The motion of an ellipsoid in tube flow at low Reynolds numbers

The motion of a rigid ellipsoidal particle freely suspended in a Poiseuille how of an incompressible Newtonian fluid through a narrow tube is studied numerically in the zero-Reynolds-number limit. It is assumed that the effect of inertia forces on the motion of the particle and the fluid can be neglected and that no forces or torques act on the particle. The Stokes equation is solved by a finite element method for various positions and orientations of the particle to yield the instantaneous velocity of the particle as well as the how field around it, and the particle trajectories are determined for different initial configurations. A prolate spheroid is found to either tumble or oscillate in rotation, depending on the particle-tube size ratio, the axis ratio of the particle, and the initial conditions. A large oblate spheroid may approach asymptotically a steady, stable configuration, at which it is located close to the tube centreline, with its major axis slightly tilted from the undisturbed flow direction. The motion of non-axisymmetric ellipsoids is also illustrated and discussed with emphasis on the effect of the particle shape and size.