We study the dynamics of a single two-dimensional elliptical particle sedimenting in a Newtonian fluid using numerical simulations. The main emphasis in this work is to study the effect of boundaries on the flow patterns observed during sedimentation. The simulations were performed using a multi-block lattice Boltzmann method as well as a finite-element technique and the results are shown to be consistent. We have conducted a detailed study on the effects of density ratio, aspect ratio and the channel blockage ratio on the flow patterns during sedimentation. As the channel blockage ratio is varied, our results show that there are five distinct modes of sedimentation: oscillating, tumbling along the wall, vertical sedimentation, horizontal sedimentation and an inclined mode where the particle sediments with a non-trivial orientation to the vertical. The inclined mode is shown to form a smooth bridge between the vertical and horizontal modes of sedimentation. For narrow channels, the mode of sedimentation is found to be sensitively dependent on the initial orientation of the particle. We present a phase diagram showing the transitions between the various modes of sedimentation with changing blockage ratio of the channel.

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Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or chan nel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical mov ing parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two dimensional channel using the Lattice Boltzmann Method(LBM). We systematically investigate the effect of variation of the relevant dimensionless paJ'ameters of the system on the paJ·ticle transport. We find , among other results, a case where an increase of Reynolds number CaJl actually lead to a slight increase in particle transport, and a case where as the wall deformation•Author to whom correspondence should be addressed. Electronic mail: kconninl @jhu.edu 1 1 increases, the motion of the particle becomes non-negative only. VVe examine the particle behavior when the system exhibits the peculiar phenomenon of fluid tmp ping. Under these circumstances, the particle may itself become tmpped where it is subsequently transported at the wave speed, which is the ma.ximum possible transport in the absence of a favorable pressure gradient . Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We fiud that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported un der conditions where tmpping occurs as the particle is typically situated in a region of innocuous shear stress levels.