Abstract: In natural rivers, suspended sediment is generally non-uniform in grain sizes, and the non-uniformity is a major factor in sediment transport and fluvial processes. However, previous studies on non-uniform sediment transport lack attention on the interactions between different grain sizes, and the non-uniformity effect on sediment suspension remains unclear. To elucidate this effect, this paper presents a constitutive equation for the drift velocity of non-uniform suspended sediment. First, applying the two-phase flow theory, we develop basic governing equations of flows and non-uniform sediment transport, focusing on the particle-particle interactions between sediment groups of different grain sizes, and derive two-phase mixture equations for non-uniform sediment-laden flows that can be used to save complicated calculation of interphase interactions. Then, drift velocity is introduced for closure of the two-phase mixture equations, and its constitutive equation is developed to describe the fact that the suspension of non-uniform sediment is attributed to influences imposed by flow turbulence, sediment particles themselves, and more importantly, interaction between particles in different grain sizes. This fact distinguishes the non-uniform sediment transport from the uniform one. Finally, we construct transport equations for non-uniform sediment using this constitutive equation, and obtain vertical concentration profiles for each grain size of the mixture. Comparison of these profiles with measurements shows a good agreement, and we demonstrate the difference from the uniform sediment cases through comparing the profiles to those calculated using Rouse formula. Result shows that when the concentration is higher and the disparity in grain sizes wider, the difference in the vertical profiles between the uniform and non-uniform methods becomes more distinct, and particle-particle interactions play a more important part in sediment suspension. The constitutive equation of drift velocity provides a theoretical way to elucidate the essence and effect of particle-particle interactions on suspension of non-uniform sediment.

Key words: non-uniform suspended sediment, drift velocity, particle-particle interaction, concentration profile