{"title":"Pulsatile Flows","authors":"Troy Shinbrot","doi":"10.1093/oso/9780198812586.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198812586.003.0004","url":null,"abstract":"Flow solutions in the presence of pulsation (e.g. from the heart) are developed. Bessel functions are introduced as an aside. The concepts of shocks and solitary waves (solitons) are then discussed as examples of nonlinear effects. The strategy for dealing with intrinsic nonlinearity is described in terms of mode coupling and the Korteweg–de Vries (KdV) equation.","PeriodicalId":202349,"journal":{"name":"Biomedical Fluid Dynamics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125206775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fundamental Equations","authors":"T. Shinbrot","doi":"10.1093/oso/9780198812586.003.0001","DOIUrl":"https://doi.org/10.1093/oso/9780198812586.003.0001","url":null,"abstract":"This chapter introduces the topic of fluid transport. The opening section provides a motivational allegory based on the sinking of the SS Edmund Fitzgerald on Lake Superior in 1975. Although the connection between the sinking of a steam ship and flow of blood in an artery is not obvious, the chapter describes how “apparently different systems, sharing little in scale, scope, or appearance, in fact share the same features, can be described by the same equations, and exhibit the same phenomenology.” The continuity and Navier–Stokes equations are then derived, and are applied to Poiseuille flow in a rigid tube.","PeriodicalId":202349,"journal":{"name":"Biomedical Fluid Dynamics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123825617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Entrances, Branches, and Bends","authors":"T. Shinbrot","doi":"10.1093/OSO/9780198812586.003.0005","DOIUrl":"https://doi.org/10.1093/OSO/9780198812586.003.0005","url":null,"abstract":"Effects of boundaries are described, including those associated with entrances, branches, and bends in tubes. Couette flow between rotating cylinders, modelling of volume-preserving flows, and chaotic flows are described. Model building is considered, and the effects of out of plane bending are discussed in the context of static mixers.","PeriodicalId":202349,"journal":{"name":"Biomedical Fluid Dynamics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124113007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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