Turbulent Flow of Non-Newtonian Suspensions in Pipes

A physical model of the turbulent now of purely viscous, non-Newtonian fluids in smooth pipes has been postulated. According to this model the chaotic motions of particles increase the opportunity for particle interaction which consequently increases the contribution of viscous stresses to total stresses. As a result of this phenomenon (viscous interaction) the viscous stresses in the turbulent field are much higher than laminar rheological relationships yield and the viscous interaction in turn, imposes a restriction on free movement of particles and reduces the turbulent stresses. Therefore in a turbulent field, the effect of viscous stresses as compared to Reynolds stresses cannot be ignored as is customary. Based on this model starting with Navier-Stokes equations two relationships are derived which permit one, a priori, to evaluate velocity profiles and head losses in a smooth pipe from the knowledge of pipe diameters, mean velocities and properties of the suspensions.