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# Gate Design in Injection Molding of Microfluidic Components Using Process SimulationsPUBLIC ACCESS

[+] Author and Article Information
David Maximilian Marhöfer

Department for Mechanical Engineering,
Technical University of Denmark,
Produktionstorvet, Building 427A,
2800 Kongens Lyngby, Denmark
e-mail: maxmar@mek.dtu.dk

Guido Tosello

Department for Mechanical Engineering,
Technical University of Denmark,
Produktionstorvet, Building 427 A,
2800 Kongens Lyngby, Denmark
e-mail: guto@mek.dtu.dk

Aminul Islam

Department for Mechanical Engineering,
Technical University of Denmark,
Produktionstorvet, Building 427 A,
2800 Kongens Lyngby, Denmark
e-mail: mais@mek.dtu.dk

Hans Nørgaard Hansen

Department for Mechanical Engineering,
Technical University of Denmark,
Produktionstorvet, Building 427 A,
2800 Kongens Lyngby, Denmark
e-mail: hnha@mek.dtu.dk

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received August 26, 2015; final manuscript received December 10, 2015; published online February 11, 2016. Assoc. Editor: Stefan Dimov.

J. Micro Nano-Manuf 4(2), 025001 (Feb 11, 2016) (12 pages) Paper No: JMNM-15-1060; doi: 10.1115/1.4032302 History: Received August 26, 2015; Revised December 10, 2015

## Abstract

Just as in conventional injection molding of plastics, process simulations are an effective and interesting tool in the area of micro-injection molding. They can be applied in order to optimize and assist the design of the microplastic part, the mold, and the actual process. Available simulation software is however actually made for macroscopic injection molding. By means of the correct implementation and careful modeling strategy though, it can also be applied to microplastic parts, as it is shown in the present work. Process simulations were applied to two microfluidic devices (a microfluidic distributor and a mixer). The paper describes how the two devices were meshed in the simulations software to obtain a proper simulation model and where the challenges arose. One of the main goals of the simulations was the investigation of the filling of the parts. Great emphasis was also on the optimization of selected gate designs for both plastic parts. Subsequently, the simulation results were used to answer the question which gate design was the most appropriate with regard to the process window, polymer flow, and part quality. This finally led to an optimization of the design and the realization of this design in practice as actual steel mold. Additionally, the simulation results were critically discussed and possible improvements and limitations of the gained results and the deployed software were described. Ultimately, the simulation results were validated by cross-checking the flow front behavior of the polymer flow predicted by the simulation with the actual flow front at different time steps. These were realized by molding short shots with the realized molds and were compared to the simulations at the global, i.e., part level and at the local, i.e. feature level.

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## Introduction

The injection molding process is a widely applied and well-established production technology in the industry and accounts for most of today's plastic parts. Due to its wide spread, it is hence naturally affected by the constant trend of miniaturization toward smaller parts incorporating increasingly more functionality. As a result, the micro-injection molding process is commonly seen as one of the key technologies of the 21st century for the large-scale and highly automated production of high precision microstructured and three-dimensional (3D) parts. The process is capable of yielding net-shaped multimaterial plastic parts with complex geometry and diverse functionality. Due to the aforementioned continuous trends of miniaturization of parts and reduction of weight and costs, the field is constantly growing and established for the production of microproducts made out of thermoplastics. Furthermore, variations of the process, e.g., micropowder injection molding for metallic and ceramic components or two-component micro-injection molding, are in the ascendant. Typical application fields of the micro-injection molding process are the medical industry, the telecommunication industry, or optics [18].

The miniaturized version of the injection molding process exhibits the same basic process cycle with the following steps [5,9]:

• melting of the plastic granules

• metering of the molten plastic

• injection of the material into the cavity of the mold (filling phase)

• packing of the part to compensate for shrinkage

• cooling to solidification and

• ejection from the mold

In the field of injection molding, process simulations are based on the method of finite element analysis (FEA). Different software packages such as autodesk moldflow®, moldex3d®, or sigmasoft® are commercially available on the market. Due to the complexity of the injection molding cycle and equipment, the increasing requirements on the part quality, and the rising number of applications of micro-injection molding, process simulations become more and more attractive and relevant. The simulations are carried out to support the part, mold, and process design at an early stage, to avoid costly re-engineering, and to shorten the development time of a new product [6,1015].

