Just Suspended Speed in Stirred Tanks

There have been many experimental stndies and theoretical analyses, with the pioneering work of Zwietering (1958) as the earliest known. He derived the following correlation from dimensional analysis and estimated the exponents by fitting to data for jnst snspended impeller speed, Njgi 

With the exception of the density difference, the influence of fluid and particle properties on Njs is not large, as indicated by the small exponents on the kinematic viscosity, v, the particle diameter, dp, and the solid loading parameter, X, in eq. (10-11). The density difference is the property with the largest influence on Njs. Its exponent reflects the effect of the terminal settling velocity of the particles. The exponent on the impeller diameter, D, represents the effect of scale. Note that an exponent of —0.67 on D would imply a scaling rule based on power per volume. 

1 Effect of Fluid Viscosity. Most studies and apphcations of solid suspension occur in the turbulent regime, so the small effect of viscosity is expected. In fact, pubhshed values of the viscosity exponent range from 0 to 0.2 for experimental studies (Zwietering, 1958 Chapman et al., 1983 Ibrahim and Nienow, 1994 Rieger and Did, 1994). This suggests that the true hydrodynamic mechanism for the just suspended condition remains fuzzy. There may actually exist a hydrodynamic regime where there is little or no influence of viscosity and another where the influence is reflected in a positive value of the exponent. 

The highest viscosity tested in the studies cited is only 100 inPa s (Ibrahim and Nienow, 1994). What happens when the fluid viscosity is even higher remains to be determined. With a more viscous fluid, or as the transitional flow regime is approached, the hydrodynamics near the vessel base may change and make it more difficult for sohds to be picked up, even though the bulk of the fluid remains turbulent. 

2 Effectof Solid Loading. Zwietering chose to represent the effect of solid loading with the parameter X defined above. The exponent on this parameter fits experimental data reliably for values of X from about 5 to 170, which corresponds to about 2 to 40 vol% by volume for sand at a solid density of 2600 kg/m.  

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