Research On The Hydrodynamic Stability Of Fiber Suspensions And Closure Model Of Fiber Orientation Tensor

Fiber is a kind of typical non-spherical particle due to its distinct preferred direction. The addition of fibers to the flow not only influences the microstructure of the flow but also greatly changes the macro-physical properties of the suspension. On the other hand, the fiber rotates and translates in the suspension, which makes the fiber suspension become a complex dynamical system. To this day it has been extensively familiar in nature and many fields of industry. But there still exist many unsolved problems. This thesis studies the hydrodynamic stability of the fiber suspension and related topics.A tensor description of the orientational structure in the fiber suspension provides an efficient way to represent the fiber orientation state at any point, but the scheme requires an accurate closure approximation for the higher-order orientation tensor. In the first part, the focus is put on testing six closures broadly used in the present. The Taylor-Couette flow is selected as the example. The numerical results show that none of these closure approximations can provide accurate solutions for all parameters in this flow field. The correction of every closure mostly relies on the values of the interaction coefficient and the aspect ratio of the fiber. When the interaction coefficient is larger than 0.01, the first composite closure proposed by Hinch and Leal exhibits good transient behavior and accurate steady-state value. In the part two, an experiment on the small aspect ratio in the semi-concentrated suspension is performed. In conjunction with the theory for the slender bodies and the viscosity value of the measurements, a modified viscosity expression of the small aspect ratio with respect to the effect of the aspect ratio and concentration of the fibers is proposed.In Taylor-Couette shear flow field, first the linear stability analysis is performed to fiber suspensions utilizing flow stability, constitutive relation of fiber suspensions, orientation tensor and closure approximation theories. The governing equations of the stability and their different forms of closure approximations are derived. Stability...