Well-posedness of the problem of fiber suspension flows |
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| Institution: | 1. CMAT - Centro de Matemática and Departamento de Matemática, Universidade do Minho, Guimarães 4800-058, Portugal;2. CEMAT, Instituto Superior Técnico, Universidade de Lisboa & Department of Mathematics, University of Trás-os-Montes e Alto Douro, UTAD, Vila Real, Portugal;3. Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Quinta da Torre, Caparica 2829-516, Portugal;4. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA;5. Centro de Estudos de Fenómenos de Transporte, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, Porto 4200-465, Portugal;1. Blast Impact and Survivability Research Unit, Department of Mechanical Engineering, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa;2. Department of Mechanical and Mechatronic Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa;3. Department Biological Sciences, Private Bag X3, Rondebosch 7701, South Africa;4. Department of Mechanical and Aeronautical Engineering, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South Africa |
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| Abstract: | The well-posedness of the equations governing the flow of fiber suspensions is studied. The fluid is assumed to be Newtonian and incompressible, and the presence of fibers is accounted for through the use of second- and fourth-order orientation tensors, which model the effects of the orientation of fibers in an averaged sense. The fourth-order orientation tensor is expressed in terms of the second-order tensor through various closure relations. It is shown that the linear closure relation leads to anomalous behavior, in that the rest state of the fluid is unstable, in the sense of Liapounov, for certain ranges of the fiber particle number. No such anomalies arise in the case of quadratic and hybrid closure relations. For the quadratic closure relation, it is shown that a unique solution exists locally in time for small data. |
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