The authors examine the time delays experienced by migratory particles inside nonuniform flow fields using experimental and numerical methods. Particle trajectories are affected by the particle-fluid density ratio and the flow direction, such that particles may precede or trail the fluid. In flow toward an orifice, the time delay suffered by a single particle is a function of the Froude number Fr and the Archimedes number Ar. When multiple particles are transported radially through a porous medium, time delays manifest through localized annular clogging when 0.05<Ar^-1 <0.15 and Fr<6. Gradual particle sedimentation occurs when Ar^-1>1. Applications include filtration and reservoir fluid extraction.