Theoretical Research And Numerical Simulation Of Fiber Orientation In Fiber Suspension Flows

Suspension flows are very popular in industries and daily life. And fiber suspen-sion flow is a model for the flow in which slender bodies suspend, such as the pulpflow, nematic liquid crystal flow, and abundant polymer flows. Fiber which standsfor slender particulate is different from spherical particulate, since fiber is orientablewhile the latter is isotropic. Fiber suspension flow always show non-isotropic proper-ties, such as huge extensional viscosity, the first normal stress difference and the secondnormal stress difference, which are among the various peculiar properties of the Non-Newtonian fluid. It is significant to research such rheological properties. Finding outthe micro flow structure of the suspensions is rudimental for the study of the macroproperties of the suspensions. The subject of this thesis focuses on the fiber orientationin the suspension flows.The rotation of a fiber is depicted by the well-known Jeffery equation. Jeffery (1922)have solved the equation in a simple shear flow. He found that the fiber rotates period-ically in such flow. In the thesis, the solution of Jeffery equation in general 2D flows isobtained, which covers Jeffery's result for the simple shear flow. It is found that thereare two modes for the fiber's rotation, periodical and asymptotical. A discriminant ispresented in the thesis to judge whether a fiber will rotate periodically or asymptoti-cally run to a specific direction in a flow. The expressions for the period and for theasymptotical direction have been given also.The apparent properties of fiber suspension flow can be derived from the contribu-tion of all the fiber orientation through the ensemble average method. In the method,the fiber orientation distribution is introduced, which describes the probability of a fiberorientates in certain direction. According to the different effects of diffusion, three meth-ods have been developed to deal with the orientation distribution. Under no diffusioncircumstance, the solution of the orientation distribution is derived from the analyti-cal solution of the Jeffery equation. Under strong diffusion circumstance, a spectralmethod which ingeniously utilizes the analytical solution of the Jeffery equation is de-veloped. The spectral method has high computational efficiency and high precision, in the same time, it avoids the singularity problem which is inevitable for the finitedifference method or the finite element method to solve the Fokker-Planck equationin spherical coordinates. Under weak diffusion circumstance, the spectral method isnot feasible because of the increasing of computational errors. A regular perturbationmethod is developed under such circumstance, which is suitable for weak diffusionproblem. The three methods, as a whole, have efficiently and completely solved theorientation distribution problem.Several important topics in the research of fiber suspension flow, i.e., diffusivity, ad-ditional stress, and the coupling solution of the orientation distribution and flow field,are discussed in the thesis also.The achievement of the thesis contributes the understanding of the movement offiber in various flows, it gives clues to reveal the complicated rheology of suspensionflow, it also can be used to numerical simulation when combined with suitable consti-tutive equations about fiber suspension flow.