This paper reports the results of lattice Boltzmann simulations of the rotation behaviour of neutrally buoyant spheroidal particles in a three-dimensional Couette flow. We find several distinctive states depending on the Reynolds number range and particle shape. As the Reynolds number increases, rotation may change from one state to another. For a prolate spheroid, two rotation transitions are found. In the low Reynolds number range 0 < R < R 1 ≈ 205, the prolate spheroid rotates around its minor axis, which is parallel to the vorticity vector of the flow. The rate of rotation is a periodic function of time. In the intermediate Reynolds number range R 1 < R < R 2 ≈ 345, the prolate spheroid precesses about the vorticity direction with a nutational motion. The angular velocities are periodic functions of time. The mean nutation angle between the major axis and the vorticity increases monotonically as the Reynolds number increases. In the high Reynolds number range R 2 < R < 467, the prolate spheroid rotates with a constant rate around its major axis, which is parallel to the vorticity. For an oblate spheroid, only one rotation transition is observed. In the lower Reynolds number range 0 < R < R 1 ≈ 220, the oblate spheroid finally spins with a constant rate around its minor axis (the symmetric axis of the revolution), which is parallel to the vorticity vector. In the higher Reynolds number range 220 ≈ R 1 < R < 467, the oblate spheroid still spins with a constant rate around its minor axis but there is a finite inclination angle between the minor axis and the vorticity vector. This angle increases as the Reynolds number increases.

A lattice-Boltzmann method has been developed to simulate suspensions of both spherical and non-spherical particles in finite-Reynolds-number flows. The results for sedimentation of a single elliptical particle are shown to be in excellent agreement with the results of Huang, Hu & Joseph (1998) who used a finite-element method. Sedimentation of two-dimensional circular and rectangular particles in a two-dimensional channel and three-dimensional spherical particles in a tube with square cross-section is simulated. Computational results are consistent with experimentally observed phenomena, such as drafting, kissing and tumbling.

An aromatic polyimide and its mixture with randomly distributed carbon nanotubes (NTs) are simulated by using molecular dynamics, repeated energy minimization and cooling processes. The glass transition temperatures are identified through volume-temperature curves. Stress-strain curves, Young's moduli, densities and Poisson ratios are computed at different temperatures. It is demonstrated that the carbon NT reduces the softening effects of temperature on mechanical properties and increases the ability to resist deformation.

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Direct simulations of flexible cylindrical fiber suspensions in a finite Reynolds number flow are reported. The simulation method is based on a lattice Boltzmann equation and a flexible fiber model. A slender solid body is discretized into a chain of cylindrical segments contacting each other at the their ends through ball and socket joints that allow adjacent segments to rotate around the joints in three dimensional space. A constraint force is imposed at each joint. In general, motion and rotational matrices of each segment are functions of constraint forces. It is necessary to linearize the rotational matrices in forces and torques so that constraint forces could be solved using joint contacting conditions. Therefore, quaternion parameters as well as rotational matrix could be expanded in a power series of the length of time step up to a second order. A half leapfrog algorithm D. Fincham, [CCP5 Quarterly, 2, 6 (1981)] is modified to ensure the ball and socket joint conditions to be satisfied at each time step. The validation of the present flexible fiber method is tested by using a rigid particle method. It is shown that the computational results are consistent with the existing experimental and theoretical results at finite Reynolds number flows. With the present method, nonlinear inertial interactions between fluid and flexible filaments can be naturally studied. A few applications are included.