Suspended sediment modelling with exponential mixing length and hindered settling

This study proposes a modified version of Hunt's model for suspended sediment concentration in turbulent open-channel flows. The classical Hunt model is enhanced by replacing its original sediment diffusivity with a modified mixing length expression l = kze–z/h that incorporates exponential turbulence decay with height. In addition, the hindered settling effect is introduced using the Richardson-Zaki formulation, allowing the model to better represent high-concentration sediment-laden flows. The resulting governing equation is solved numerically using a shooting method combined with the classical fourth-order Runge-Kutta scheme in Mathematica 12®. Model predictions are compared with experimental datasets from both dilute and concentrated regimes, demonstrating improved agreement over the original Hunt model, particularly in the upper flow region where traditional formulations often deviate.