The general theory of Taylor dispersion phenomena in time-periodic flows, developed in Part I [Phys. Fluids A 2, 1731 (1990)], is used to analyze convective-diffusive transport processes for noninteracting neutrally buoyant Brownian particles suspended in a plane Poiseuille flow within a duct bounded laterally by two parallel plates, and subject to the influence of transverse oscillating forces acting upon the suspended particles. The mean axial particle velocity and Taylor-Aris dispersivity are calculated in the large transverse Peclet number limit ("large particle" limit), corresponding to circumstances for which particle transport is dominated by convection over diffusion. Effects arising from the externally imposed oscillatory frequency and amplitude are described in terms of a single dimensionless parameter, one whose magnitude may be manipulated to control the axial solute flux. Increasing the dimensionless oscillation period T̄ significantly decreases the axial dispersivity, whereas the functional dependence of the mean axial particle velocity upon T̄ exhibits a maximum. Physicochemical phenomena arising from the oscillatory force thereby furnish a novel field-flow fractionation (FFF) scheme for separating Brownian particles of different sizes.