Parameters to quantify mixing efficiency of static mixers

Depending on the material to mix and the pre-defined application, different mixer characteristics are of particular importance. This chapter focuses on characteristics that describe the properties of the mixer itself (mixer specific characteristics) rather than the application system as a whole (system specific characteristics).

Table 1 - Categorization of characteristics

The mixing efficiency of a mixer can be characterized by the pressure drop across the length of the mixer length, the shear rate acting on the material in the mixer, the mixing quality, the volume of material remaining in the mixer and its residence time behavior (see Table 1). Dimensionless characteristics have been defined to provide a quantitative and comparable description of these properties. This makes it possible to evaluate the mixing efficiency independently of the material properties of the components to be mixed and the operating conditions

1.1. Characteristics to assess the efficiency of a mixer

1.1.1. Mixing quality

Due to the high viscosity of the two components, 2K materials for industrial and dental applications almost always have a laminar flow. As a result, mixing is not achieved by turbulence, but only by repeated separation, shearing and recombination of the components to be mixed. Mixing quality is often expressed in terms of the COV (Coefficient of Variation), which is a purely stochastic quantity defined as the standard deviation of the concentration distribution divided by its mean. The lower the CoV, the better the quality of the mixture. In the case of laminar flow, the CoV achievable by a given mixer depends only on the rheology of the material being mixed, the type of mixer and the number of mixing elements, but is independent of the operating conditions.

1.1.2. Pressure loss

The pressure drop in the mixer - or from the user’s point of view, the force required to dispense the material - is a key characteristic , as this force must be applied by a user or a dispensing device. If the discharge force is already given (e.g. by a manual, pneumatic or electrical dispenser), the maximum achievable flow rate is limited by the pressure drop across the mixer. The pressure loss Δp per mixing element can be written as:

1.1.3. Waste volume

The waste volume is the material remaining in the mixer that needs be disposed of after use. As these materials are often expensive and/or environmentally hazardous, minimizing the waste volume saves money and helps to protect the environment.

 Kv is the dimensionless key figure for describing the loss volume of a mixer element.

1.1.4. Shear strain rate

Shear rate is used in rheology as a measure of the mechanical stress acting on a fluid. Knowing the average shear rate S in a mixer is important for several reasons. On the one hand, for shear-thinning materials, high shear rates result in lower pressure losses in the mixer, thus facilitating the mixing process. On the other hand, however, excessive shear can damage sensitive materials and adversely effect the curing reactions.

1.1.5. Residence time behavior

Static mixers are generally designed for efficient radial mixing, i.e., to compensate for radial concentration differences. This property can be assessed using the mixing quality characteristics above. In some applications, particularly mobile dispensing systems, there may be variations in the mixing ratio. The mixer should therefore also have good axial mixing capability to compensate for these problems. This is achieved by mixers that have a wide residence time distribution, meaning that some fluid elements flow quickly through the mixer while others take longer. One implication of this is that the component that enters the mixer later can still catch up with the other slower moving components, ultimately balancing the mixing ratio at the mixer outlet.

1.2.Advantages and disadvantages of different mixer types

To achieve homogeneous mixing of the two components, high shear forces are generated in a mixer. In general, the better the pressure energy is converted into shear, the more efficient a mixer will mix. In Figure 1 , the average shear rate of a particular mixer type is plotted against the pressure drop of that mixer. It is interesting to note that all mixers of a given type (regardless of their diameter and the number of mixing elements) can be plotted on one curve. This is true for both Newtonian and non-Newtonian fluids.

Quadro and T-mixers are the most efficient at converting the energy from the discharge force into shear. This higher mixing efficiency can also be observed in real applications. For a given pressure drop, Quadro and Helix mixers provide the best mixing quality with the least amount of waste volume

Figure 1 - Average shear strain rate in a mixer over its pressure loss

Unfortunately, this relationship only applies to materials that are easy to mix. For 2K-materials with increasingly higher mixing ratios and/or viscosity ratios of the two components, the mixing efficiency of these mixer types decreases and sometimes it is even impossible to obtain a homogeneous mixture with them. Application tests have shown that helical mixers, although not quite as efficient, are suitable for a wider range of applications. A good guide to the type of mixer to choose is the flow chart in Figure 2.

Figure 2 - Selection of the optimum mixer type

The optimum size (inner diameter) and number of mixing elements depends mainly on the flow rate to be applied and the viscosity of the material. Due its broad portfolio of different mixer types with a wide variety of mixer sizes and number of mixing elements, medmix can offer an optimal mixer for almost all applications.

1.3. System specific characteristics

In addition to an efficient mixer as an individual product, the smooth functioning of the entire mixing system, consisting of the cartridge, piston/plunger, mixer, and applicator tip, is of great importance. In particular, the following features have to be ensured: 

• Tightness: No material escapes during application and contaminates the mixing system
• Bubble-free application: The discharged material does not contain any air bubbles.
• No cross-contamination: The components to be mixed should only come into contact with each other in the mixer. Contamination of the A component with material from the B component and vice versa in the cartridge must be avoided in all operating cases. 
• Simplify the handling of the system: The mixing system should be intuitive to use. The mixers and application tips should be easily interchangeable to ensure fast and highly accurate application of the materials.

A subsequent article will delve into these system-specific characteristics in greater detail and explore methods for achieving a fully operational mixing system.

About the author:

"Joachim Schöck has been working as a senior technology expert at Sulzer Mixpac and medmix Switzerland AG for 12 years. His main activity is the optimization and further development of high-precision application and mixing systems. This is done to a large extent using modern simulation tools such as CFD and FEM. Another focus is on the further development of test methods for predicting the mixing quality of 2K adhesives and sealants."