Particles in non-Newtonian liquids

As for settling of single particles in Newtonian liquids, the fundamental hydrodynamic characteristic for particle motion in non-Newtonian fluids is again the drag coefficient. Its prediction allows calculations of terminal settling velocities. Note that equation 18.10, which applies to low particle concentrations (below 0.5% by volume) in Newtonian liquids at low Reynolds numbers, can, in principle, also be used non-Newtonian fluids where viscosity // then becomes the apparent viscosity but, depending on the type of the non-Newtonian behaviour (= model), its determination may require an iterative procedure. Each model redefines the particle Reynolds number so that, for example, for a power law fluid characterized by constants n and K 

Prior to 1993 the results of theoretical and experimental smdies on the flow of non-Newtonian fluids past a sphere have been reviewed by Chabra . Since then a number of research smdies have been published, most notably by Machac and co-workers at the University of Pardubice. They investigated experimentally the drag coefficients and settling velocities of spherical particles in power law and Herschel-BuUdey model fluids, in Carreau model fluids (spherical in ref. 13 and non-spherical in ref. 14) and also the effect of the wall in a rectangular ceU, for power law fluids.  

Chabra et al have shown that the Richardson and Zaki equation (represented by equations 18.12 and 18.15) can be used for prediction of sedimentation velocities with power law fluids in the range of flow index 0.8 n 1. This was to some extent confirmed by an experimental investigation using a conductivity meter although much larger discrepancies were found than for Newtonian fluids, attributed to the observed development of local nonhomogeneities. 

As the use of non-Newtonian fluids in industry is increasing, the interest and research in the fundamentals of flow through packed and fluidized beds for non-Newtonian fluids are also growing. The latest example is the recent work of Machac and co-workers on purely viscous and viscoelastic fluids. The application of their work to cake filtration is discussed in section 9.9 of chapter 9. 

The most fundamental and also practical tasks in fluidization are to describe the transition from a fixed bed to a fluidized bed, and to predict the fluidized bed expansion as a function of the flow rate and of the rheological behaviour of the fluid. For the fluidization with Newtonian liquids, the bed expansion is usually well described by the Richardson and 

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Little is known about the effect of visco-elasticity on the motion of bubbles and drops in non-Newtonian fluids, though a preliminary study suggests that spherical bubbles are subject to a larger drag in a visco-elastic than in an inelastic liquid. Recent surveys clearly reveal the paucity of reliable experimental data on the behaviour of fluid particles in non-Newtonian liquids [Chhabra, 1993a DeKee et al., 1996]. 

Siska, B., Machac, I. and Leejaks, Z., Sedimentation of spherical particles in non-Newtonian liquids (in Czech), Zbomik 23. konferencie SSCHI, Zavazna Poraba... 

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