Mixing Technology at medmix AG

    1. Core Technologies at Medmix

    Inspired by more than a century of innovation, medmix develops and delivers leading technologies in high-precision delivery devices and fluid mixing for applications in healthcare, industry and consumer segments. Our mission is to provide innovative solutions in the field of high-precision delivery devices of to help millions of people live healthier and more confident lives. As the world's leading manufacturer of hand-held mixing and dispensing systems for adhesives and sealants medmix has special expertise in Mixing Technology, Application Technology, Functional Packaging and Dispenser Technology. To further serve our customers with optimal and highly-efficient discharge systems and to remain the number one in the upper competencies a deep knowledge in material science, a continuous digital development chain and a sustainable mind view of the hole product life cycle are key requirements. Two-component adhesives and sealants are becoming increasingly important in the dental, industrial and healthcare sectors. These materials must be mixed efficiently and reproducibly before application. Therefore, this article focuses on the core competence Mixing Technology and what needs to be considered in order to always use the optimal mixing system for the respective application.

    2. Introduction in Mixing Technology

    As already mentioned above, two-component adhesives are being used more and more because of their special properties and static mixers are the most frequent choice of device for mixing the two-component material before application. The advantage of using such mixers is that they mix two-component materials consistently regardless of who is operating them. This means reproducible mixing outcomes and high reliability since they contain no moving parts. The first key factor when it comes to achieving a high level of efficiency is the mixer design and mixing method. However, the interaction between the mixer itself and the rheological properties of the material, the specified mixing ratio and the viscosity ratio of the individual components must also be taken into account.

    2.1. Mixing principles in laminar flow regimes

    The materials to be mixed for industrial and dental applications are often highly viscous. This high viscosity, combined with a low flow velocity in static mixers, means that a laminar flow regime is always present in static mixers in the intended applications. As shown very nicely in Figure 1, laminar flow means the absence of turbulent eddies, which additionally allow mixing perpendicular to the main flow direction. Therefore, in laminar flow mixing happens by convective and dispersive mixing, only.

    Figure 1 Left: Laminar Flow, Right: Turbulent Flow

     

    Convective mixing describes the elongation and folding of the fluid by convective shear forces. Dispersive mixing means the repeating parting of the fluid at the walls of the mixer geometry. A smart mixer geometry combines both processes in an optimal way to generate ever thinner layers of the components. This increases the interfacial area between them. The speed and quality of the curing reaction depends on precisely this size of the interfacial areas and on the relevant concentration gradients.. Due to the close correlation between mixing quality and the course of the chemical reaction, it makes sense to consider the appropriate mixing technology at an early stage in the development of new 2K materials.

     

    Figure 2 Illustration of dispersive and convective mixing,

    2.2. How do we implement these principles in medmix mixers?

    As a leading supplier of mixing and application solutions for the industrial and dental market, medmix offers a wide range of different mixer types in various sizes. These mixer types and their mixing principles are shown in Figure 3. Typically, the flow and thus the components present are parted in half, then re-oriented by different procedures (rotated in case of Helical mixer, resp. squeezed and rearranged in case of Quadro and T-mixer) and elongated, again. For all mixers shown in Figure 3, the number of theoretical material layers doubles resp. the layer thickness is halved with each mixing element. For example, for a mixer with 12 mixing elements, this ends up with 212 = 4096 material layers which are usually no longer visible to the naked eye. X-Grid mixers provides a different mixing technology. Due to the alternately crossed bars, material is repeatedly fed from the outer wall into the core of the mixer. This avoids unmixed zones and leads to a highly-efficient mixing process. To reach the same mixing quality, X-Grid mixers are therefore generally shorter than equivalent helical mixers.

    Figure 3 Different mixer designs and their mixing principles

     

    Based on the material properties (especially viscosity and viscosity ratio), the mixing ratio, and the operating conditions (flow rate, dispensing device) the customer can choose the optimal mixer for his application.

    Figure 4 X-Grid mixer design and its mixing principle

    3. 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 which 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 over the mixer length, by the shear rate to which the material is exposed to in the mixer, by the mixing quality, by the volume of material remaining in the mixer and by its residence time behavior (see Table 1). In order to obtain a quantitative and comparable description of these properties, dimensionless characteristics were defined. This makes it possible to evaluate the mixing efficiency independently of the material properties of the components to be mixed and the operating conditions

    3.1. Parameters to assess the efficiency of a mixer

    3.1.1. Mixing quality

    Due to the high viscosity of the two components, 2C materials for industrial and dental applications almost always have a laminar flow. As a result, mixing does not occur by turbulence, but can only be achieved by repeatedly separating, shearing and recombining the components to be mixed. The mixing quality is often expressed in terms of the COV (Coefficient of Variation), which is a purely stochastic variable and is defined as the standard deviation of the concentration distribution divided by its mean value. Therefore, the lower the CoV value, the better the quality of the mixture. In the case of laminar flow, the CoV that can be achieved 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.

