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Lagrangian statistics are explored as a means of describing the transport of solids in a turbulently flowing liquid. The essential feature of the approach is to represent the concentration field as resulting from a distribution of sources of particles. It is argued that this provides a better framework to understand the physics than the Eulerian analysis currently being used. Fully developed concentration fields are calculated, using the assumptions of homogeneous turbulence and plug flow. It is found that the configuration of solids and the suspended load depend primarily on the ratio of the settling velocity to the friction velocity, which is a measure of the relative importance of turbulence and of settling in depositing particles. The analysis emphasizes the need for a better understanding of the mechanism and the rate of entrainment of particles into a turbulently flowing liquid.

Transport properties of various uncross-linked and cross-linked non-Newtonian slurries in horizontal pipes are studied. Flow data are gathered in three long, different diameter, transparent horizontal pipes. Investigated are the effects of the pipe size, polymer concentration, fluid rheological properties, cross-linking effects, particle size and density, solids concentration, fluid density, and slurry rate on the critical deposition velocities and particle resuspension velocities. It is found that critical deposition and resuspension velocities for the non-Newtonian carrier fluids tested are significantly lower than those for water. Both velocities depend greatly on pipe size and particle density. Higher critical velocities are required to minimize settling (1) in larger pipe sizes and (2) for pumping solids denser than sand. For less viscous fluids, critical deposition and resuspension velocities increase slightly with increasing solids concentration. They are, however, independent of solids concentration for more viscous fluids.

In slurry transport, the critical velocity is defined as the minimum velocity demarcating flows in which the solids form a bed at the bottom of the pipe (bed load flows) from fully suspended flow. An analysis based on balancing the energy required to suspend the particles with that derived from dissipation of an appropriate fraction of the turbulent eddies is used to develop a correlation for prediction of the critical velocity. Comparison of the results with available experimental critical velocity data, relating to a rather wide variety of slurry systems, confirms that the present correlation does a superior job of prediction than all previously proposed critical velocity correlations.

An analysis was made of flocculated slurries outside of their compaction zone. The analysis of the flocculated slurries was complicated by the fact that measurements of solid particle size and density are not necessarily indicative of those of the flocs. Successful correlation of availabie experimental data appears to justify the supposition that the mechanism for particle suspension in conduits is similar to that in mechanical mixers. It was concluded that in order to transport a nonflocculated slurry outside its compaction zone without deposition of solids, it is necessary that the flow be turbulent. For very slowly settling particies in small lines, the only requirement is that the flow be fuliy turbulent. For more rapidly settling particles or larger conduits, greater eddying movements are necessary to supply the vertical forces that keep the particie in suspension. (P.C.H.)