Applying a coefficient of 10.7 makes the expression dimensionless for typical engineering units of in. for impeller diameter, rpm for rotational speed, specific gravity for density and cP. for viscosity. As viscosity increases or size, as indicated by impeller diameter, decreases, NRe becomes smaller.
The primary effect of fluid properties on both blend time and power are reflected in the impeller Reynolds number (NRe), which is expressed in terms of impeller diameter, rotational speed, density (ρ) and viscosity (μ): NRe = (D2Nρ)/μ (6)
NRegreater than 20,000 is characteristic of turbulent conditions — in which flow fluctuates in both magnitude and direction about a mean. NRedoesn't describe the intensity of mixing, only the type of flow conditions. At very lowNRe, less than 10, flow becomes laminar and velocities follow streamlines. In the transition region between turbulent and laminar conditions, fluid motion may be less turbulent away from the impeller.
With less turbulence mixing becomes slower, as both average and random velocities decrease. This slower blending correlates to larger values for Θ. For convenience, this effect can be handled as a correction factor for different impeller types (Figure 3). The factors show that blend times may increase by orders of magnitude as viscosity rises and NRe becomes smaller. Other correction factors must be applied to power calculations in the transition and laminar range.
Other effects of density and viscosity occur when one of the blended liquids has a distinctly different property. A significant density difference, especially when blending begins with stratified layers in a tank, may extend blend times by as much as a factor of five to eight. Avoid starting a blend with stratified layers if possible. Blending of different viscosity liquids is a very real and often difficult problem. Some common "kitchen" examples are mixing corn syrup or ketchup in water. Corn syrup is a viscous liquid. Ketchup not only is viscous but also has a yield stress. Figure 4 shows some correction factors for the effects of viscosity ratio on blend time at different bulk NRe. At high NRe even a large viscosity ratio between the feed and bulk has only a minor impact. Effects of different relative quantities of liquids with different properties and effects of nonNewtonian viscosities lengthen required processing times.
Estimation of blend time isn't a precise science — blending of individual batches may vary as a function both of turbulence variations and operating procedures. Thus, designing for a calculated blend time of a few minutes is probably inappropriate. However, if an estimated blend time is less than 5 min., then mixing for an hour or even one-half hour may be unnecessary. Some blending applications require other processes to take place, thus justifying longer mixing times. Understanding some major factors influencing blend time, from the inverse relationship with respect to rotational speed of the mixer to the effects of viscosity and viscosity difference, will help improve process results and efficiency.
David S. Dickey is senior consultant at MixTech, Inc., Dayton, Ohio. E-mail him at email@example.com.
1. Dickey, D. S., and L. B. Fenley, "Make Your Portable Mixer Work for You," Chemical Processing, p. 34, March 2007 (www.ChemicalProcessing.com/articles/2007/040.html).