    3.1.2. Pressure loss

    Δp=K_L (μ v)/D L/D - with  =dynamic viscosity [Pa s]; v=axial flow speed [m/s]; L=mixer length [m]; D=mixer diameter [m] KL is the dimensionless characteristics to describe the pressure loss per unit of mixer length.

    3.1.3. Waste volume

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

    V_w=K_v 〖 D〗^3 - with VW=waste volume [m3]; D=mixer diameter [m] Kv is the dimensionless key figure for describing the loss volume of a mixer element.

    3.1.4. Shear strain rate

    The 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 have a negative effect on the curing reactions.

    S=K_S v/D - with KS= dimensionless characteristic [-]; v=axial flow velocity [m/s]; D=mixer diameter [m]

    3.1.5. Residence time behavior

    Static mixers are generally designed for efficient radial mixing, i.e., to compensate for radial concentration differences. This property can be evaluated using the above-mentioned characteristics for mixing quality. Fluctuations in the mixing ratio can occur in certain applications, in particular when using mobile dispensing systems. The mixer should therefore also have a good axial mixing ability in order to compensate for these problems. This is achieved by mixers which own a broad residence time distribution, meaning that some fluid elements flow rapidly through the mixer while others take longer. One implication of this is that the component which enters the mixer later can still catch up with the other slower moving components, ultimately balancing the mixing ratio at the mixer outlet.

    3.2. Advantages and disadvantages of different mixer types

    To obtain 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 efficiently a mixer mixes. An interesting fact is 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. In Figure 5 , the average shear rate of particular mixer type is plotted against the pressure drop of that mixer. It is easy to see that 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 lowest waste volume.

    Figure 5 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 ratio and/or viscosity ratio 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 helix mixers, while not quite as efficient, are suitable for a wider range of applications. X-Grid mixers are particularly recommended for applications with low to medium viscosity, but very high viscosity ratios. For such difficult-to-mix materials, the X-Grid technology convinces with exceptionally high mixing quality. A good guidance which mixer type to choose gives the flow chart in Figure 6.

    Abbildung 6 Auswahl der optimalen Mischerart

    The optimal size (inner diameter) and number of mixing elements mainly depends 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 provide an optimal mixer for almost all applications.

    4. Influence of rheology on mixing behavior in static mixers

    When selecting the optimum static mixer, the rheological properties of the starting components and their mixing ratio play an important role. In particular, highly viscous materials with a high proportion of fillers often have a pronounced non-Newtonian behavior. Therefore, a good understanding of the rheological behavior of the components to be mixed is important.

    4.1. Basics of rheology

    A nice classification of the different material properties can be found in the table below:

     

    Table 2 Rheological Classification of materials, Source: Wikipedia Rheology - Wikipedia

    For Newtonian fluids viscosity is independent of load. This means that the viscosity depends on the temperature, but not on the shear stress. Only a small group of mostly low-viscous fluids (such as water, milk, salad oil) exhibit such constant viscosity. For most fluids, the viscosity changes under shear stress; these are called non-Newtonian fluids. Non-Newtonian fluids can exhibit shear-thinning (structurally viscous) or shear-thickening (dilatant) flow behavior. Shear-thinning flow behavior is characterized by a decrease in viscosity with increasing shear rate. Typical materials exhibiting this behavior are coatings, adhesives, polymer solutions and polymer melts. Shear thickening means that viscosity increases with increasing shear rate. Materials that typically exhibit such behavior include highly filled dispersions, such as ceramic suspensions, starch dispersions, sometimes dental fillings (dental composites), and special composites for protective clothing. Since non-Newtonian fluids are shear dependent, measured viscosities should always be reported together with the exact shear conditions and, in the best case, as a function of shear rate. Often the viscosity can be approximated section-wise by a power law.

    A material is called viscoelastic if it shows a mixture of viscous and elastic behavior. Plasticity is the behavior if a material that behaves as a solid under low applied stresses starts to flow above a certain level of stress, called yield stress. Often the viscosity is not only a function of the shear rate, but additionally also time-dependent. If such materials are exposed to shear stresses, they do not change their viscosity instantly, but over time. As time dependent shear-thinning materials are called thixotropic, shear-thickening materials are called rheopectic. In addition to the rheological behavior, the viscosity of a material is also strongly dependent on temperature. Generally, in the case of liquids the viscosity decreases with increasing temperature. This can have a strong impact. For example, the viscosity of a typical engine oil decreases by a factor of 3 when the temperature is increased from 23°C to 50°C.

