Results of experiments on the low-Reynolds-number flow of liquid drops through a horizontal circular tube with a diameter that varies sinusoidally with axial position are reported. Measurements of the contribution of the drop to the local pressure gradient and the relative velocity of the drop are correlated with the time-dependent drop shape. Both Newtonian and viscoelastic suspending fluids are considered. The viscosity ratio, volumetric flow rate and drop size are varied in the experiment, and both neutrally buoyant and non-neutrally buoyant drops are studied. Comparison with previous results for a straight-wall tube shows that the influence of the tube boundary geometry on the drop shape is substantial, but the qualitative effect of the tube shape depends strongly on the relative importance of viscous forces compared to interfacial tension for the particular experiment. For Newtonian fluids, two modes of drop breakup, which are distinguished by the magnitude of the viscosity ratio, are observed. When the suspending fluid is viscoelastic, both shear-thinning and time-dependent rheological effects are present.
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