In general, commercially available simulation software is—at least up till now—officially made for macroscopic plastic parts and conventional injection molding. The software packages can be applied in micro-injection molding to yield qualitatively adequate results, yet the numerical results still lack quantitative accuracy. As a consequence, process simulations are not fully implemented in the process of designing and developing a microplastic part, although it is state of the art for macroparts [6,14,16].

First, one reason might be the lack of reliable and comprehensive rheological data and models for the materials, as the data are collected by macroscopic experiments with for microparts improperly specified boundary conditions, e.g., the no-slip condition at walls which is not necessarily true for microparts. Additionally, there is the insufficient implementation or handling of microscopically relevant phenomena and particular characteristics of microparts. This includes the higher surface-to-volume ratio as well as the change and the pressure and viscosity-dependency of the heat transfer coefficient. Both increase the sensitivity to process conditions in the filling, packing, and cooling phases. Also, the higher cooling and shear rates in small cavities lead to different solidification behavior and micromorphology. Besides, the effect of flow hesitation, the microscale rheology, the wettability, the surface tension of the melt can significantly influence the polymer behavior in the microcavity [5,6,9,14,17].

Nevertheless, the software tools can yield more precise results for microparts by using a proper strategy to carefully and comprehensively model and implement the part and the entire injection molding system [9,13,18,19].

Extensive research has been carried out in the field of the application and validation of micro-injection molding simulations. However, research is limited to the study of simplified geometries in order to improve the understanding of the performance of simulations on microcavities. Yet, studies become more advanced and issues and weaknesses of the simulation tools are nowadays clearly identified.

Also, the software manufacturers release new and improved software tools every year, address deficiencies of the software, and claim to achieve more reliable results than previously possible. Encouraged by this development in research and industry, this work attempts to go one step further and focuses on the application of the simulation during the design and engineering process of two complex microfluidic prototype products. The simulations assisted in particular the gate design process of the devices. In addition, the current work presents how the insight coming from the simulations was eventually applied in practice, as the molds were machined based on the simulation results and molded parts were produced.

## Microflow Behavior

###### Viscosity.

Simulation software packages commonly use the Cross-WLF model for describing the viscosity. This model describes the shear rate dependency of the viscosity over a wide range of shear rates very well, because it combines a Newtonian region at low shear rates with a power law shear thinning region at higher shear rates [20]. The viscosity is mathematically given by the Cross model as Display Formula

(1)

where $η0$ is the zero shear rate viscosity, $T$ is the temperature, $p$ is the pressure, $γ˙$ is the shear rate, and $τ$ is the shear stress. The term $1−n$ with the power law index $n$ describes the slope of the viscosity curve in the power law region, when logarithmically plotted versus the shear rate.

###### Thermodynamics.

The commonly used model for describing the thermodynamic $pvT$ data of polymers in simulation tools is the 2-domain Tait model which is given as [20,21] Display Formula

(2)$v(p,T)=v0(T)⋅[1−Cln(1+pB(T))]+vt(p,T)$

where $C=0.0894$ is a constant. The term $B(T)$ describes the pressure sensitivity of the specific volume. The two domains are equal to the solid and molten phase of the plastic which are separated by the transition temperature $Tt$ which is again given as Display Formula

(3)$Tt=b5+b6p$

In the lower temperature region, i.e., the solid phase with , the missing functions of Eq. (2) are given as Display Formula

(4)

Respectively, the upper temperature region, i.e., the molten phase with , is described by Display Formula

(5)

The unknowns $b1s,b2s,b3s,b4s,b1m,b2m,b3m,b4m,b5,b6,b7,b8,$ and $b9$ in Eqs. (3)(5) are without exception data-fitted coefficients.

## Study Cases

###### Microparts.

When dealing with micro-injection molding, the question arises about what exactly is the definition of “micro” or how small are the parts supposed to be considered in the micro-injection molding domain. After some proposals and revisions, three common definitions of different types of micromolded plastic products nowadays exist [2,3,5,8,22]:

• microfeatured parts with outer dimension in the millimeter range or larger, but locally featuring structures in the micrometer range, typically less than 100–200 μm

• microparts with very small outer dimensions, typically 1–2 mm or even entirely in the micrometer range, and shot weights in the order of milligrams

• parts with larger dimensions, but dimensional tolerances in the micrometer range

The present work includes two different study cases of the first kind of microproducts, which will be presented in the following. Both microplastic parts are of microfluidic nature. In general, the main difference to parts made by conventional injection molding is the aspect ratio, i.e., the thickness-to-lateral dimensions ratio, of the micropart or incorporated microstructures being larger than one. This means the thickness of the part is often not negligible in comparison to the other dimensions [2].

