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Mixing, Blending & Size Reduction

6 things process engineers should consider when scaling up (or down) mixing processes

June 10, 2021

There is no single way to determine how well a process will scale, so your experiments must combine
experience, CFD modeling and understanding the application and fluid dynamics.

Richard Kehn

SPX Flow

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When designing new mixing processes, it is often necessary to either scale up or scale down. Scaling up
is a necessary step in the design of a new mixing process, which should use both computational and
experimental methods to justify the approach. Combining these methods with past experience and
published literature often yield the best result. But when embarking on scaling a mixing process, what
should process engineers consider?

Let us first touch briefly on the reason for scaling down a process. This may be required if a process is
not working well, as a practical approach to reproduce problems and test possible fixes in an
experimental setting. Scaling down may also be part of a wider process benchmarking or optimization
exercise.
Whether scaling up or down, the methods used varies based on factors, such as the application and the
use of fluids with complex rheologies that may include solids and gas. The Handbook of Industrial
Mixing, which was published in 2004, as well as Advances in Industrial Mixing, which was published in
2016, are great resources to investigate fluid mixing, coupled with the application and scale-up
knowledge of agitator manufacturers. But even with close to 100 years of mixing application experience,
SPX FLOW Lightnin’s sizing procedures do not cover every new application being developed. Process
engineers should consider these six steps:

1. Ensure geometric similarity

It may seem obvious, but process engineers must consider the shape of the tank, the location of the
impellers, the placement of the anti-swirl wall baffles and the mixer mounting arrangement (top, side,
bottom, on center, off center, etc.) You can use 3D printing technology to produce impellers
geometrically similar to full-scale counterparts, but even if the overall diameter-to-tank ratio (D/T) is
similar, be cautious about whether lab-scale impellers will perform the same as when they are full-size.
If the measurement of impeller diameter over tank width deviates by more than 5%, this can affect
scale-up predictions, especially if starting with a large D/T of more than 0.4. The effect of continuous
sampling or probes on the flow pattern in the small scale should also be taken into consideration
because they can act like a baffle, especially if the tank size is small.

2. What scale to use?

Right from the start, it is important to understand how large of a volume will be mixed at full scale so
you can select the appropriate volume in the small scale. Typically, the smallest vessels for testing
should be 12 to 18 inches in diameter. For multi-phase applications, especially when evaluating gas
dispersion, a larger scale vessel should be considered and 24 inches should be considered the minimum
size. New formulations are often performed in the beaker-size scale by many companies (1,000 to 4,000
mL), but that will not address all the hydrodynamics concerns related to mixing the product.

SPX Flow

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3. Kinematic similarity will not a give a complete picture

Velocity in the mixing vessel is related to the tip speed of the impeller, which is the peripheral speed of
the tip of the impeller at a given rpm. If this is kept constant as the process is scaled up, the velocity field
in small scale will look similar to the velocity field at large scale. The distances involved in traveling from
points within the large-scale vessel are much larger, thus blend time increased dramatically by scaling
with this method alone. Scaling up using tip speed will also mean a much lower energy level and less
turbulence within the flow field, especially near the impeller and the vessel floor. This will negatively
impact solids suspension at the bottom of the tank and can adversely affect controlling both chemical
reactions within the flow field and dispersion of a gas.

4. Consider dynamic similarity

If the system is geometrically similar, process engineers must consider how the mixer energy is
dissipated within the volume, because the combination of mixer energy with a particular flow pattern
leads to a desired mixing result. It is important to consider dimensionless numbers from classical fluid
mechanics, such as the Reynolds number, Froude number and Weber number. The Reynolds number is
the ratio of the inertial forces created by the impeller on the fluid versus the viscous forces trying to stop
the fluid from moving. The Froude number is the ratio of the inertial forces created by the impeller on
the fluid versus the gravitational forces acting on the fluid. Finally, the Weber number is the ratio of the
inertial forces created by the impeller on the fluid versus the effect of surface tension of the fluid. All
these force ratios, coupled with the power density and circulation, should be used together to scale up
and down mixing processes for different applications.

5. The flow pattern is important

Impellers create different flow patterns depending on the Reynolds number they operate at. At a
Reynolds number over 10,000, there is turbulent flow. Transitional flows are between 50 and 10,000
(with noticeable changes starting to occur lower than 1,000) and laminar flows are less than 50. Thicker
fluids will create less circulation, and impellers will behave differently as the scale of the process
changes. The best way to fully illustrate the scale-up method is to combine the use of experimentation
and Computational Flow Dynamics (CFD).

If surface effects, such as vortices, are important, the Froude number must be maintained across scales
while matching flow regime (turbulent vs. transitional vs. laminar) as closely as possible. An impeller’s
ability to disperse gas in a liquid also scales with the Froude number. Again, if the Reynolds number is
kept similar, this helps predict the gas dispersion of an impeller across scales. For immiscible liquid
dispersions and applications that require a certain drop size, it is more important to compare the Weber
number across scales. Immiscible dispersions and emulsions, however, require additional comparisons
that are typically rather complex.

Ultimately, all these dimensionless numbers are significant, but they cannot be considered in isolation.
Practical scale-up requires process engineers to understand what factors dominate the mixing process
by understanding limiting factors. This requires experimentation coupled with computational fluid
dynamics modeling.

6. Some general guidelines

Maintain key geometric ratios, such as impeller-to-tank diameter ratio, style of impeller and the relative
off-bottom distance of the impeller. For multiple impeller systems, maintain relative spacing distances
between impellers and relative impeller coverages.

For blending applications, maintain a similar power level across scales. Blend times will get longer as the
equipment and vessel get larger, but this can be predicted. Process engineers must know at the
beginning of a project what batch time to target in the full-scale to frame the small-scale and pilot-scale
testing correctly. In other words, to achieve a 30-minute blend time in the full scale, the small-scale test
needs to be completed in a time much shorter than 30 minutes.

Changing flow regimes between scales adds complications. Consider adjusting the viscosity of the
simulant fluid to avoid this when scaling down a viscous blending application. Do not just assume
matching Reynolds number at the impeller between scales is appropriate. You must be mindful of the
fluid rheology and understand how non-Newtonian the actual fluid may be, including whether the
material has a yield stress.

A common approach for solids suspension applications is to scale up on power per unit volume for off-
bottom suspension applications. Remember to also evaluate suspension cloud height relative to the tank
outlet position. For abrasive solids, consider how the impeller blades may wear as you scale up. When
you do that, it will scale up a similar power density, and the tip speed of the full-scale impeller design
will increase. Abrasive slurries can lead to premature wear of metal impeller blades when tip speeds
exceed 5.5 to 6 m/s.

When designing a new mixing process through experimentation, ensure you vary both mixer rpm and
impeller diameter when measuring mixing performance. Do not settle for one impeller set up. Consider
different impellers and choose impellers that are designed for the process (i.e. don’t choose a Rushton
impeller for a suspension application as that isn’t the industry standard — use a hydrofoil). It is also
useful to learn when a process stops working, because it will help optimize energy usage and could help
save initial capital investment costs.

Consider your budget for full-scale mixing equipment to ensure a solution from the lab or pilot scale will
be affordable. This will help frame your experimentation effectively.

Always combine both CFD and experimentation when designing a new mixing process.
Be careful which mixing laboratory equipment you select, ensuring they can deliver impellers that are
geometrically similar to full-scale impeller design.

When partnering with a mixing solutions vendor, choose one that has in-house testing and modeling
capabilities.