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Hello everybody, and welcome for a course on the principles of extrusion processing. In the first chapter, which is denoted as extrusion one, I will present the following subchapters to you. Behind the introduction, so there will be extrusion definitions, then extrusion principle and related mechanical fundamentals, process structure. Relationships in extrusion processing will then be addressed. And finally, I will summarise and conclude. At the beginning there is some nomenclature information for you to read through the scriptum. And with this I would like to enter into explanations on process-structure-property relationships. Process makes structure. Structure codes property. This relates process, structure, and properties.

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And when we start with the properties which is most relevant for consumers, the preference, acceptance, and needs of the consumers are in front, and techno functional properties and economy and price are certainly also of interest. On the structural side we have a hierarchical structure from micro to meso to macro scale. And on the processing side we are certainly looking, according to this course topic, to extrusion processing. You can define it in one sentence as fluid mechanical operation of viscous mass forcing it through a restriction die in order to generate or transform specific product structure and shape. Having said that, structure is a hierarchic scheme.

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So we have to look at different characteristic length scales which we identify specifically for products, and on each of these length scale levels, molecular, meso, macro, you’ll have this process makes structure. Structure defines properties. And the characteristic length scales have to be complemented by timescales because the systems are mostly nonequilibrium. We can recruit information from molecular dynamics, Brownian dynamics, and continuum dynamics in order to have some basic principle support how to tackle these dynamic aspects. So to each length scale we have timescales of dynamic change of structure. When we look at the extruder principle, it’s kind of a shaft with a screw. The screw is transporting the material by rotation.

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Typically there is one or two screws, but can be other ones with several screws. Powder and fluid are added or mixed to a pasty type of material and then pressed through a die-entrance section and the die, whereas the die can have different geometries as shown here. So from a dosing zone it goes into a pressure-buildup zone into a thermal and mechanical-treatment zone, and particularly in the last zone there is a lot of changes in structure which can be adjusted at the same time you can heat or cool the system. Key elements in such an extruder is the screw. The screw can be, let’s say, a serial arrangement or different screw geometries.

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As you see them here, this would be a simple conveying screw but certainly can be much more complex. We see some real screw elements in the next picture– forward, reverse, conveying, as well as forward and reverse mixing elements. And this is only four typical types of several hundred modifications which may only slightly differ but have different, let’s say, characteristics for making the material move in the screw channel. The screw channel then is formed by, let’s say, a serial arrangement of many of these screw elements. And here you can see the transport mixing pressurisation, structural transformation, and shaping zones.

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And just as an example because the driving force for bringing the material through the screw channel is certainly the acting pressure difference. And you can see screw elementwise or the screws sectionwise you have different pressure profiles increase or reduction of pressure. It goes down to atmospheric pressure at the outlet of the die. Different configurations can look like shown in this figure. They are all inserted, in our case, in two of these screws combined in such a barrel construction which can be heated and which can be cooled. Arrangements of screws– typical ones are single-screw extruder or twin-screw extruders, nonintermeshing or intermeshing. These are the most common ones even though there is multiscrew extruders as well existing.

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You can see from the type of modifications that either, let’s say, the screw channel or the housing can be changed in geometries in order to have, let’s say, the pressure build up and the flow-through characteristics change. Most interesting for us is certainly intermeshing ones because these grooves clean themselves, and we have a well-defined flow-through profile accordingly. When we look at the screw channel in common terms, so what we have typically is a drag flow because we are moving, let’s say, the screw relative to the barrel wall, and that means we have a drag flow.

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And counteracting is a pressure back flow because we build up a pressure in front of the narrowest section, which is the die entrance and the die section, and that means building up a pressure. We have the pressure back flow in the opposite direction. These two superimpose, and depending on the ratio of this superposition you can see the resulting profile. We certainly are keen to have a resulting profile which still gives the majority of the material to be transported into the flow direction. That means not too high pressure back flow should act. When we want to do experiments in the lab, we can do this in a simple on lab scale in a simple piston-driven extruder.