    4.2. Impact of rheological properties on the performance of static mixers

    As already discussed in Chapter 3, the optimal achievable mixing quality which can depends on the type of mixer, the number of mixing elements, the mixing ratio and the viscosity ratio of the two components. A pre-defined mixer generally achieves the best mixing quality when materials with a mixing ratio of 1 to 1 and the same viscosity are mixed. In many cases, however, this optimum condition does not exist and a rather high-viscose, shear-thinning resin is to be mixed with a rather low-viscose Newtonian curing agent. Since optimum mixing occurs at equal viscosity, it is advantageous to select a mixer that mixes at a shear rate that results in equal viscosities of the two components. However, the rheological behavior of the material not only influences the mixing quality, but in particular also the pressure loss in the mixer. If, for example, a high-viscous material is to be discharged with a high volume flow, the resulting high pressure loss in the mixing element leads to high mechanical loads on the cartridge and the mixer housing. These loads can have a negative impact on functionality (pre-flow of one component, blow-up of the cartridge or mixer housing) or ultimately even damage the plastic parts. In such a case, it is advisable to choose a mixer with a bigger diameter which reduces the pressure loss significantly.

    4.3. Material guideline to achieve good mixing results

    It is advantageous if material manufacturers, together with the mixer manufacturer, ensure the easy mixability of new materials and components already in the formulation phase. At this stage, it is even possible to design a customized mixer for such an application. But even if an exclusive solution is not desired, good mixability of the components can be ensured in advance, which then leads later on to shorter mixers with fewer mixing elements and lower pressure loss. From a rheological point of view, good mixability is achieved by observing the following guideline:

    1. Both components should have a similar rheological behavior. Similar rheological behavior means that the viscosity over shear strain rate curves runs in a log/log diagram in parallel and very close to each other. In such a case it is guaranteed that in a wide range of operating conditions similar mixing quality can be achieved.
    2. The volumetric mixing ratio of both components should be close to 1. Application tests with material with a high volumetric mixing ratio yield a much higher number of mixing elements necessary to reach an adequate mixing quality.
    3. Due to the shear thinning behavior of many materials, the actual viscosity of the material in the mixer is lower than specified in the data sheet because of the high shear rates in the mixer. Typical shear rates in a static mixer are in the range of 20 > S > 200 1/s. Nonetheless, a too high actual viscosity should not be exceeded, as this will at best result in the desired volume flow not being achieved. In the worst case, this will lead to a loss of function or mechanical failure.
    4.4. Special mixer geometries for materials with challenging rheology

    If for various reasons it is not possible to follow the above formulation guideline of an easy to mix material, medmix® also offers systems to mix materials with challenging rheological behavior:

    Blueline System

    This system has been specifically designed for applications where a high viscosity material is to be applied at a high flow rate. From the cartridge, to the mixer, to the mixer tip, the individual parts of the Blueline system have been optimized for the lowest possible pressure drop. This enables the user to discharge even material with a very high actual viscosity at an acceptable flow rate.

    X-Grid Mixers

    The X-Grid mixer is ideally suited for resin/hardener systems that are difficult to mix, e.g. 2K adhesives, epoxies, polyurethanes, silicones, resins or varnishes, as well as for components with a large viscosity and/or mixing ratio. In addition, the dispersing effect of insoluble materials is significantly higher. Thus, X-Grid technology can be used for low- and medium-viscose materials that are difficult to mix with current static mixing technology. For such materials, the use of X-Grid technology can result in mixers that are significantly shorter than current mixers.

    Figure 7 Left: Blueline Mixer; Right: X-Grid Mixer

    5. Comparison of static and dynamic mixing systems

    For mixing 2K materials, the use of static mixers is generally the preferred choice, as they are simple in design, easy to use and relatively inexpensive. In some cases, however, static mixers do not provide the required mixing performance. Dynamic mixers offer an alternative solution for applications where either very high mixing quality or a solution for rheological demanding materials is required. For instance, mixing and metering with static mixers proves difficult when the components have significantly different viscosities or high mixing ratios. Such applications often require a large number of mixing elements to achieve sufficient mixing quality. This results in very long mixers, which again results in high discharge forces and limited handling. In addition, these sometimes very long mixers have to be disposed of after use, which increases both the amount of plastic waste and the waste volume of the material remaining in the mixer. Due to the high pressure drop in static mixers, very high-viscose materials often cannot be discharged at the required flow rate because the discharge devices (guns or dosing machines) do not provide the required discharge forces.

