Mixing 101: Low rpm, High Torque Mixing
We often find that in the process industry, the definition of ‘Power’ is often misunderstood. It’s often used as the singular criteria for evaluating or comparing ‘apples to apples’ when it comes to mixer manufacturers – let’s say that a high G-Value or velocity gradient value correlates to higher horsepower (rpm), that in turn offers greater energy output and increased mixing rates – well, the reality is that it’s not that simple.
This misconception that higher horsepower – not torque – aids in higher mixing is common even although torque is a more significant variable in achieving greater mixing than horsepower alone. The G-value alone is not sufficient in measuring fluid behavior. Other variables like tank geometry flow rates or shearing within a given process are also part of the equation. Indeed a mixer’s horsepower output can be applied for those applications that require high-shear and turbulent flow (Re > 4000). When mixers are designed to perform at high speeds the liquid mixture’s fluid viscosity and fluid behavior patterns affect the flow created by a rotating agitator and also the shearing affect created by these harsh tip-speeds.
Before looking at how we measure efficiencies in low speed versus high speed mixing, it’s important to understand the common mixing categories involved in all industrial mixing processes.
Solid-liquid mixing; powder chemicals, pigments, dyes or dry polymers are dispersed into liquid fed by hand or thru hoppers then mixed to break up lumps of fine agglomerated solids. This mixing application is used in many operations for adsorption, suspension polymerization, crystallization, solid-catalyzed reaction and activated sludge processes. Here the particle size and particle specific gravity play a huge role in producing enough turbulent flow and impeller rotation to disperse solids against the settling rate – high shear and axial flow pumping should be considered. There are two types:
- Solid Suspension – axial flow and low shear mixing is ideal for this type of mixing where the goal is to provide enough pumping to disperse particles into buoyancy.
- Solid de-agglomeration – radial and pitch impellers provide high shear and pumping to break up larger particles.
Liquid-gas mixing; used for chemical reactions or to promote bio-organic reactions to occur, a low-density compressible gas is dispersed into denser liquids with long detention times to ensure gas bubbles remain in contact with the liquid. This mixing application is used in chlorination, hydrogenation and organic oxidation – or the most recognizable example is carbonated water or soda. Some liquids characteristics and fluid behaviors vary when gases are introduced; some decrease in viscosity while others become viscous Newtonian fluids and require different mixing strategies.
Liquid-liquid mixing; The fluid dynamic characteristics of liquid-liquid mixing produces several phenomena such as drop breakup and coalescence, mean flow pattern and turbulence, drop suspension, inter-facial area, and drop size distribution. Mixing time and Circulation Time are the two most significant parameters in liquid-liquid mixing. Impeller speed, the diameter of the vessels and impellers, the number and placement of baffles, and fluid characteristics such as viscosity are the effective parameters for determining mixing time while the mass fluid motion produced by the pumping of liquid is done by circulation time. The circulation and mixing times are helpful in recognizing the scalar transport in a tank. There are two types:
- Miscible liquids mixing – water and ethanol, for example, are miscible because they do not form visible layers when combined – take for example, vinegar and water – they mix and seldom require aggressive mixing due to the ability to completely dissolve when combined.
- Immiscible liquids mixing – two liquids with different polarity molecules or known as enthalpy are mixed, blended or their hydrophobic properties are used for solid suspension; an example would be how oil and water react when combined.
As you can see, there are various categories in applied mixing practices each with a desirable conclusion and each with its own mixing strategy – but in most instances substituting high speed in favor of low speed mixing you can achieve favorable results by measuring the pumping rate inside the tank.
Regardless of type, the most basic action of all mixing processes is to transfer energy from a power source to the product under process. This action creates shear, flow and heat in the product. In low speed mixing systems, the amount of heat input is negligible, so the power input can be said to be the product of the flow produced, and the shear or head.
The flow type is primarily indicated by blade or impeller design:
- Radial — at right angles to the shaft along the radii of the blade
- Axial — up and down parallel to the shaft
- Mixed — a mixture of the two above, generally considered true turbulent mixing
Blade types used in low speed mixing are also classified as flow, pressure or shear impellers. Low speed paired with a large blade is used for high flow processes, while a smaller impeller running at high speeds creates high shear. In general, gate blades are considered to have the highest flow and lowest shear. Radial flow turbines, bar turbines and flat blades are considered to have a higher shear component than flow component. During mixing, the outer diameter of the blade performs the most pumping or shear as it is operating at the highest velocities.
The place where low speed and high speed mixing deviate is in tank design. Flow is the most important component of low speed mixing and requires a large diameter to wall height tank. In a large volume tank where the intention is to keep product within specification during storage, a large impeller is mounted on the bottom of the shaft and run at a very low speed. This keeps fine particulate in suspension and maintains uniformity. The optimum tank design for adequate solids suspension is a round tank with an aspect ratio of about 1:1. It must either be baffled with a center mounted mixer or the mixer can be angle-offset mounted.
Low Speed Tank with Baffles
It is difficult to establish vertical flow in low viscosity fluids. When mounted at 90 degrees around the periphery of the tank, baffles assist in reaching this goal by promoting a vertical flow and discouraging the entire tank contents from rotating as a plug. Baffles introduce shear into the process and can lead to destratification, so they are not welcome in all mixing.
| Low Speed Tank with Baffles
= 1/12 of the tank diameter
= starts approximately 6 inches from the bottom and ends just above the maximum liquid level
= 1/6 of the baffle width off the tank wall
While baffles can be beneficial in low viscosity operations, they are not necessary when mixing high viscosity fluids due to the dynamic baffling effect created by viscous drag.
With axial-flow impellers, an angular off-center position where the impeller is mounted approximately 10-15° from the vertical, can be used. It’s worth noting that the angular off-center position used with axial impeller units is usually limited to those delivering 3 HP or less. The unbalanced fluid forces generated by this mounting can become severe with higher power.
Axial Flow Turbines
To find the power you need in a system, you can use the same mathematical expression as is used to determine the horsepower necessary to drive a pump. Power required is relative to the cube of the rotation speed and proportional to the fifth power of the diameter, as follows:
P = N3D5
However, this is true only for turbulent activity in low viscosity materials. As soon as flow in the tank transitions from turbulent to laminar, forces multiply, and the expression is no longer true. As with all multidimensional power and load relationships, comparison of power use is best done with a dimensionless number, in this case called the Reynolds number (NRe). The Reynolds number is a comparison of the mass inertia of the fluid system to its viscosity. Mass inertia is the product of the square of the impeller diameter (area) and density of the fluid system.
Except for a few very special cases, high viscosity systems have low Reynolds numbers, and low viscosity systems have high Reynolds numbers, when considering thixotropic and Newtonian fluids. Applications with Reynolds numbers above 10,000 are considered to be in turbulent flow and those between about 100 and 9999 are considered to be in transition, supporting both turbulent and laminar flow. Below that, flow is considered laminar.
Although we all tend to use high shear mixers for almost every application in the paint plant, there are still many applications that are better served by a low rpm, high torque processes. They can save energy, are generally gentler with formulations, and can be more efficiently used in large volume applications. When designing a system, it is important to choose impeller types wisely and power the system appropriately. This will allow you to come to grips with low speed mixing. The total flow in the basin will exceed the impeller’s primary pumping capability by a factor of two to four times due to the induced flow resulting from the effects of viscosity. However, a correctly designed system will ensure sufficient flow to utilize the maximum volume of the basin and distribute effectively the incoming flow.
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