Thomas, AD 2018, 'Some observations regarding non-Newtonian turbulent flow and transition, especially in relation to the Wilson–Thomas (1985) theory', in RJ Jewell & AB Fourie (eds), Paste 2018: Proceedings of the 21st International Seminar on Paste and Thickened Tailings, Australian Centre for Geomechanics, Perth, pp. 205-216, https://doi.org/10.36487/ACG_rep/1805_16_Thomas
(https://papers.acg.uwa.edu.au/p/1805_16_Thomas/)
Abstract: Pipe loop data from Thomas (1978) is compared with trends predicted by the Wilson and Thomas (1985) turbulent flow theory. For a Bingham plastic clay slurry, the theory predicts that as the velocity reduces towards transition, the pressure gradient tends closer towards the water curve. When granular particles, such as sand, are added to the clay slurry, the behaviour changes. Depending on the particle size of the sand and the rheology of the clay slurry, the mixture pressure gradient may trend away from the water curve as the velocity reduces or it may tend to parallel the water curve, or it may trend towards the water line in a similar manner as for clay slurry. These differing behaviours are determined by the size of the sand particles relative to the thickness of the viscous sub-layer. If the sand particles are small enough to reside within the viscous sub-layer they will increase the viscosity within the sub-layer and increase the pressure gradient. Conversely, if the sand particles are too large to reside within the sub-layer, the viscosity is not increased and the pressure gradient is lowered. These d/effects are separate from heterogeneous settling effects which may accentuate the effects.
Fitton (2015, 2017) has noted a wide range of behaviour for different slurries in the transition region. 
The d/ effects explored in this paper may explain some of these differing behaviours.

Keywords: Bingham plastic, non-Newtonian, turbulent pipe flow, viscous sub-layer