Spreading and deposition of particulate matter in uniform flows

We consider the fate of a cloud of heavy particulate matter instantaneously released from either a line or a point source in a uniform ambient flow. The particles are advected by the flow as well as sedimenting from it. The behaviour of the current is determined by a non-dimensional parameter that represents the ratio of the advected flux of the ambient flow to the downward particle flux to the boundary. We determine the horizontal extent of the particulate matter and the density of the deposit as functions of time in terms of this parameter. In particular we evaluate the maximum upstream penetration distance of the particles.We also present the results of a series of experiments for a line release in a channel (the two-dimensional situation) and find excellent agreement between our theoretical predictions and the experimental data for: the upstream and downstream lengths of the current as functions of time; the final areal density of deposit on the floor; and the maximum upstream penetration of the current.