Centrifugal instability of semidilute non-Brownian fiber suspensions

Linear stability of the Taylor-Couette (TC) flow of semidilute non-Brownian suspension is investigated by utilizing the fiber orientation model developed by Hinch and Leal [J. Fluid Mech. 76, 187 (1976)] in conjunction with a quadratic and hybrid closure proposed by Advani and Tucker [J. Rheol. 34, 367 (1990)]. It is found that irrespective of the closure approximation used the fiber additives suppress the centrifugal TC instability, i.e., the critical Reynolds number (Re) increases with the fiber volume fraction and aspect ratio as well as the interfiber interaction coefficient. This increase in the critical Re is significantly larger than that in the total viscosity, except for very small values of the volume fraction and the interaction coefficient. The enhanced stabilization can be attributed to the fact that the suspension develops negative first and second normal stresses in the TC flow when the inner cylinder rotates and the outer one is stationary, i.e., the fluid is in a state of compression. Moreover, the interfiber interactions result in alignment of the fiber orientation tensor with respect to the rate of deformation tensor. This coupling enhances the ability of the fluid elements to resist the amplification of radial velocity disturbances that give rise to the centrifugal instability. This mechanism is substantiated based on a rigorous energy analysis, demonstrating that the coupling between the fiber orientation and perturbation radial velocities gives rise to fiber-induced perturbation shear stresses that are dissipative. Specifically, the coupling of fiber-induced perturbation shear stresses with the base flow velocity leads to a compressive force that dissipates energy leading to the suppression of the centrifugal instability.