| Low-Reynolds-number particle transport occurs in a range of applications, from sedimentation to microfluidics. Since the early 1800s, low-Reynolds-number flows in bounded or semi-bounded domains have been studied extensively by many researchers. However, existing models and experimental results for the motion of rigid particles between parallel plane walls are not accurate for large particles that are close in size to the gap between the walls. The goals of this dissertation are to develop models for the motion of spheres and spheroids in narrow channels that are accurate for these relatively large particles and to validate these models for spherical particles in low-Reynolds-number microfluidic and inclined-channel applications.; We developed a novel boundary-integral simulation, which we first used to obtain the translational and rotational velocities of spheres with diameters up to 95% of the channel depth for gaps as small as 0.5% of the particle diameter from a wall. An asymptotic formulation using lubrication theory for a sphere and a plane wall allowed extension of the results to arbitrarily small spacings between the sphere and the walls. The simulation results were validated experimentally using a narrow microfluidic channel and neutrally-buoyant spherical polymer particles suspended in a glycerol-water solution driven through the microchannel by a syringe pump, with good agreement obtained between the experimentally measured translational velocities and the simulation results. In addition, analysis of the distribution of particle center locations for different channel entrance geometries showed that a blunt entrance provided significant hydrodynamic focusing towards the center of the channel, while an offset-angled entrance caused slight focusing towards the wall encountered first in the entrance region.; The novel boundary-integral algorithm was modified to tabulate the nonsingular portions of resistance coefficients for use in a three-dimensional dynamic simulation of the motion of neutrally-buoyant spheroidal particles in a parallel-plate Poiseuille flow. Adaptive meshing near the walls allowed accurate calculation for gaps as small as 1.3% of the spheroid's major axis, while lubrication asymptotics developed for an ellipsoid and a plane wall provided results to arbitrarily small spacings between the particle and wall(s). The extremely fast and accurate dynamic simulation was used to obtain a wide range of particle images, trajectories, and velocities for three prolate spheroids, one with a major axis greater than the channel spacing, and one oblate spheroid. (Abstract shortened by UMI.)... |
