A New Twist on a Rotor-Stator Mixer

By Tiffany Kalva

In adhesives and sealants industry literature, we know that any number of physical forces can cause the phenomenon of dispersion. For the most part, today's dispersions are done by shear induced by radial motion. This includes the action of the high-speed disperser and multishaft mixer.

In understanding the application of mechanically induced pressure dispersion, we can examine the mechanism of shear induced by radial motion, as many of the same physical laws apply to both types.

In a high speed disperser, for example, the active mechanism of dispersion is differential laminar flow. A flat disc is spun at the end of a shaft at high speed in a tank containing a slurry comprised of the material to be dispersed and the dispersing medium, vehicle, or resin. This disk differentially accelerates the medium and material, with the material moving fastest at the surface of the disc. Further away from the disk, the material moves proportionately slower, depending on the viscosity, or 'stickiness' of the medium. This is the reason that the higher the viscosity of the material to be dispersed in a high-speed disperser, the greater the input efficiency or the ability to couple the drive horsepower to the material under process. The major limitation of this type of dispersion device is its ability to circulate the medium in the process tank. The circulation of a high-speed disperser blade is provided by the saw-tooth shaped blades located at the periphery of the disk. These function as vanes to impel the material to flow radially from the tip of the blade, much like small segments of a radial turbine, but operating at speeds where radial turbines take too much power to be considered efficient.

In addition to causing shear to be used in mixing or dispersion, this type of differential laminar acceleration causes some unwanted byproducts. The most destructive is heat. Excess heat is caused by the inability of the material to adsorb all of the kinetic energy applied. When excess kinetic energy is manifested in the form of heat, it causes the dynamic viscosity of the material under process to decrease, further impeding its ability to absorb energy. Soon, no additional dispersion work is done and eventually the energy state of the system will reach homeostasis with a majority of the energy in the system being expending on flow.

It is safe to say, then that nearly 100% of the work done by high speed disperser is done on, or with respect to the large, flat radial area of the blade. Understanding this, it is easy to understand the limitations of the device as a disperser. The rapidly spinning disk grabs a layer of the premix material and causes it to be spirally accelerated off the face of the blade. This layer drags along the next layer at a slightly slower speed. The second layer drags along a third layer, and so on. The speed differential between these layers causes a shear stress at the interface between the layers. It is this force which tends to tear agglomerates apart, and move the particles into the bulk of the premix. This energy transfer process between the blade and the premix in not efficient, and a significant energy loss is incurred at each layer boundary. There are, then, a limited number of boundary areas that can be formed, depending on viscosity, before the energy level of the accelerated layer is very close to the molecular energy of the slurry. In fact, this might translate millions of microscopically thin layers that occupy no more than a few inches of space. As a general rule, sufficient energy to do work only exists in an area 1/3 of the blade diameter away from the blade. Therefore, for a 10" blade, the overall area of efficient work is described by a section of a cylinder 13 " in diameter and 6 " thick. A high speed disperser, then, must be able to circulate the bulk material of the batch into and out of the high shear area (adjacent to the blade) enough of times to build the residence time necessary (at that given shear rate) to effect dispersion.

The exact quantifiable level of the force exerted on the material in this system is traceable and proportionate to the Reynolds number, a dimensionless quantity that describes the degree of turbulence in the flow produced by an impeller. A high Reynolds number (over 10,000) describes turbulent flow, whereas a low Reynolds number (below 10,000) describes laminar flow. It is generally thought that laminar flow is necessary for dispersion, while conditions of turbulent flow are necessary for wetting. The actual quantity is arrived at in your application by multiplying 10.7 times the material specific gravity, times the impeller rotational speed in feet per minute, times the impeller diameter squared. This product is then divided by the material's dynamic viscosity in centipoise. The mathematical expression is:

If this calculation yields an answer between 101 and 10,000, it is likely that your operating conditions favor dispersion, and that the energy transferred by your disperser blade is pulling your agglomerates apart in the velocity differential layers of the laminar flow area.

To fully understand the mechanism of dispersion let us examine the topology of an agglomerate. An average agglomerate is a tightly packed mass of smaller, unique particles which are informally arranged around a nucleus of air or some other impurity. The space between the particles varies from material to material, but remains remarkably uniform within a single material type, such as carbon black, titanium dioxide or calcium carbonate, a phenomenon related to the material's packing density. In order to determine the residence time necessary to break agglomerates apart, we can model the particle interstices as capillaries, and apply the following expression:

... where L is the distance to which the formulation vehicle penetrates into a pigment capillary channel of radius "W' in a give time period(t). From this expression, it follows that the tightly packed pigment agglomerates with very small pores and high viscosity vehicles tend to retard penetration. Even under more favorable conditions viscosity and pore size, if mechanical separation is not provided, wetting would proceed slowly and to only a limited extent. There are many ways to effect particle breakup. It is here that the standard high-speed disperser blade stumbles and the rotor/stator type device takes over.

Up until the recent development of the pressure wedge device, the rotor/stator devices that actually worked were devices of extremely close tolerances and high speeds, which had the reputation of being power hungry and unable to handle high viscosity materials. Let's take a look at why this was so.

