Transport equation for nonuniform suspended sediment

Theoretical research on nonuniform sediment suspension is limited due to difficulties of elucidating nonuniform particle interaction. A new transport equation is generalized for nonuniform suspended sediment based on multi-dispersed two-phase flow theory, to account for nonuniform particle interaction and its effect on sediment suspension. Instead of implementing numerical discretization, constitutive relation of drift velocity is derived by solving the momentum equations with the aid of the Sherman–Morrison–Woodbury formula and the perturbation asymptotic technique. Applied to open channel flows, concentration profiles for each grain size of sediment are derived and a satisfactory consistency is obtained in comparison with both experimental and field data. Nonuniform sediment suspension is attributed to fluid turbulence, gravity, particle inertia and nonuniform particle interaction. The nonuniform effect plays an important role in the vicinity of the riverbed and is positively correlated to sediment concentration and grain size ratios, which helps bring insight into the suspension mechanics.