5: Heterogeneous transport, Cvt≈Cvs.
The turbulent forces interacting with the particles are not strong enough to create a uniform composition throughout the cross-section of the pipe. A definite concentration gradient exists along the vertical profile of the pipe with the highest concentration at the bottom. There are no deposits and all the particles move in suspension or sheet flow. There is however an interaction between the particles and the bottom of the pipe. These interactions, collisions, cause the loss of kinetic energy of the particles and are the main cause of the pressure losses. Since the number of collisions per unit of time depends mainly on the terminal settling velocity of the particles, it will be almost constant, resulting in pressure losses that are reversely proportional with the line speed or the line speed to a higher power. The pressure losses can be determined according to Durand & Condolios (1952), Jufin & Lopatin (1966) or Miedema et al. (2013). The heterogeneous model is the same for fine and coarse particles.
The Shields parameter is very high above the Shields curve, resulting in a suspension. The total pressure loss is determined by the collisions between the particles and the bottom of the pipe.