The object of a rotor/stator is dual. First is to produce a semi-closed system in which the shear content of the energy applied is magnified. Second is to provide the ability to replace the sheared material, after having been acted upon by the rotor/stator, by fresh material which has not. Most of the activity that happens in a rotor/stator can be looked upon similarly to what happens in a media mill, in that we can successfully predict how much work is being done in the shear zone by knowing the temperature and residence time. Problems in designing a rotor/stator are not generally in designing sufficient shear into the system, but rather in balancing this with a flow component that will replace material in the rotor/stator head predictably at a wide range of viscosities. Increasing shear is relatively easy. It can be accomplished by:

1. Increasing the speed of the rotor so that greater amounts of energy can be sinked to the material under process.
   
2. Increase the number of shear surfaces on the stator so that more shear can be generated. This act often causes a lowering of the open area of the stator, assuming that the stator diameter is held constant.
   
3. Decrease the volume of material that is being worked on at any one time by the rotor/stator, in effect distributing a fixed amount of shear energy over a smaller volume of material under process.

It is easy to see that as we optimize a standard high-speed rotor stator for maximum shear, we are unavoidably also minimizing its ability to provide flow. A short elaboration follows:

1. The vanes of most rotors operate as radial turbines operated in their least efficient operation area—high speed. These systems often experience cavitation, which is only remedied by increasing open area, thereby decreasing shear.
   
2. Increasing shear surfaces requires decreasing the open area of the stator, which exacerbates the rotor's tendency to cavitate. Increasing the size of the inlets or baffling them to direct flow are useless, since the problem with the system is hydraulic in nature and at the numerous outlets of the stator. Often stators are designed with excessive open area to enhance flow, then baffled to increase shear. This is usually adjustable during operation and attempts to compensate for a material's tendency to increase in viscosity as solid surface area (and therefore interparticular interference) increases.
   
3. To decrease the volume of a rotor, the designer often fills the low-energy space of the rotor with ballast. (To decrease the volume in the head, the volume of the rotor is increased.) This is usually done to the detriment of system flow, although the additional mass makes the rotor run truer.

In order to solve the flow problems in these high-speed, high shear systems, external devices are normally called into use. Examples range from mounting a marine propeller coaxially with the rotor shaft to increase flow to the old multishaft trick of mounting a low speed sweep blade in the tank along with the rotor/stator head. These patches work to a degree, but come at the cost of power expenditure and efficiency.

It is pretty obvious that in order to be able to accommodate high viscosity slurries, our entire thought process regarding rotor/stators must be changed, and we must move from thinking about shear to consider some other dispersion mechanism like pressure.

What would happen if, rather than trying to get the entire dispersion process done at once with shear, we instead opt to accomplish the process little by little with a mechanically actuated, repeated and prolonged application of pressure. This is the "pressure wedge" theory of rotor/stator design. The upshot of the design is that a rotor/stator can now be designed with sufficient work area to effect a dispersion on a material while still being capable of pumping that material, even if its viscosity peaks out at a million centipoise or more. Moreover, it is more suited to modern power transmission techniques since it is essentially a low speed operation; it is rarely necessary to drive an eight-inch rotor at greater than 1800 RPM. The process requires torque rather than speed. Excess energy is rarely introduced to the material, which allows dispersions to be attained at lower temperatures and therefore higher efficiencies. Add to this the fact that dispersions can be made at much higher formulated viscosities and still be circulated in the batch.

First, we start with a much larger rotor /stator assembly conveniently built into the bottom of the subject tank and occupying roughly ½ the tank diameter. On the bottom of the stator, there are radial plates with serrated surfaces on them similar to the surface found on a mill bastard file-that is, triangular in section, but with alternating slope. Held closely adjacent to this "washboard like" surface is a rotor with an extremely large swept area, much like a radial turbine blade, but leaned forward on the leading edge and beveled on the trailing edge. This rotor conforms to the more or less conical aspect of the stator. On the tip of the rotor is a concentrator cone to deliver material more efficiently to the rotor stator, and at the exit of the head, there are diffuser strakes which straighten the flow out of the head.

Material is introduced to the rotor-stator in the center and is then "smeared" between the rotor and stator. As the rotor turns the material adjacent to the stator is progressively pressurized and allowed to relax. This action forces vehicle material into the interstices of the agglomerates and eventually stresses the cluster until it falls or is blown apart. The material is acted on progressively across the surface of the stator until it is discharged through the diffuser strakes into the bulk of the material. A draft tube is provided to eliminate bypassing of partial batches.

The benefits of the pressure wedge type rotor/stator follow:

1. The rotor/stator is effective in processing an exceptionally wide range of viscosities. Materials between 0 centipoise and 1 million centipoise are easily accommodated.
   
2. Lower energy consumption per application. The rotor/stator utilizes power in a high torque low speed setting, which is easier for most drives to deliver compared to the very high power high speed drives required by most present rotor/stators.
   
3. Designs allow the efficient mixing of volumes down to 20% of the total tank volume. In normal rotor/stator and multishaft devices, volumes less than 50% of optimum capacity are difficult to run without specially designed tanks which can negatively effect the mixing efficiency of the rotor/stator.
   
4. Because of the pressure-wedge design, less energy is transferred as heat, which means that the viscosity of the product will be more consistent product.
   
5. Materials can be processed at elevated temperatures with no change to machine set-up. Hot melts in particular benefit from the machine's ability to handle product temperatures in excess of 400 degrees Fahrenheit.

Tiffany Kalva is marketing assistant at CB Mills in Gurnee, IL CB Mills manufactures Fillworth Pressure Wedge Rotor-Stators. For more information on these machines, call (847)662-4000.