# Solid-Liquid Mixing In Agitated Vessels (Just Suspended Speed)

Dear All,

Solid suspension and dispersion in a liquid is an important operation carried out in mixing systems. The primary objective of solid-liquid mixing is to create and maintain a solid-liquid slurry, and to promote and enhance the rate of mass transfer between the solid and liquid phases. Such processes are typically carried out in mechanically agitated vessels and reactors. In agitated vessels, the degree of solids suspension is generally classified into three levels: on-bottom motion, complete off-bottom suspension, and uniform suspension. Refer the sketch below. For many applications, it is often important just to provide enough agitation to completely suspend the solids off the tank bottom. Below this off-bottom particle suspension state, the total solid-liquid interfacial surface area is not completely or efficiently utilized. Therefore, it is important to be able to determine the impeller agitation speed, Njs, at which the just suspended state is achieved by the particles.

Correlation for Just Suspended Speed:

where:
Njs = minimum impeller speed to just suspended solid particles in vessel, rps
S = Zwietering constant
ν = Kinematic viscosity of the liquid, m2/s
gc = gravitational constant = 9.81 m/s2
ρs = denisty of solid particle, kg/m3
ρl = denisty of liquid, kg/m3
X = mass ratio of suspended solids to liquid or solid loading'=kg of solids / 100 kg of liquid
D = Impeller diameter, m

Table for Zwietering Constant (S):

Snapshot of an Example Problem in Excel:

This concludes today's blog entry. Would to receive comments from the learned members of "Chereosurces"

Regards,
Ankur.

Shamsey

It is a very helpful content as I am designing a preparation and storage tank equipped with an agitator to keep the solids suspended in water. However the particle size is unknown but I will have its sieve analysis done soon. Could you please share the calculation sheet so that I may be able to calculate Kinematic viscosity and Njs as soon as possible?

Best Regards
Faraz Shamsey

This is very informative content.Can you please provide the Zwietering Constant for the plain bottom tanks (reactors).Please share the calculation sheet so that I may be able to calculate Kinematic viscosity and Njs of my tanks.

shakila21

Hi ankur,

I have a question. I need to calculate the needed torque for the Impeller. Is it simply achieved by the T=r.V formulation? it means just multiply the speed of impeller to its radius?

regards

ankur2061

Hi ankur,

I have a question. I need to calculate the needed torque for the Impeller. Is it simply achieved by the T=r.V formulation? it means just multiply the speed of impeller to its radius?

regards

Shakila,

Have a look at eqn (2) in the link below:

http://turbolab.tamu...proc/P19/17.pdf

Regards,

Ankur

shakila21

HI Ankur,

Thank you vary much for your reply. It was so helpful.

Regards

shakila

dharam

bartlika

Hi Ankur,

I came across your entry as I am looking into calculating the just-suspended mixing speed in agitated vessels. I tried to replicate your calculation but get a value of 3.76 rps for Njs. I wonder what I am missing. I checked the units and they all cancel out fine. Can you share the Excel file please? Thanks, Karsten

Reddy Kona

Helpful calculations. But could you please explain how Njs depends on scale of manufacturing and liquid height inside the reactor?

According to the given formula, Njs would be same for a given impeller irrespective of batch size and % volume of reaction mass.

Reddy Kona

Hi ankur,

I have a question. I need to calculate the needed torque for the Impeller. Is it simply achieved by the T=r.V formulation? it means just multiply the speed of impeller to its radius?

regards

Hi Shakila21,

You can get the value of torque by multiplying the radius and force applied at a given RPM. But one needs to calculate Njs, P/V, Nre kind of parameters w.r.to lab scale to ensure the given RPM would be sufficient.

Santosh Neralla

Hi Ankur,

Can you please share the Zwietering constant values for Gas induction turbine agitator.

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