A single particle (365–640 μm) is injected into a 0.1% w/w solution of polyisobutylene (Mv=1.5×106), dissolved in polybutene (Mn=800), held between a plate and a 21‐cm disc. When rotation of the disc is begun at 4–9 rpm, with a disc‐plate separation of 3.6–6.6 mm, an anomalous discontinuity in the direction of lateral migration is observed at an initial radial location r=rcr: for r<rcr, the particle migrates radially inward and vertically downward; whereas, for r>rcr, the particle migrates radially outward and vertically toward a plane midway between the disc and plate. By improving the apparatus used in Part I [J. Rheol. 28, 381 (1984)], more reproducible measurements of rcr are obtained. rcr is found to be inversely proportional to rotation speed, directly proportional to disc‐plate separation, and independent of particle radius. The proportionality constant, 6.3/s, represents a critical shear rate for the direction of lateral migration in this fluid and this geometry. A qualitative interpretation for this anomalous behavior is presented in which this critical shear rate is associated with the relaxation time for the polymer molecules.