Well-posedness of the problem of fiber suspension flows

The well-posedness of the equations governing the flow of fiber suspensions is studied. The fluid is assumed to be Newtonian and incompressible, and t he presence of fibers is accounted for through the use of second- and fourt h-order orientation tensors, which model the effects of the orientation of fibers in an averaged sense. The fourth-order orientation tensor is express ed in terms of the second-order tensor through various closure relations. I t 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, f or certain ranges of the fiber particle number. No such anomalies arise in the case of quadratic and hybrid closure relations. For the quadratic closu re relation, it is shown that a unique solution exists locally in time for small data. (C) 1999 Elsevier Science B.V. All rights reserved.