    5.1. Advantages of dynamic mixers

    Dynamic mixers overcome these problems. In contrast to the aligned layered mixing pattern of statical mixers create the rotating blades of dynamic mixers a chaotic multi-directional pattern which enables fast dispersion and mixing (see Figure 8). 

    Figure 8 Typical mixing pattern in static (left) vs dynamic (right). Dynamic mixing allows multi-directional mixing and dispersion

    For materials with a high mixing ratio or with significant viscosity differences, this prevents the so-called channeling effect. Channeling describes the compression of the lower-viscus component by the higher-viscous component and the formation of narrow channels through which the thinner component is forced through the mixer at high speed and almost unmixed. In addition, the fast rotating blades in dynamic mixers lead to high shear rates in the mixer. Due to the higher shear energy, this not only leads to faster mixing, but in the case of shear-thinning materials also significantly reduces the viscosity and thus the metering force by orders of magnitude. Figure 9 impressively illustrates this behavior in dynamic mixers by means of the viscosity curve of a typical adhesive.

    Figure 9 Rheological behavior of a typical shear-thinning material. Light blue and grey area indicate typical shear rates of static and dynamic mixers

    Dynamic mixing thus increases mixing efficiency on the one hand and reduces pressure loss on the other. Therefore, comparable dynamic mixers have a more compact design, which in turn leads to less plastic waste, less loss volume and better handling (shorter mixer). The lower pressure drop in the axial direction also allows very high-viscose material to be metered.

    5.2. Applications of dynamic mixing systems at medmix

    Dynamic mixing systems are widely used in metering machines to mix high-viscose 2-component adhesives or silicones with high mass flow. In such applications, mainly metal mixers are used which are cleaned or flushed after each usage. To avoid flushing with expensive material and time-consuming cleaning, some applications use disposable dynamic mixers, also.  But there are also cartridge-based applications where dynamic mixing systems are used. medmix offers systems for both dental and industrial segments.

    Figure 10 Examples of dynamic mixers in the medmix® portfolio

    In the dental segment medmix® provides a dynamic system to apply high-viscose material into trays to support dentists in the production of highly accurate dental impressions. These materials are often offered with a 5 to 1 mixing ratio. In collaboration with Sika a dynamic mixer optimized for extreme mixing ratios (50:1) has been developed to enhance the application quality of Sika’s Booster/PowerCure technology. The mixer applies a range of sealants and adhesives based on polyurethane; silane terminated polymer as well as silicone chemistry. It’s used mainly in the automotive industry and for glazing applications.

    5.3. Why are dynamic mixers less common than static ones?

    Despite the unchallenged advantages, there are only a few cartridge-based applications where dynamic mixing systems are used. The reason is the more complicated design of the dispensing system needed. Since dynamic mixers require an additional drive to rotate the mixer blades, this must also be housed in a discharge unit, making them heavier, more unwieldy, and more expensive. In addition, finding the optimal combination of flow rate and rotational speed can be challenging and needs additional training of the operator. And especially for industrial applications the ease of operation and cost competitiveness is often a key criterium.  In short, dynamic mixing increases mixing quality, reduces waste, and improves application accuracy due to the reduced overall length of the mixer, but at the expense of additional complexity and cost. Therefore, dynamic mixing systems are used for applications where no other solution is possible to accomplish the mixing task or where the benefits outweigh the additional cost and effort.

    6. Numerical Flow Simulation of mixers

    Flow simulations or CFD (Computational fluid dynamics) is an established procedure to analyze and solve problems that involve fluid flows with the help of computers. With this method it is possible to examine the internal or external flow field of a product virtually before a first prototype has been produced. In this way, a design version can be analyzed realistically and, if necessary, optimized by constructive adjustments. In the best case, only a few necessary tests are carried out later. Thus, CFD simulations can accelerate development cycles and lead to a reduction in development costs.

    6.1. Introduction to CFD

    CFD involves the solution of the governing laws of fluid dynamics numerically. The complex set of partial differential equations are solved on in geometrical domain divided into small volumes, commonly known as computational mesh The aim of this article is to give an overview of how a typical CFD simulation is set up and how it can be used during the product development process of mixing and applicator systems. In general, a typical CFD analysis consists of three steps:

    1. Pre-processing phase
    2. Execution of the simulation
    3. Post-processing of the results for visualization, parameter extraction and optimization
    6.2. Pre-processing

