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Calculation of time needed to mix liquids

How to calculate the time for mixing ?

Calculation for pitch blade impellers

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1. STEP 1 : calculate the Reynolds number
2. STEP 2 : calculate the dimensionless blend time
3. STEP 3 : Calculate the mixing time required
4. STEP by STEP example : blending time requirement calculation
5. Free Excel calculation tool for time required for uniform blending calculation

This page is explaining step by step how to calculate the time required for a pitch blade agitator to homogenize a liquid mixture.

Introduction

Tanks holding liquid are often equipped with an agitator. The agitator is often used to homogenize different liquid.

One of the key design parameter to calculate when implementing such an agitator is the time required to reach a uniform blending.

WARNING : the calculation is only an estimation, for miscible liquids, and for a specific type of impeller, however it is not giving assurance that the agitation in the tank will be adequate, further calculations or further date for other types of agitators are required.

1. STEP 1 : calculate the Reynolds number

The Reynolds number for an agitator can be calculated with the following formula :

NRe = D2.N.ρ / μ

With :

NRe = impeller Reynolds number (-)
D = impeller diameter (m)
N = agitator speed (r/s)
ρ = liquid density (kg/m3)
μ = liquid viscosity (Pa.s)

2. STEP 2 : calculate the dimensionless blend time

The Reynolds number allows to calculate a dimensionless blend time by using an abacus.The graph for pitch blade impellers is give below :

Dimensionless blend time as a function of Reynolds number

Graph 1 : dimensionless blend time as a function of NRe = D2.N.ρ/μ

This graph is valid for pitched blades impellers, if another impeller is used, another graph should be established.

The dimensionless blend time is defined with the following equation :

dimensionless blend time = tb.N.(D/T)2.3

With :

tb = Blend time (s)
D = impeller diameter (m)
N = agitator speed (r/s)
T = tank diameter (m)

3. STEP 3 : Calculate the mixing time required

Now that the value of the dimensionless blend time is known, it is possible to go back to the definition of the dimensionless blend time to calculate the required power :

dimensionless blend time = tb.N.(D/T)2.3

The time required to mix a liquid in a tank to reach homogeneity can be calculated by the following formula :

tb = dimensionless blend time / (N.(D/T)2.3)

With :

Dimensionless blend time as read on the graph above
tb = Blend time (s)
D = impeller diameter (m)
N = agitator speed (r/s)
T = tank diameter (m)

4. STEP by STEP example : blending time requirement calculation

A mixing is done in a tank of diameter 2 m with an agitator of diameter 0.5 m. The impeller is a pitched blade turbine rotating at 50 rpm. The liquid mixture has a density of 1100 kg/m3 and a viscosity of 0.4 Pa.s. One component is added quickly to the mixture for an acid-base reaction, which is a fast reaction. How long should we plan to mix for a uniform blending ?

D = impeller diameter = 0.5 m
N = agitator speed = 50 rpm
ρ = liquid density = 1100 kg/m3
μ = liquid viscosity = 0.4 Pa.s
T = tank diameter = 2 m

Step 1 : Calculate the Reynolds number

The Reynolds number can be calculated as :

NRe = D2.N.ρ / μ = 0.52*(50/60)*1100/0.4 = 573

Step 2 : Calculate the dimensionless blend time

The dimensionless blend time can be calculated thanks to the graph 1, by using the Reynolds number.

The dimensionless blend time is 40.

Step 3 : Calculate the required blend time

From the definition of the blend time :

tb = dimensionless blend time / (N.(D/T)2.3) = 40 / (50*(0.5/2)2.3) = 524 s

A margin should be taken in practice, the responsibility of the tank operator, typically 2 times this duration or more, which should be validated through actual trials.

5. Free Excel calculation tool for time required for uniform blending calculation

The power required to agitate a tank can be calculated thanks to this free Excel calculator : Calculation Tool - time required for uniform blending calculation

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

Screenshot Time Blending calculator


Sources

[Chopey] Handbook of Chemical Engineering calculations, Chopey et al, McGraw Hill, 2004