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So we have a die here. We have a piston which presses the material through, pressure measurements along the die, and in the barrel it can be done. So this is a so-called high-pressure capillary rheometer setup which is a typical piston extruder. When we go for lab or pilot scale, real extrusion systems– so there would be the piston replaced by the screw, and then pressing through a nozzle. And this is what we compare based on the theory for capillary flow. The capillary-flow type of profiles is shown in this section of the picture. And so we have this inflow, and let’s say the related superimposed shear and elongation of the flow types acting.

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We can compare the two with related measurements of the viscosity. We have to take into account the so-called wall shear rate, which is proportional to the volume flow rate. If we measure the velocity profile or we assume the velocity profile, we can get, by the first derivative, the wall shear rate after correction if there is slip of the wall and the non-Newtonian behaviour to be considered. On the wall-shear-stress side, so we have to consider another correction, which is the entrance pressure lost due to elastic effects or inflow effects. If this is corrected, the wall shear stress divided by the wall shear rate according to Newton’s law gives us the locally acting viscosity.

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So with this, we can get for non-Newtonian fluids viscosity functions. And we did this for, let’s say, the two devices shown before. Here we have the extruder with a screw inside and the die attached. Here we have the piston extruder or the high-pressure capillary rheometer type of setup. And when we compare the apparent viscosity versus apparent shear rate results, as seen from the curve with the full and the open symbols, we are in good agreement.

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Now, the most important parameters for the extruder design for the process are certainly the kinetic flow parameter– so what can we get through the extruder, which is proportional to the volume flow rate– and the dimensionless type of parameter as well as the dimensionless pressure, which is the driving force for the flow. So you see some constant A1 and A2. And we can see the coupling of the kinematic flow parameter and the dimensionless pressure with the second equation. Where do we get E1 and A1 and A2 from? So you can see this kind of plot where we have the dimensionless flow through or kinematic-flow parameter versus the dimensionless pressure.

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And within this section obviously the crossing of this line with a y-axis and the x-axis giving us the values A1 and A2, which is in principle the conveying screw characteristics. Having non-Newtonian characteristics, we may have not a straight line for the screw characteristic shown in red. For the die we will have the blue characteristics and where the crossing point of these two characteristics for the flow are meeting each other. So we have the working point of the arrangement, screw plus die construction. The relationship for the pressure characteristics, the kinetic parameter are given here. For the power characteristic, we would just have similar type of linear assumptions.

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For Newtonian fluids, just would A1 and A2 would be replaced by B1 and B2. Another overall approximative energy balance is also of interest for a first approximation because the power we invest via the shafts by a rotation of the screws which are placed on the shafts which is transferred into an inner energy flux and other energy portions, which we can set to 0 if there is no phase change and no heat exchange. And so we only keep the inner energy flux as well as the energy by pressure increase, which we can then formulate as inner energy flux as moth flow rate times heat capacity times temperature difference.

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And from this we can certainly get an explicit solution on the temperature difference. That means how is the input energy translated into a temperature difference by extrusion treatment? If you want to go into some further details, numerical simulation approaches are certainly giving local information on different screw elements– for example, as shown here, conveying, mixing, and kneading elements one, two, three as they are filled and placed on the shafts. And on the left-hand side we see the pressure distribution, on the right-hand side the velocity distribution in these channels. The extruder, how it is built up is shown in this schematic view. So the main aspect is the screw-barrel assembly and the die.

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So everything else is kind of the kinematics, drive aspects, and the frame. In reality, they look like following as shown these two examples from Clextral in France and Buhler in Switzerland. So huge devices which can make up to several tonnes an hour of throughput rates. On the pilot scale, we are certainly working in the range of, let’s say, 10 to 100 kilos an hour and very flexible devices with local different cooling and heating zones possible. And let’s say the arrangement of several unit operations, let’s say from at the dosage, the pressurisation, the heat treatment, then the structuring transformation close to the die entrance domain, and then the shaping at the end.

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Accordingly, the screw is configured such that the different sections for the different unit operations can be arranged in a serial manner. And this is certainly a nice integrative toolbox, let’s say, to do this in such extrusion devices. If you go to the fluid-mechanical aspects, so we have an inflow into the orifice, and we have, let’s say, an acceleration into flow direction, which would leads to an elongation, as we can see here for the example of a droplet which is elongated. In the centre we have pure elongation.

