Transport Equation for Suspended Sediment Based on Two-Fluid Model of Solid/Liquid Two-Phase Flows

Abstract

Most theoretical and numerical studies employ diffusion theory to investigate suspended sediment distributions in fluvial rivers, yet diffusion-theory-based descriptions are strictly valid only in the limit of small particle inertia and low concentrations. This paper presents a transport equation for sediment in suspension based on a two-fluid model of solid/liquid two-phase flows. The transport equation is derived from the consideration of mass conservation for solid particles. The velocity of the solid phase is obtained from an asymptotic solution of the momentum conservation equation for solid phase. Moreover, this transport equation is a typical convection-diffusion equation that includes the conventional diffusion equation as a special case when particle inertia is small and concentrations are low. Retaining the essential features of two-fluid models, the transport equation is applicable to sediment-laden flows with a wide range of particle inertia and sediment concentrations. Comparisons of the results with available experimental observations are presented, and fairly good agreement is obtained.