Newtonian fluids drag curve

Extensive comparisons of predictions and experimental results for drag on spheres suggest that the influence of non-Newtonian characteristics progressively diminishes as the value of the Reynolds number increases, with inertial effects then becoming dominant, and the standard curve for Newtonian fluids may be used with little error. Experimentally determined values of the drag coefficient for power-law fluids (1 < Re n < 1000 0.4 < n < 1) are within 30 per cent of those given by the standard drag curve 37 38. ... 

The motion and sedimentation of particles in non-Newtonian fluids was considered by direct numerical simulation in [129, 130,193, 194, 207,484], The books [92, 112, 272] present a detailed review of investigations related to the motion of particles, drops, and bubbles in a non-Newtonian fluid, as well as numerous formulas and curves determining the drag force. 

With this definition all the steady-state drag data on single, smooth spheres moving in infinite , quiescent, newtonian fluids at moderate velocities can be represented by aj single curve on Fig. 6.22. This figure shows also drag coefficients for disks and cylinders, to be discussed later. It is limited to steady velocities of less than about one half the local speed of sound velocities higher than this are discussed elsewhere [18]. 

Unlike the flows considered in Chapter 3 which were essentially imidirectional, the fluid flows in particulate systems are either two- or three-dimensional and hence are inherently more difficult to analyse theoretically, even in the creeping (small Reynolds number) flow regime. Secondly, the results are often dependent on the rheological model appropriate to the fluid and a more generalised treatment is not possible. For instance, there is no standard non-Newtonian drag curve for spheres, and the relevant dimensionless groups depend on the fluid model which is used. Most of the information in this chapter relates to time-independent fluids, with occasional reference to visco-elastic fluids. 

On the other hand, many investigators (Barnett et al, 1966 Yamanaka and Mitsuishi, 1977 Acharya and Ulbrecht, 1978) have put forward empirical correlations for drag on bubbles in a variety of viscous and viscoelastic fluids, up to about Re 700-800. However, none of these have been tested using independent experimental results, and little is known about their applicability. More recently, De Kee and Carreau (1993) have attempted to develop a generalized drag curve for bubbles in non-Newtonian fluids. Following the approach of Metzner and Otto (1957), De Kee and Carreau introduced the... 

The unknown constant k was evaluated in such a manner that the Newtonian drag curve could also be used for non-Newtonian fluids by evaluating the viscosity at 7 = yeff. However, the utility of this approach was severely limited by the fact that it was not possible to correlate ki with the rheological parameters of the continuous phase. Hence, it is not possible to evaluate kj a priori in a new application. 

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