Supercritical circular Couette flow devices with a suspension in the annulus between an inner rotating cylinder and an outer fixed cylinder are used for continuous mixing of suspensions and for rotating filtration. The motion of particles in suspension depends on both centrifugal sedimentation and transport due to the vortical motion of Taylor vortices, a centrifugal flow instability that results in a stack of toroidal vortices in the annulus. We have modeled the motion of particles in Taylor Couette flow using computational particle tracking in an analytic velocity field. The fluid velocity field was based on an analytic model that has been shown to accurately represent the flow field just above the transition to supercritical Taylor vortex flow. Particles of various densities were computationally placed in the analytic flow field and tracked to determine the preferential steady state particle positions. Since the centrifugal field goes to zero near the outer cylinder, particles near the outer cylinder are easily carried by the Taylor vortices toward the inner cylinder where they are exposed to the centrifugal field. Due to their density, particles near the inner cylinder centrifugally sediment outward. As a result, particles that start near the inner cylinder or the outer cylinder both tend toward a limit cycle orbit resulting in a region of clear fluid near the inner and outer cylinders and at the centers of the vortices.