B = Weight of solids to weight of liquid, %;
ρ1 = Liquid density, kg/m3; and
D = Agitator diameter, m.
A minimum speed doesnt guarantee that solids wont be resting on the bottom. Zwieterings equation assures that settling will be limited to 1-2 seconds of contact. Also, satisfying this condition doesnt mean that solids are uniformly distributed in the tank. Even low concentrations of solids cannot be considered well mixed. If fact, low concentrations of solids often present the greatest problems in turbulent flow due to the formation of clusters or pockets of solids near the bottom of the vessel.
Tank shape and design details are integral parts of the agitator design. Dished bottoms and baffles help prevent settling in cylindrical tanks. Baffles impart a high vertical component of velocity, help eliminate dead zones, and can allow high agitator speeds before aeration occurs. If baffles are undesirable due to slime build-up or heterogeneous reactions, the agitator should be offset and mounted on an angle to reduce swirl and increase vertical motion (Figure 1: 10 degrees -15 degrees from vertical + offset).
Figure 1. Sometimes baffles are a cleaning problem but orientation of the agitator is crucial for good mixing.
Another option is the use of rectangular tanks since the corners provide baffling, especially for these higher viscosity systems. Agitators and impellers arent multi-purpose: choices must be made. While an impeller can handle a variety of services its functionality isnt limitless. The selection of an agitator requires a balance in power consumption, vendor claims, suspension efficiency, attrition (especially in crystallizers), number needed and type of agitator.
The most common impellers for slurries are marine propellers, 4-bladed/45° pitched turbines, and hydrofoils (usually proprietary designs). Two or more impellers may be required, either on separate shafts or on the same shaft, to provide suspension of solids, as well as mixing or blending of the tank. These impellers may, or may not, be of the same type. Often a choice has to be made between the blending or suspending the slurry, while preserving the desired reaction or products in the vessel. A variety of design procedures have been proposed for specifying impeller diameter and shaft speed for a specific duty. One that is widely available is cited in Reference 9.
An additional consideration for slurry systems is re-starting agitation after a power failure. Agitators are often unable to re-suspend the solids once they have settled. Most pumps are designed for light slurry loads and cant handle the settled solids, usually due to the high viscosity. Sparging with a liquid is the best solution for agitation. Liquid jets can recover the solids suspension, provided the solids arent extremely cohesive. Nozzles should have the capability of either back flow or solids-free liquid injection after power failures. Pumping should be stopped until the suspension is restored unless the pump is designed for such a duty. Positive displacement pumps can handle very high solids concentrations (maybe as high as 95%), but add considerable cost to the project.
Measurement of Slurry Properties
Measurement of slurry properties and process conditions is often much more difficult than with liquids and gases. However, instrumentation advances have made slurry measurements more reliable, primarily due to non-intrusive and/or non-restrictive sensors, and the durability of these devices. Examples of some selected instruments are given below: (Click to enlarge.)
A much more comprehensive analysis of these specific instruments can be found in reference 11, which has several other references to selection documents for viscometers and many other devices for process operations involving slurries.
Installation of slurry instrumentation is a little more complex than for liquids and requires a little more consideration during design. Major points are:
- Proper orientation of an intrusive sensor in the flow to compensate for erosive effects, any entrained gases, and flow conditions (laminar or turbulent);
- The effect of flow disturbances on the uniformity of the slurry and erosion;
- Providing a design that allows for bypass of the instrument;
- Providing a way to calibrate the instrument in the field, and on the actual slurry under process conditions; and
- Determining what effect long-term buildup of deposits will have on performance, and providing for sampling or audits of the process.
Not maintaining a suspension in a transport line can really ruin your day. While a slurry can sometimes be treated as dense and highly viscous liquid, the particle size and distribution create additional problems. Using a larger diameter line to lower pressure drop will cause settling of the solids and slug flow. This leads to higher pressure drop, abrasion, and excessive mechanical stress on the pipeline. In addition, slime may form on the interior of the pipe. And, abrasion can reduce wall roughness over time.
The easiest way to design a pipeline is to maintain non-settling conditions, similar to the design of dilute-phase pneumatic conveyors. As with pneumatic conveyors, operating too close to the saltation velocity can be problematic, and once a minimum velocity has been calculated, a safety factor of at least 25% should be applied. The saltation velocity is determined through an empirical relationship based on the solids loading, particle size, and physical properties of the system. Practical experience and experimental work are preferable to any theoretical model. One method to estimate saltation is shown in Figure 2  and represented by Equation 2.