Chemical Engineering April 2023 - 26

Facts At Your Fingertips
Mixing Intensity in Stirred Tanks
Department Editor: Scott Jenkins
he ability to quantify liquid motion
in a stirred tank is a basic
step toward understanding how
mixing influences process results.
Quantifying mixing according to a
mixing index (MI) can evaluate and
predict mixing intensity related to fluid
velocities in stirred tanks.
MI provides a measure of mixing
intensity in stirred-tank applications
with turbulent or transitional flow. The
idea of a liquid mixing index is that
most of the mixing effects in a stirred
tank can be related to the liquid velocities
in typical flow patterns. MI is
not intended to be a test for subtle
differences between mixing situations,
but rather a simple way of evaluating
or designing mixers for stirred
tanks. It tries to capture the degree to
which fluid flow will promote the dispersion
of dissolved solutes or suspended
materials in a fluid.
For more discussion of mixing intensity
calculations and background
literature, see Ref. 1.
One-to-ten scale
When MI is determined, a one-toten
scale is used to describe the
fluid motion associated with mixing
intensity. An MI of one is considered
to be the minimum level of
liquid motion capable of moving all
of the liquid in a stirred tank. An MI
of ten is an upper limit to intensities
encountered in most industrial process
applications. The difference in
intensity between consecutive mixing-index
values on the scale (such
as the difference between an index
of two and three) is about the limit of
differentiation possible with any description
of mixing intensity.
As with most scientific and correlated
mixing results, the effects of
transitional flow conditions, different
liquid levels, multiple impellers, and
adjustments to impeller geometry
are not provided in the reported results.
By focusing on a practical definition
of the MI and years of experience
with the method for estimating
mixing intensity, calculations can be
reduced to simple formulas and correction
factors.
26
T
The basic idea of a mixing index
comes from the article by Hicks and
others [2]. The assumption is that by
using a " pumping number " that is a
function of both D/T (the ratio of impeller
diameter to tank diameter) and
Reynolds number, a " bulk fluid velocity "
across an equivalent tank crosssectional
area can be calculated [1].
The " bulk fluid velocity " is a representation
of the recirculation
Multiplying the pumping index for
each impeller, times the rotational
speed, times the impeller diameter
cubed and replacing the equivalent
tank diameter with a cube root
function of the tank volume forms
the basis for the MI formulation [1].
Rearranging the terms and pumping
index numbers, coefficients can be
found to calculate MI values for each
impeller type.
MI guidelines and characteristics
The following are mixing characteristics
for various MI values associated
with stirred tanks.
MI 1-2. MI values of 1 and 2 are
characteristic of applications requiring
minimum fluid velocities to achieve
the process result and are often applied
in liquid storage applications.
Mixers capable of a MI = 2 will:
*Blend miscible fluids to uniformity
if the specific-gravity differences are
less than 0.1
* Blend miscible fluids to uniformity
if the viscosity of the most viscous
component is less than 100 times the
viscosity of the other fluid
* Establish
complete
fluid-batch
control
* Produce a flat but moving fluid
batch-surface
MI 3-6. Mixing indices of 3 to 6 are
characteristic of fluid velocities in
most industrial mixed batches, especially
those used to accomplish a
physical process, such as formulations
and heat transfer.
Mixers capable of a MI = 6 will:
* Blend miscible fluids to uniformity
if specific-gravity differences are less
than 0.5
* Blend miscible fluids to uniformity
if the viscosity of the most viscous is
References
1. Dickey, D., Liquid Mixing in Stirred Tanks, Chem. Eng., August
2019, pp. 24-35.
2. Hicks, R.W., Morton, J.R., Fenic, J.G., How to Design Agitators
for Desire Process Response, Chem. Eng., April 26, 1976, pp.
102-110.
Editor's note: the text for this column was adapted from Ref. 1.
CHEMICAL ENGINEERING WWW.CHEMENGONLINE.COM
APRIL 2023
FIGURE 1. The liquid mixing index is related to the
liquid velocities of typical flow patterns in a stirred
tank
less than 5,000 times the viscosity of
the other fluid
* Suspend trace solids (<0.2%) with
settling rates from 2 to 4 ft/min
* Produce surface rippling at lower
viscosities
MI 7-10. Mixing indices of 7 to 10 are
characteristic of applications requiring
high fluid velocities for a rapid process
result, such as chemical reactors.
Mixers capable of a MI = 10 will:
* Blend miscible fluids to uniformity
if specific-gravity differences are less
than 1.0
* Blend miscible fluids to uniformity if
the viscosity of the most viscous fluid
is less than 50,000 times that of the
other fluid
* Suspend trace solids (<0.2%) with
settling rates of 4 to 6 ft/min
* Provide surging surfaces at low viscosities
Process
results
will
vary, especially
if the average viscosities put
the Reynolds number in the transition
range. Any time the viscosity is
considered to be non-Newtonian,
process applications become more
difficult and the effective mixing index
will be reduced. No MI calculations
should be taken as absolute results,
but rather considered as approximations
to typical industrial conditions.n
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