Vertical sediment concentration distribution revisited with shear-induced diffusivity: An explicit series solution based on homotopy analysis method

TL;DR

This paper develops an explicit analytical solution for vertical sediment concentration profiles in open channel flow by incorporating shear-induced diffusion using the Homotopy Analysis Method, providing new insights into sediment transport mechanisms.

Contribution

It introduces a novel analytical approach using HAM to solve the Hunt diffusion equation with shear-induced diffusion, enhancing understanding of sediment concentration distribution.

Findings

Shear-induced diffusion significantly affects sediment profiles.

The analytical solution aligns well with experimental data.

Turbulent factors like Schmidt number influence concentration distribution.

Abstract

The present study revisits the vertical distribution of suspended sediment concentration in an open channel flow with a special attention to sediment diffusion coefficient. If turbulent diffusivity is considered to follow a parabolic-type profile, the diffusivity coefficient is zero at the bed and very small near the bed; so alone it may not be enough to diffuse the particles from bed-load layer to suspension region. Leighton & Acrivos (J. Fluid Mech., vol. 181, 1987, pp. 415-439) introduced the idea of shear-induced diffusion that arises due to the hydrodynamic interactions between solid particles. This work considers the Hunt diffusion equation incorporating the concept of shear-induced diffusion and reinvestigates the vertical sediment concentration profile. Analytical solution is derived using a non-perturbation approach, namely Homotopy Analysis Method (HAM), and is verified with numerical solution as well as compared with available experimental data. The behaviour of the shear-induced diffusion coefficient with vertical distance and varying particle diameters have been interpreted physically. In addition, the effects of important turbulent factors such as inverse of Schmidt number, hindered settling velocity on concentration profile, have been investigated considering relevant sets of experimental data.