The creeping motion of liquid drops through a circular tube of comparable diameter: the effect of density differences between the fluids

Abstract

Results of experiments on the low-Reynolds-number flow of non-neutrally buoyant drops through a straight circular tube are reported. The undeformed radii of the drops are comparable to the size of the tube, and the drops adopt an eccentric lateral position owing to a density difference between the drop and the suspending fluid. Measured values for the extra pressure difference caused by the presence of the drop, the relative velocity of the drop, and the shape of the drop are correlated with the minimum gap width between the eccentrically located drop and the tube wall using simple lubrication approximations. The viscosity ratio, density difference, volumetric flow rate and drop size are varied in the experiment. Comparisons with previous results for concentric, neutrally buoyant drops show that the effects of eccentric position can be substantial for surprisingly small values of the density difference. Both Newtonian and viscoelastic suspending fluids are considered, and the results suggest that both viscometric and time-dependent non-Newtonian effects are present. For the Newtonian case, the data are compared with the predictions of available theories which account explicitly for the eccentric drop position.