    The keyword pre-processing includes all activities that are carried out before the actual simulation is executed. This starts with the use of computer aided design (CAD) to build up the geometry and suitable physical boundaries of the problem. Geometry preparation and simplification: From there, the fluid volume to simulate has to be extracted. During this step it is often useful to remove geometrical details that are not important for the intended analysis. For example, this can be small holes, radii or gaps without flow. The aim of this work is to reduce the complexity of the model and to focus on the essential details in order to ultimately reduce analysis time and costs without losing accuracy

    Figure 11 Process of geometry preparation and discretization

    Discretization: In the second step the volume occupied by the fluid is divided into discrete cells (the mesh). The mesh generated should be fine enough to cover the major physical effects. The type of mesh should be advantageously hexahedral-dominant or at least of polyhedral type. Simple tetrahedral meshes are not adequate to obtain appropriate results. Physical models: Depending on the type of problem to be solved during an investigation, simulations with different complexity in terms of physical models and numerical effort can be carried out. In the easiest case a steady state solver is used to simulate the flow of an incompressible and isothermal fluid in laminar flow. Multi-component or multi-phase models can be added to cover the flow of several components in one fluid domain. In the case of low viscous materials, a turbulence model has to be switched on. To solve time-dependent effects or flow fluctuations a transient solver has to be taken. Boundary condition and fluid properties: The last step includes the definition of the fluid properties of all fluid involved. In simple cases this is the fluid density and the fluid viscosity. In more sophisticated cases with heat transfer and multiple materials this can also be thermal expansion, heat capacity, surface tension and contact angle. Operating and initial conditions are defined at the boundaries of the simulation domain.

    6.3. Execution of the simulation

    To run the CFD simulation the so-called Navier-Stokes equations have to be solved. In physics, the Navier–Stokes equations are partial differential equations which expresses the conservation of mass, momentum, energy and additional scalar fields.

    Figure 12 Convective form of Navier-Stokes momentum equation

    6.4. Postprocessing

    Postprocessing refers to the evaluation of the CFD simulation results. This can be done graphically in terms of contour, vector or streamlines plots, videos or quantitatively by tables of values. Like for all numerical simulation it is suggested to prove the plausibility of the numerical results. This can be done by comparing them with rough hand calculations or measurement data of similar designs. Qualitative flow analysis is often done graphically by means of contour or vector plots. Generally, the pressure and velocity field are of main interest. In the case of mixer simulations, the concentration field of the components to mix is relevant. These plots can be analyzed to find critical areas, for example with high pressure losses or unwanted death zones with almost no flow. Quantitative flow analysis of variables or flow parameters (for example: mixing quality or pressure loss) are generally determined at pre-defined locations within the simulation domain. For example, in simulations of static mixers the evaluation of mixing quality over the mixer length is of interest. In the case of transient simulations, these values can also be evaluated over time.

    Figure 13 Mixing quality in a static mixer

    A combination of both quantitative and qualitative evaluation is shown in Figure 13. Here, the underlying picture is a contour plot of the mass fraction of component B in a static mixer. The overlaid blue curve shows the progress of CoV (Coefficient of Variation) which is a measure for mixing quality over the mixer length. While the CoV remains unchanged (no mixing) in the mixer head and mixer outlet, it decreases nearly linearly in the mixing elements if the CoV is plotted logarithmically..

    6.5. Advantages of CFD in comparison with measurements and its limitations

    Nowadays CFD is found in almost all fields ranging from medical research to engineering. And there are important advantages because CFD is used:

    • CFD can be used as a qualitative tool for pre-evaluation of various designs. Designers and analysts can study prototypes numerically, and then test by experimentation only those which show promise. This leads to a great time and cost reduction in the development process.
    • CFD can provide results for flow problems which can hardly be analyzed by means of measurements or which are even dangerous, for example if hazardous substances had to be tested.
    • CFD offers the capacity to study products or systems under conditions beyond their limits. This can be interesting to understand how a system reacts when used incorrectly.
    • CFD allows observation of flow properties without disturbing the flow itself, which is not always possible with conventional measuring instruments.
    • CFD generates colorful pictures and graphs which helps to understand the system. And finally, it can be used for marketing reasons to convince development partners of the functionality of a product.

    State of the art CFD solvers can handle a wide range of different physical models. But with increasing complexity (multi-phase, multi-components, chemical reactions, ….) and highly transient behavior with phenomena which often appears at different time scales the numerical effort to obtain a meaningful result increase dramatically. In addition, often the exact fluid properties of the fluids of interest are not known in detail or are confidential for different reasons. And even the most sophisticated CFD model is still a particularly good simplification of the reality, only. Thus, in many cases measurements are still the means of choice and a particularly crucial resource to validate the simulation models. It has often been shown that the best development results were achieved with a well-considered combination of simulations and measurements.

    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."