Computational flow in a collapsed tube with wall contact |
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| Affiliation: | 1. INRIA, BP 105, F-78153 Le Chesnay and LBHP URA CNRS 343, Université Paris 7, F-75251 Paris, France;2. LGMPB, IUT de Cachan, BP 140, F-94234 Cachan, France;1. Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas;2. Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas;3. Department of Gastroenterology Hepatology and Nutrition, The University of Texas MD Anderson Cancer Center, Houston, Texas;1. Institute of Cotton Research of Chinese Academy of Agricultural Sciences (ICR, CAAS)/State Key Laboratory of Cotton Biology, Anyang, Henan 455000, China;2. Henan Collaborative Innovation Center of Modern Biological Breeding, Henan Institute of Sciences and Technology, Xinxiang, Henan 453003, China;3. Crop Sciences Department, Zalingei University, Central Darfur, Sudan;1. Section of Geriatric Psychiatry and Institute of Gerontology, Department of Psychiatry, Heidelberg University, Germany;2. Computer Assisted Clinical Medicine, Medical Faculty Mannheim, Heidelberg University, Germany;3. German Cancer Research Center, Heidelberg, Germany;4. Department of Psychiatry, Heidelberg University, Germany;1. Department of Life Sciences, The Natural History Museum, Cromwell Road, London SW7 5BD, United Kingdom;2. Department of Terrestrial Ecology, Zoological Institute, University of Cologne, Zülpicher Str. 47b, 50674 Cologne, Germany;3. Research Unit Protistology and Aquatic Ecology, Biology Department, Ghent University, Krijgslaan 281 (S8), 9000 Gent, Belgium;4. Department of General Ecology, Zoological Institute, University of Cologne, Zülpicher Str. 47b, 50674 Cologne, Germany;1. State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China;2. School of Information Technology, Beijing Institute of Technology, Zhuhai, Zhuhai 519088, China |
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| Abstract: | Biofluids are transported in deformable vessels. When the transmural pressure is negative, the vessel collapses; opposite walls can come into contact. The dynamics of collapsible pipes depend upon the coupling between the biofluid and the biosolid via the tube law, which is described in the present paper. A brief review of experimental and theoretical modelling is also given, with emphasis on the one-dimensional theory. However, this fruitful model has many limitations; three-dimensional studies must now be carried out. As an illustration, the laminar steady flow has been computed in a rigid pipe corresponding to a highly collapsed tube with wall contact (Reynolds number of 1 210). The Navier–Stokes equations, associated to the classical boundary conditions, were solved by a finite element method. Where the opposite walls are in contact, the fluid flows through two small tear-drop-shaped outer passages. In the downstream divergent, in- and up(bottom)ward jets are associated to flow separations and to flow characteristics behind a stationary immersed wall. |
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