The motion and rotation of an ellipsoidal particle inside square tubes and
rectangular tubes with the confinement ratio R/a∈(1.0,4.0) are studied by the lattice
Boltzmann method (LBM), where R and a are the radius of the tube and the semimajor
axis length of the ellipsoid, respectively. The Reynolds numbers (Re) up to 50 are
considered. For the prolate ellipsoid inside square and rectangular tubes, three typical
stable motion modes which depend on R/a are identified, namely, the kayaking mode,
the tumbling mode, and the log-rolling mode are identified for the prolate spheroid.
The diagonal plane strongly attracts the particle in square tubes with 1.2 ≤ R/a <3.0.
To explore the mechanism, some constrained cases are simulated. It is found that the
tumbling mode in the diagonal plane is stable because the fluid force acting on the
particle tends to diminish the small displacement and will bring it back to the plane.
Inside rectangular tubes the particle will migrate to a middle plane between short walls
instead of the diagonal plane. Through the comparisons between the initial unstable
equilibrium motion state and terminal stable mode, it is seems that the particle tend to
adopt the mode with smaller kinetic energy.