Dynamic settling is the phenomenon whereby a relatively dense particle settles through a sheared flow of a non-Newtonian fluid at a speed that depends on the shear rate of the background flow. This means that due to the nonlinear rheology, the settling velocity may vary spatially and temporally as the background shear rate of the suspending fluid varies, an effect which does not occur in Newtonian fluids. In this contribution, the consequences of this dependency are explored for a dilute suspension of particles released uniformly from a source in a sustained and externally-driven flow of shear-thinning fluid. It is shown theoretically that the concentration field does not remain uniform, but evolves downstream, allowing calculation of the runout length, settling times and distribution of the deposited particles. Flows with a velocity maximum are demonstrated to affect the concentration field very strongly as they develop a 'kinematic barrier' over which settling times are considerably lengthened. Flows with bi-disperse suspensions are shown to produce deposits that vary non-monotonically in thickness and composition with distance downstream, an effect which is solely due to dynamic settling. Finally flows of viscoplastic fluids which exhibit yielded and unyielded regions may accentuate the role and effects of the kinematic barrier to settling. (C) 2016 Elsevier B.V. All rights reserved.