Nonuniform Diffusion of Suspended Sediment

In a recent study, Apmann and Rumer analyzed the nonuniform diffusion of suspended sediment in an open-channel flow. Experiments were performed for the situation in which a uniform open-channel flow enters from a region of rigid bottom to a region of sediment-laden bottom. The gradual development of concentration profiles is studied by measurements across the depth and along the flow direction. Theoretical calculations were also made on the basis of an approximate convective-diffusion equation; and the predicted concentration profiles agreed well with experiments. A numerical method of finite differences was used while the possibility of analytical solutions was apparently overlooked. In view of the significance of their work in extending the validity of the diffusion model for sediment suspensions, it seems worthwhile to present herein an analytical solution by Laplace transform. An approximate formula for the development region is derived from the Laplace inversion integral, which is indistinguishable in accuracy from the computer results.