Equilibrium solutions of a spheroidal particle’s rotational motion in Couette flow

Authors: Rosén, T., Lundell, F., Do-Quang, M., Aidun, C. K.
Document Type: Conference
Pubstate: Published
Journal: 8th International Conference on Multiphase Flow (ICMF), Jeju, Korea (2013)
Year: 2013


Understanding the behavior of non-spherical particles suspended in shear flow is fundamental for all suspension simulations and is of importance in several industrial applications. For example in papermaking and composites manufacturing, the orientational behavior of elongated suspended fibers directly determines the quality of the final product. Here, numerical simulations of a single spheroidal particle in a Couette flow are considered, with the purpose of studying the different states of rotational motion. Firstly, the motion depends on the fluid inertia [1], determined by the Reynolds number, Re_p=Gl^2/\nu, where G is the shear rate, l is the particle length and \nu is the kinematic viscosity of the fluid. For a neutrally buoyant particle several equilibrium rotational states were found with increasing Re_p [2] (Figure 1), including “tumbling” (T), “log-rolling” (LR), ”inclined rolling” (IR) and above a certain critical Reynolds number, Rec, the particle remains in a stationary position (S). Secondly, the motion depends on the particle inertia [3], determined by the Stokes number, St=\alpha*Re_p, where \alpha is the density ratio between particle and fluid. It was proven that above a certain Stokes number, St_{0.5}, the particle makes the transition from a long period “tumbling”-motion to rotating with a constant angular velocity (R). The results from Lattice Boltzmann simulations with External Boundary Force are used to determine the different rotational states in a Re_p/St-plane (Figure 2). It was found that there are several regions where two equilibrium rotational states co-exist and where the final solution is dependent on the initial conditions. The bifurcation points are studied in detail in order to describe the hysteresis effects at increased/decreased Re_p, \alpha and aspect ratio r_p (length/width) of the particle. [1] E-Jiang Ding & C. K. Aidun. The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423 317-344 (2000) [2] H. Huang, X. Yang, M. Krafczyk & X-Y. Lu. Rotation of spheroidal particles in Couette flows. J. Fluid Mech. 692 369-394 (2012) [3] F. Lundell & A. Carlsson. Heavy ellipsoids in creeping shear flow: Transitions of the particle rotation rate and orbit shape. Phys. Rev. E 81 016323 (2010)