Using the method of process-oriented hydrodynamic modelling, this work investigates the dispersal of particles in stratified fluids on continental margins. The focus is placed on steady-state density distributions that are governed by an advective-diffusive balance. In this case, particles can still be advected across isopycnal surfaces, given that turbulent fluctuations do generally not offset the advective displacement of a particle. The validity of this fundamental principle is demonstrated here with the diapycnal upslope sediment transport in a bottom Ekman layer that forms under a stratified geostrophic slope current. Similarly, this study demonstrates that interaction between slope currents with a submarine channel can facilitate a continuous diapycnal upslope flux of particles, confined to the lowermost 10-20 m of the water column. Velocity anomalies that facilitate this upslope sediment flux are the signature of standing topographic Rossby waves, that can only develop for slope currents that are left-bounded (right-bounded) by shallower water in the northern (southern) hemisphere. Findings of sensitivity studies confirm the existence of up-channel flows for a wide range of parameter values. Under the assumption that particles remain suspended in the water column, the inclusion of gravitational settling significantly increases the up-channel sediment flux. Sediment settling operates to trap particles close to the seafloor within the core of bottom-intensified up-channel flow. The author postulates that this mechanism plays an important role in biogeochemical cycles at continental margins.