The effects of closure model of fiber orientation tensor on the instability of fiber suspensions in the Taylor-Couette flow

Abstract

An analysis for the linear stability of fiber suspensions in the Taylor–Couette flow is conducted. The orientation state of fibers is determined using the linear, quadratic and composite HL-I closure model and the model of the fiber contribution to the total stress is established based on the slender-body theory. The linear stability equation is derived and solved with the Chebyshev spectral method. The results show that the suppression effect is most predominant for the composite HL-I model, while least predominant for the linear closure model. The longer fibers and suspensions with high volume fraction have a more predominant influence on suppressing the instability. The contribution of the suspending fluid to the change rate of the disturbance energy dominates the energy dissipation. While the contribution of the fiber shear stress increases monotonously with increasing fiber aspect ratio for the three closure models, the contribution based on the composite HL-I closure model is the largest, and that based on the linear closure model is the smallest. The effect of fiber aspect ratio on the change rate of the disturbance energy caused by the fiber shear stress is more predominant than that of the fiber volume fraction. The positive energy caused by the fiber shear stress consumes the gross energy of the fluid system and leads to a suppression of the flow instability.