Sedimentation of an ellipsoidal particle in narrow tubes

Abstract

Sedimentation behaviours of an ellipsoidal particle in narrow and infinitely long tubes are studied by a multi-relaxation-time lattice Boltzmann method (LBM). In the present study, both circular and square tubes with 12/13 ⩽ D/A ⩽ 2.5 are considered with the Galileo number (Ga) up to 150, where D and A are the width of the tube and the length of major axis of the ellipsoid, respectively. Besides three modes of motion mentioned in the literature, two novel modes are found for the narrow tubes in the higher Ga regime: the spiral mode and the vertically inclined mode. Near a transitional regime, in terms of average settling velocity, it is found that a lighter ellipsoid may settle faster than a heavier one. The relevant mechanism is revealed. The behaviour of sedimentation inside the square tubes is similar to that in the circular tubes. One significant difference is that the translation and rotation of ellipsoid are finally constrained to a diagonal plane in the square tubes. The other difference is that the anomalous rolling mode occurs in the square tubes. In this mode, the ellipsoid rotates as if it is contacting and rolling up one corner of the square tube when it settles down. Two critical factors that induce this mode are identified: the geometry of the tube and the inertia of the ellipsoid.