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More closely to the wall we get more and more shear impact because we have relative motion of neighbouring particles of fluid elements, and this makes a certain shear in blue, shear-rate distributions and elongation-rate distributions along the tracks which I have shown here. So if we want to know about the stresses or the forces which are really impacting on the structure– this is of interest if we want to modify structure in a well-defined way. So we have to calculate the flow stresses, which are competing with the structure-preserving stresses. So the flow stresses I calculate viscosity times gradient, velocity gradient. For shear, it’s shear velocity times shear gradient means shear rate. For elongation, it’s elongational viscosity times elongation rate.

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This would be the stresses acting in the flow. And the structure-preserving stress, for my example here of a little droplet, would be the capillary pressure, which is 4 times into interfacial tension sigma divided by the diameter x of this drop. When we look at such a deformation of an element of any type– it can be molecular element. It can be something which is more large scale like the droplet or like the cylinder as shown here. Whenever a critical flow stress is exceeded, we will get a deformation. But the critical flow stress is not only deciding about whether or not we will have an impact. Remaining impact on structure means an irreversible change.

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For this we also have to exceed– as shown here in the lower part of the slide– we have to exceed also a critical defamation DC. If this is done, we have an irreversible change. So for our droplet as an example, it would be the formation of a filament which breaks up like shown in this little simulation here, really break up into single droplets, and then you had the droplet structure. This would be an irreversible dispersed type of characteristics of the structure, which may be desirable. Now to go even a bit further, in looking for local stress situations for structures to be changed, we went in to some synchrotron tomography.

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A little extruder has been built which could be moved and rotated in the synchrotron field, the X-ray field where the tomography was applied. And we can then follow with high resolution in time and space to go through or follow such elements at the inflow region. And if you look at the 3D projection or the 3D information we can receive for this, we can derive from such pictures, let’s say, the local shape along a particle track. Having the local shape– so we can derive from this what we call a shape tensor. So all the information of the three projection planes gives us the shape tensor.

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If you know the time dependency or the time-dependent change of the shape, we get the deformation rate tensor from this. And knowing interfacial tension and rheology of the surrounding fluid, we can then calculate the stress tensor by a constitutive equation for the rheology of the surrounding fluid system. Having on top, let’s say, followed such a particle as a tracer, we can also have the velocity along a particle track. So we use it kind of as a particle imaging velocimetry tool and from this get the velocity fields and from the derivatives of the velocity fields get the strain rates, the local strain rates. Local stress divided by local strain rate will be local viscosity.

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So it means such a little deforming element, a bubble or a droplet, can be a stress sensor– a stress tensor sensor. With this, I’m ready to summarise. So extrusion processing can certainly be applied on different length scales for structuring. So timescales have to be considered because we are in nonequilibrium. We run through in an extruder typically through, let’s say, domains where we are more on the powder-mechanics side, then go into tribological domains, and finally end up with pasty material which are shaped. So rheology is most important. Then we have mixed shear and elongation fields which are acting on the structure and giving impact on the structuring.

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The coupled screw and die entrance geometries are deciding about the throughput rates and, let’s say, how back mixing and the flow stresses are acting in the extruder. So we have these kind of combination to be worked out for the best structuring of relevance for our food systems. Then we have several unit operations that can be combined. So an extruder is kind of an integrated building block for a serial arrangement of different unit operations from dosing via heat treatment, pressurisation, shear-induced structuring by deformation, orientation, dispersing, and finally the shaping.

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We have seen that or I demonstrated that offline rheometry or, let’s say, lab-scale type of extrusion systems, flow visualisation by synchrotron tomography as well as numerical simulation, which I have just briefly mentioned, are appropriate tools to investigate more mechanistic detail. This is where the research goes to. So with this, I would like to end up here. We certainly have just got a glimpse to the complex extrusion processing. It’s up to me now to think a lot of my co-workers which are listed on this last slide as well as the funding organisations supporting this, and those of you who are interested to follow other course parts on extrusion.

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So that there will be some further detail going into products by extrusion processing. Thanks a lot.