Print page

Print page

Are there limitations to the Zwietering correlation for suspending solids in liquids?

Q: I'm curious as to the limitations of the Zwietering correlation for suspending solids in liquids.

I'm particularly interested in how well it applies to very large tanks, say 500,000 gallons, and how to determine a representative mean particle diameter in a substance where particle diameter can vary dramatically.

Furthermore, how can I be sure of uniform suspension? If the Zwietering correlation is not a good fit for this application, can you recommend another method for determining the impeller speed and estimating the power requirement?

A: The Zwietering Correlation is a good start for determining an off-bottom conditions for solids suspension.  A number of other studies have found the correlation to be quite adequate, although other methods of expressing the relationship are easier to use.  Of course large tanks, 500,000 gallons, are further from the test results and predictions will be less accurate than for smaller tanks, but the correlation has been successfully used to design large tanks.
 
A bigger problem than particle size may be particle density.  Most of Zwietering's tests were with sand and glass, with densities in the mid range (sp.gr. 2 to 3).  Low density polymer particles and high density (sp. gr. > 6.0) mineral particles may not be as well represented.  A wide distribution of particle sizes, also needs to include a wide difference in densities.  A rough guide used in the mineral processing industries is to design for the 85%ile particle, but they plan to dig out the tank every few years as part of routine maintenance.  If you don't want any settled particles, you probably need to design for the largest, densest particle, with the emphasis on densest.
 
Uniform suspension is a completely different story.  The Zwietering correlation only tells you if you can get everything off the bottom.  If the particles settle slowly it takes only a modest increase in mixing intensity for uniform suspension.  If the particles settle rapidly, the amount of mixing intensity must increase by a large amount.  In the case of very rapidly settling particles and moderately tall tanks, uniform suspension my be nearly impossible.
 
In most cases, with the complexities you describe, the only way of determining how much power or mixing intensity you need will require testing, with geometric similarity, followed by scale-up.  Not all characteristics of solids suspension are handled by simple correlations.

Here are more of the latest questions on: Mixing

How do I select the optimal location for an impeller inside a tank?
I am new to tank mixing and I have a question about selecting the optimal location (and orientation) for an impeller inside a tank. I am dealing with a tank that contains very light materials (0.7 and 0.8 SG). The contents have been sitting in the tank and are stratified. Please let me know if there is some sort of general process for selecting the proper impeller position.

The tank is 120 ft. in diameter, 45 ft. high. It is allowed to only have one mixer. The first layer of material has a specific gravity of 0.75 is 32 ft. high. The second layer of the tank has a specific gravity of 0.67 and is 10 ft. high; making the total contents of the tank 42 ft. high. The purpose of the mixer is to have complete mixing within 6 hours.

Is a UDIF impeller suitable?
We have been using a UDIF agitator for emulsion polymerization mixing for 1cp to 8,000 cp. Is this type of agitator suitable for mixing?

What kind of agitator is suitable for a range of viscosities?
Our process dissolves several types of polymers in appropriate solvents. During the solving process, the viscosity might reach to the value of 8,000 cp. Our vessel dimension is 30 cm in diameter and 70 cm in height. What kind of agitator is suitable for this purpose?

What is the best way to approach gas-gas mixing?
I want to mix two low viscous gas streams in laminar regime. I am planning to mix them by passing through a pipe filled with spherical pebbles or some structured packing. I want to calculate the length required for the mixing expected. My required process stream details are as follows:

Q = 1Nm³/hr
He= 0.99
H₂= 0.01
P= 1.2 bar
Dia of pipe = 1/2 inch
Temp= 25 degrees C

I have gone through the text book "Handbook of Industrial Mixing." But that textbook has procedure for only commercially available static mixers. Please guide me through the design. Is dispersion model helpful in finding the length? If so, how?

We would like to have a general idea of pumping number for our reactors. Can you help us with blend-time calculations?
To characterize one of the reactors at plant scale, we use the discoloration method. The parameters for the mixing time are calculated based according to the following formula:

t_mix= K/(aN(D/T)^b (T/Z)^0.5 )
N = impeller speed
D = diameter stirrer
T = diameter tank
Z = liquid height
The divisor is known as Kmix

Because we don't really know the uniformity (U) reached with this method we don't replace K with

K = -ln (1-U)

But get the best fit for K, a and b by means of the least square method. It is known that the pumping number can be determined by

N_Q= (Vk_mix)/(ND^3 )

We would like to have a general idea of pumping number for our reactors. So if we would like to deviate the pumping number from the above method would it be correct that for T=Z (so at a fixed volume based on the reactor geometry) we use the following formula.

N_Q= (VaN(D/T)^b)/(ND^3 )

Working in a turbulent regime, this result in a constant pumping number related to the tank geometry. Would the above approach be correct to compare pumping and mixing time capabilities of different reactor set ups? I think that not working at a fixed uniformity results in a gap in the above approach.

Back to Ask the Experts