Environmental Fluid Mechanics

, Volume 17, Issue 3, pp 449–472 | Cite as

A mathematical model for type II profile of concentration distribution in turbulent flows

Original Article


This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.


Suspension distribution Type II profile Particle inertia Granular temperature Drift diffusion 

Mathematics Subject Classification

76F25 76R50 76T20 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Basic Sciences and HumanitiesIIIT BhubaneswarBhubaneswarIndia
  2. 2.Department of MathematicsIndian Institute of TechnologyKharagpurIndia

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