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
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), Proceedings of the 21st International Seminar on Paste and Thickened Tailings
, Australian Centre for Geomechanics, Perth, pp. 205-216.
Bain, AG & Bonnington, ST 1970, The Hydraulic Transport of Solids by Pipeline, Pergamon Press, Oxford.
Daily, WD & Roberts, PR 1969, ‘Rigid particles suspensions in turbulent shear flow’, Tappi, vol. 49, no. 3, pp. 115–125.
Durand, R 1953, ‘Basic relationships of the transportation of solids in pipes – experimental research’, Proceedings of the 5th Minnesota International Hydraulic Convention, American Society of Civil Engineers, New York, pp. 89–103.
Durand, R & Condolios, E 1952, ‘Experimental investigation of the transport of solids in pipes’, Colloquium on Hydraulic Transport, National Coal Board, London.
Fitton, TG 2015, ‘A note on non-Newtonian laminar/turbulent transition’, in J Sobota and C van Rhee (eds), Proceedings of the 17th International Conference on Transport and Sedimentation of Solid Particles, Delft University of Technology, Delft, pp. 79–86.
Fitton, TG 2017, ‘A hydraulic model for predicting the slopes of alluvial deposits’, Proceedings of the 20th International Hydrotransport Conference, BHR Group, Cranfield, pp. 239–250.
Govier, GW & Aziz, K 1972, The Flow of Complex Mixtures in Pipes, Krieger Publishing, Florida.
Landel, RF, Moser, BG & Bauman, AJ 1963, in EH Lee (ed.), Proceedings of the Fourth International Congress on Rheology: Part 2, John Wiley & Sons, New York, pp. 663–692.
Murphy, G, Young, DF & Burian, RJ 1955, Progress Report on Friction Loss of Slurries in Straight Tubes, Report ISC-474, United States Atomic Energy Commission, Germantown.
Schriek, W, Smith, LG, Haas, DB & Husband, WHW 1973, Experimental Studies on the Transport of Two Different Sands in Water in 2, 4, 6, 8, 10 and 12 Inch Pipelines, Report E73-21, Saskatchewan Research Council, Saskatoon.
Shook, CA, Schriek, W, Smith, LG, Haas, DB & Husband, WHW 1973, Experimental Studies on the Transport of Sands in Liquids of Varying Properties in 2 and 4 Inch Pipelines, Report E73-20, Saskatchewan Research Council, Saskatoon.
Slatter, PT & Van Sittert, FP 1997, ‘The effect of pipe roughness on non-Newtonian turbulent flow’, in J Sobota (ed.), Proceedings of the 9th International Conference on Transport and Sedimentation of Solid Particles, pp. 621–635.
Slatter, PT & Van Sittert, FP 1999, ‘Analysis of rough wall non-Newtonian turbulent pipe flow’, Proceedings of the Hydrotransport 14 Conference, BHR Group, Cranfield, pp. 209–222.
Thomas, DG 1965, ‘Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles’, Journal of Colloid Science, vol. 20, pp. 267–277.
Thomas, AD 1977, ‘Particle size effects in turbulent pipe flow of solid-liquid suspensions’, Proceedings of the 6th Australasian Hydraulics and Fluid Mechanics Conference, pp. 113–116.
Thomas, AD 1978, ‘Coarse particles in a heavy medium-turbulent pressure drop reduction and deposition under laminar flow’, in HS Stephens and L Gittins (eds), Proceedings of the 5th International Conference on Hydraulic Transport of Solids, BHR Group, Cranfield, pp. 63–78.
Thomas, AD 1979, ‘Pipelining of coarse coal as a stabilized slurry – another viewpoint’, Proceedings of the 4th International Technical Conference on Slurry Transportation, Slurry Transport Association, Washington, DC, pp. 196–205.
Thomas, AD 1999, ‘The influence of coarse particles on the rheology of fine particle slurries’, Proceedings of Rheology in the Mineral Industry II, United Engineering Foundation Inc, New York, pp. 113–123.
Thomas, AD & Wilson, KC 2007, ‘Rough-wall and turbulent transition analyses for Bingham plastics’, Proceedings of the 17th International Conference on the Hydraulic Transport of Solids, BHR Group, Cranfield, and The South African Institute of Mining and Metallurgy, Johannesburg, pp. 76–86.
Thomas, AD 2010, ‘Method of determining the inherent viscosity of a slurry and other rheological trends as illustrated by a data bank of over 200 different slurries’, Proceedings of the 18th International Conference on Hydrotransport, BHR Group, Cranfield, pp. 325–342.
Wasp, EJ, Kenny, JP & Gandhi, RL 1977, Solids-liquid Flow Slurry Pipeline Transportation, Trans Tech Publications, Clausthal.
Wilson, KC & Thomas, AD 1985, ‘A new analysis of the turbulent flow of non-Newtonian fluids’, The Canadian Journal of Chemical Engineering, vol. 63, pp. 539–545.