong Kim , and Nuttapong Chentanez . 2012 . Fast simulation of inextensible hair and fur .. In Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation , Vol. 12 . 39--44. Matthias M\u00fcller, Tae-Yong Kim, and Nuttapong Chentanez. 2012. Fast simulation of inextensible hair and fur.. In Proceedings of the Workshop on Virtual Reality Interaction and Physical Simulation, Vol. 12. 39--44."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0017-9310(97)00008-2"},{"key":"e_1_2_2_44_1","doi-asserted-by":"crossref","unstructured":"C. Py R. Bastien Jos\u00e9 Bico B. Roman and A. Boudaoud. 2007. 3D aggregation of wet fibers. Europhysics letters 77 4 (2007) 44005.  C. Py R. Bastien Jos\u00e9 Bico B. Roman and A. Boudaoud. 2007. 3D aggregation of wet fibers. Europhysics letters 77 4 (2007) 44005.","DOI":"10.1209\/0295-5075\/77\/44005"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360645"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1088\/0953-8984\/22\/49\/493101"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03191.x"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/0301-9322(82)90029-5"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360663"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2014.102"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311548"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.3021477"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766969"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1021\/la902578j"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8354-1"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.5555\/1272690.1272721"},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201400865"},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.30"},{"key":"e_1_2_2_59_1","volume-title":"Lin","author":"Ward Kelly","year":"2004","unstructured":"Kelly Ward , Nico Galoppo , and Ming C . Lin . 2004 . Modeling hair influenced by water and styling products. In Computer Animation and Social Agents . Kelly Ward, Nico Galoppo, and Ming C. Lin. 2004. Modeling hair influenced by water and styling products. In Computer Animation and Social Agents."},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1162\/pres.16.3.237"},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1109\/PCCGA.2003.1238265"},{"key":"e_1_2_2_62_1","doi-asserted-by":"publisher","DOI":"10.1109\/CASA.2003.1199302"},{"key":"e_1_2_2_63_1","volume-title":"The dynamics of capillary flow. Physical review 17, 3","author":"Washburn Edward W","year":"1921","unstructured":"Edward W Washburn . 1921. The dynamics of capillary flow. Physical review 17, 3 ( 1921 ), 273. Edward W Washburn. 1921. The dynamics of capillary flow. Physical review 17, 3 (1921), 273."},{"key":"e_1_2_2_64_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00141261"},{"key":"e_1_2_2_65_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstl.1805.0005"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3072959.3073630","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3072959.3073630","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3072959.3073630","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:37:23Z","timestamp":1750217843000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3072959.3073630"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,20]]},"references-count":65,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,8,31]]}},"alternative-id":["10.1145\/3072959.3073630"],"URL":"https:\/\/doi.org\/10.1145\/3072959.3073630","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,20]]},"assertion":[{"value":"2017-07-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}