High-shear mixer
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A high shear mixer disperses, or transports, one phase or ingredient (liquid, solid, gas) into a main continuous phase (liquid), with which it would normally be immiscible.
Input of energy
This phase transport is accomplished by an input of energy, usually through an electric motor and rotating propeller or high speed rotor. When sufficient energy input results in a final product that resembles a quasi mono-dispersion fluid with no differentiation between separate components, the fluid is said to be homogenized. In this case, the fluid is almost monodisperse: the ingredient input into the main continuous phase has almost constant density and, if relevant, particle size.
When the total fluid is composed of two or more liquids, the final result is an emulsion; when composed of a solid and a liquid, it is termed a suspension and when a gas is dispersed throughout a liquid, the result is a lyosol. Note that each class of dispersion may or may not be homogenized, depending on the amount of input energy.
Mixers
A wide variety of equipment is used to transform raw electrical energy into useful mechanical energy to "work" the fluid. The primary function of any mixer is to dissipate the energy in the form of flow and shear.
Shear
To define shear, we can say that a fluid is undergoing shear if a volume, plane, parcel, etc., of fluid travels with a certain velocity relative to an adjacent volume, plane or parcel. The differential of this velocity along a defined path is known as shear rate (units of sec-1). The velocity, or tip speed of the fluid at the outside diameter of the rotor is imparted by the force exerted through a rotating or moving piece of equipment, i.e., propeller, rotor.
A stationary component may be used in combination with the rotor and is referred to as the stator. The stator creates a close clearance gap between the rotor and itself and forms an extremely high shear zone for the material as it exits the rotor. The rotor and stator combined together are often referred to as the mixing head, or generator.
In order to determine how one generator will perform compared to another, we must have a quantitative way of estimating the performance of any given design. If we compare various generators of the same diameter, rotational speed and input horsepower, we will see that the geometry has a large effect on how the generator will perform. The performance of a generator design may be evaluated by considering several factors.
Key factors in generator design
- Diameter of the rotor
- Rotational speed of the rotor, rpm
- Distance, or gap, between the rotor and stator
- Geometry of the rotor and stator teeth, including:
- Number of rows of teeth
- Width of openings between teeth
- Angle of openings between teeth
- Height of teeth
- Residence time
- Number of generators in series
Before we can evaluate the geometry of a generator design, we must first determine the tip speed of the rotor, which is a function of the rotor diameter and the rotational speed.
Tip Speed
Tip Speed: V(m/s) = PI(3.14) x D x n
Where, D is the diameter of the rotor, in meters n is the rotational speed of the rotor, in rpm
Note: units of feet/min (ft/min) are also commonly used for tip speed, and D must be in feet.
Although the tip speed is the primary factor in determining the performance of a generator, it does not take into account the factors related to geometry. When using a stator in conjunction with a rotor, we must also consider the gap between the rotor and stator, since this area is where a significant amount of the shearing takes place. We can relate the gap and tip speed with the shear using the following equation,
Shear Rate
Shear rate: Sr(s-1) = V / g
Where, V is tip speed, in m/s g is the gap between the rotor and stator, in m
Now, we must take into account the effects of the other geometric properties of the rotor-stator design.
Each time a rotor opening passes a stator opening, this high shear zone will occur. As the fluid passes radially through the generator, it is subjected to intense acceleration and de-acceleration, causing fluctuations in velocity and pressure, in three dimensions. Furthermore, each row of teeth slots breaks our fluid down into progressively smaller volumes as it moves radially outward. The result is a fluid being broken down into smaller parcels, subjected to intense velocity/pressure fluctuations, as well as the above mentioned shear. This superimposition of shearing frequency and tangential shear is known as the Gradient Impulse method of dispersion. Here, particles are broken down by intense shearing and particle-to-particle interaction, and are simultaneously transported, or dispersed, throughout the fluid. To calculate the total number of occurrences of high shear that occur for every rotation, we can use the following equation:
Shear Frequency
Shear frequency: fs = Nr x Ns x n
Where, Nr is the number of rotor teeth Ns is the number of stator teeth n is the rotational speed of the rotor, in rpm
Note that if there are multiple rows of teeth on a generator, we would have to evaluate this for each row. In addition, since each row will have a different diameter due to the nature of the geometry, the tip speed and shear rate will also be different for each row. The amount of energy input for each row is related to the geometry and the tip speed, therefore, we must relate these two parameters for each individual row with the following equation:
Shear Number
Shear number: S = fs x Sr
Where, fs is the shear frequency Sr is the shear rate
Both of these equations demonstrate the effect of having multiple teeth on the rotor and stator, and how the energy input for shear is effected by them.
In normal practice, these calculations are applied to the outer row only. The reason the inner rows are not included is because they have fewer teeth and a smaller tip speed, thus, their energy input is less significant. When comparing one generator to another, it is usually suffice to consider the outer row of teeth only. However, when designing a generator for scale up or accurate performance, the designer must always consider all rows and their energy input into the fluid. The inner rows provide a successive dispersing action that helps with size reduction and homogenization before the product reaches the outer row.
If we look at the pictures of different generators that were shown in figure 1.2, it is now somewhat apparent what the differences are between the generator designs. The colloid mill generator has a very small gap, and therefore, a high shear rate. This will greatly restrict the flow rate, so these machines have limited flow ranges, and become costly as the flow rates get high. The medium shear (homogenizer) generator has only four rotor teeth and has relatively large stator openings, giving it high pumping capabilities, and moderate shear energy input. The high shear disperser has multiple rows, and significantly more teeth, giving a much higher shearing effect, while allowing a moderate flow capability. Note that in machines with interchangeable generators, a generator with a high pumping capacity can easily be substituted for one that produces high shear. If a multiple stage unit is used, the possibilities are greatly expanded, because now we have multiple choices for each stage. For example, if a three stage machine has generator options for coarse, medium, fine, superfine and pumping, we can combine these options for up to a total of 15 different combinations. This allows the machine to be tailored to any product requirements, and offers the maximum in flexibility.
Alternative Shear Mixing Technologies
Different from the standard rotor-stator concept, there are other technologies to generate shear forces, e.g. ultrasonics. Ultrasonic cavitation is known to generate high speed liquid jets of up to 600mph resulting in a shearing of the liquid. This technology is used, e.g. to disperse, dissolve or mill materials in liquids.
Summary
In summary, the design of rotors and stators, along with the high peripheral rotor tip speeds and narrow concentric gaps, allow the user to produce a wide range of extremely stable dispersions quickly and efficiently. The high shear, Gradient Impulse, mechanisms enable the user to enter a new area of cost-effective, efficient fluid processing. We may now produce highly stable emulsions, suspensions and lyosols via the Gradient Impulse method.