Nonlinear Partial Differential Equation for Unsteady Vertical Distribution of Suspended Sediments in Open Channel Flows: Effects of Hindered Settling and Concentration-Dependent Mixing Length

Abstract

A model on one-dimensional unsteady suspended sediment transport has been developed in this study by including the effect of hindered settling and from mixing length point of view. The sediment diffusion term has been related to mixing length, which has been taken as a function of concentration. The mixing length and settling velocity are reduced due to the presence of particles in the flow. By considering these effects in the governing equation, the resulting partial differential equation (PDE), which becomes highly nonlinear, has been solved numerically using the most generalized boundary conditions available in the literature. For the purpose of validation, the derived model is compared with similar existing works under certain specified conditions. Apart from that, the obtained solution has also been compared with available laboratory data for steady and uniform flow because over a large span of time, the model behaves like a steady one. Furthermore, effects of damping function and hindered settling are explained both graphically and physically.