The basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (Re-p) and Stokes number (St), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by Re-p = 4Ga(2)/nu, where G is the shear rate, a is the length of the spheroid major semi-axis and nu is the kinematic viscosity. The Stokes number is defined as St = alpha . Re-p, where alpha is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle (St = Re-p) of aspect ratio (major axis/minor axis) r(p) = 4 is considered. The long-term rotational motion for different initial orientations and Re-p is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high Re-p, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, Re-p = Re-c, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as vertical bar Re-p - Re-c vertical bar(-1/2). Analyses in this paper show that if a transition from tumbling to steady state occurs at Re-p = Re-c, then any parameter beta (e. g. confinement or particle spacing) that influences the value of Re-c, such that Re-p = Re-c as beta = beta(c), will lead to a period that scales as vertical bar beta - beta c vertical bar(-1/2) and is independent of particle shape or any geometric aspect ratio in the flow.

The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that the case of a single neutrally buoyant particle is a surprisingly rich dynamical system that exhibits several bifurcations between rotational states due to inertial effects. It was observed that the rotational states were associated with either fluid inertia effects or particle inertia effects, which are always in competition. The effects of fluid inertia are characterized by the particle Reynolds number Rep=4Ga²/ν, where G is the shear rate, a is the length of the particle major semi-axis and ν is the kinematic viscosity. Particle inertia is associated with the Stokes number St=α· Rep, where alpha is the solid-to-fluid density ratio. Previously, the neutrally buoyant case (St=Rep) was studied extensively. However, little is known about how these results are affected when St≢Rep, and how the aspect ratio rp (major axis/minor axis) influences the competition between fluid and particle inertia in the absence of gravity. This work gives a full description of how prolate spheroidal particles in the range 2≤ rp≤ 6 behave depending on the chosen St and Rep. Furthermore, consequences for the rheology of a dilute suspension containing such particles are discussed. Finally, grid resolution close to the particle is shown to affect the quantitative results considerably. It is suggested that this resolution is a major cause of quantitative discrepancies between different studies. Thus, the results of this work and previous direct numerical simulations of this problem should be regarded as qualitative descriptions of the physics involved, and more refined methods must be used to quantitatively pinpoint the transitions between rotational states.

This work describes the inertial effects on the rotational behavior of an oblate spheroidal particle confined between two parallel opposite moving walls, which generate a linear shear flow. Numerical results are obtained using the lattice Boltzmann method with an external boundary force. The rotation of the particle depends on the particle Reynolds number, Rep = Gd-2 nu(-1) (G is the shear rate, d is the particle diameter,. is the kinematic viscosity), and the Stokes number, St = alpha Re-p (a is the solid-to-fluid density ratio), which are dimensionless quantities connected to fluid and particle inertia, respectively. The results show that two inertial effects give rise to different stable rotational states. For a neutrally buoyant particle (St = Re-p) at low Re-p, particle inertia was found to dominate, eventually leading to a rotation about the particle's symmetry axis. The symmetry axis is in this case parallel to the vorticity direction; a rotational state called log-rolling. At high Re-p, fluid inertia will dominate and the particle will remain in a steady state, where the particle symmetry axis is perpendicular to the vorticity direction and has a constant angle phi(c) to the flow direction. The sequence of transitions between these dynamical states were found to be dependent on density ratio alpha, particle aspect ratio r(p), and domain size. More specifically, the present study reveals that an inclined rolling state (particle rotates around its symmetry axis, which is not aligned in the vorticity direction) appears through a pitchfork bifurcation due to the influence of periodic boundary conditions when simulated in a small domain. Furthermore, it is also found that a tumbling motion, where the particle symmetry axis rotates in the flow-gradient plane, can be a stable motion for particles with high r(p) and low alpha.