  We present a new numerical model to simulate settling trajectories of
discretized individual or a mixture of particles of different geometrical
shapes in a quiescent fluid and their flow trajectories in a flowing fluid.
Simulations unveiled diverse particle settling trajectories as a function of
their geometrical shape and density. The effects of the surface concavity of a
boomerang particle and aspect ratio of a rectangular particle on the
periodicity and amplitude of oscillations in their settling trajectories were
numerically captured. Use of surrogate circular particles for settling or
flowing of a mixture of non-circular particles were shown to miscalculate
particle velocities by a factor of 0.9-2.2 and inaccurately determine the
particles' trajectories. In a microfluidic chamber with particles of different
shapes and sizes, simulations showed that steady vortices do not necessarily
always control particle entrapments, nor do larger particles get selectively
and consistently entrapped in steady vortices. Strikingly, a change in the
shape of large particles from circular to elliptical resulted in stronger
entrapments of smaller circular particles, but enhanced outflows of larger
particles, which could be an alternative microfluidics-based method for sorting
and separation of particles of different sizes and shapes.