###### Microfluidic Distributor System.

The first plastic part was a microfluidic system which served as distributor of liquid. It is shown as a computer-aided design (CAD) model in Fig. 1. The fluid entered at a single inlet at the top and was then distributed to several outlets at the bottom by a treelike structure. The part was approximately 25 mm × 7 mm × 2 mm (length × width × height) large. It could be classified as microplastic part though, as it exhibited microfluidic structures. The fluidic channels were down to 500 μm wide and less than 200 μm deep. The biggest challenge for this part was the walls separating and limiting the fluidic channels which reached thicknesses down to about 100 μm. The total weight of the part was about 0.25 g (equal to a part volume of approximately 0.19 cm3).

The part was chosen due to its complex structure resulting from the ribbing and coring out. It was considered difficult to empirically estimate the flow pattern and the influence of the gate design on the part quality.

Process simulations were applied to this plastic part in order to optimize its gate design and position. Therefore, three different gate layouts for the final part at different positions were given (CAD models shown in Fig. 2) and investigated in a first iteration.

• A: fan gate at the long side with a fan width of 25 mm and a minimal fan thickness of 0.5 mm; the total weight and volume of part and feed system were about 0.57 g or 0.45 cm3, respectively.

• B: fan gate at the short side with a fan width of 7 mm and a minimal fan thickness of 0.5 mm; the total weight and volume of the part and feed system were about 0.50 g or 0.39 cm3, respectively.

• C: pin gate at the long side with approximated semicircular cross section of 0.5 mm diameter; the weight and the volume yielded values of approximately 0.47 g or 0.37 cm3, respectively.

In a second iteration, the design C was investigated more in detail. The diameter was varied in three steps, namely 0.50 mm, 0.75 mm, and 0.90 mm. The change in gate diameter did not noticeably influence the volume or mass or the model, because of the quite small increase compared to the rest of the part. Since gates frequently cause short shots, the investigation elaborated on this issue.

The overall flatness of the part was evaluated, however, as major quality criterion of the gate performance. This was because the component was part of an assembly and therefore could not exceed a certain value in flatness. Besides, the process conditions were taken into consideration in order to remain in a suitable process window, ensuring, e.g., no excessive shear stress on the polymer, injection molding machine copes with injection pressure and clamping force, sufficient packing, etc. Additionally, the behavior of the polymer flow front was examined, i.e., even filling of the part was required.

The material choice for the final part and hence the simulations in this case were Ultem 1000, a polyetherimide (PEI) grade produced by Sabic, Riyadh, Saudi Arabia. The viscosity and $pvT$ data of the material are shown in Fig. 3. Hence, the melt and mold temperature were chosen accordingly as 380 °C and 160 °C, respectively. The part was supposed to be molded on an injection molding machine of type Allrounder 370 A 600-70 made by Arburg, Loßburg, Germany, with a screw diameter of 18 mm and a maximum clamping force of 60 tons. This machine was thus chosen for the simulations. The RAM speed was automatically determined by the software in order to reach a target filling time in the simulation of 0.4 s.

The material choice for the experimental short shots and the simulation validation was the polypropylene (PP) BJ356MO produced by Borealis, Vienna, Austria. The melt temperature was accordingly set to 230 °C, whereas the mold temperature was kept at 40 °C. The injection speed was set to 75 mm/s. The used injection molding machine was the same as for the gate investigations.

###### Microfluidic Mixer System.

The part was of great interest in this simulation-based investigation because of the micropillars. The large number and the regular pattern enabled to use them as flow markers. Moreover, these aspects made them suitable to perform the qualitative comparison of the simulations with short shots.

The simulation results were evaluated with regard to the overall filling pattern and the filling of the micropillars. Furthermore, the thickness of the film gate was varied and set to three different values (280 μm, 420 μm, and 560 μm). The gate thickness resulted from available best practice recommendations about film gate design in tooling engineering. The gate thickness should be between 20% and 70% of the wall thickness where the gate is attached (this corresponds to 0.28 mm and 0.96 mm) [2427]. Because of easier degating, it was decided to use gate sizes at the lower end of the recommended range. It was therefore also of interest whether the gates produce a short due to insufficient cross section.

The part weight did not noticeably differ between the three gate configurations. The three layouts were evaluated based on the filling characteristics of the polymer, e.g., flow, shear stress, temperature, packing performance, shrinkage, etc.

The material choice for the final part and thus the simulations was a cyclic olefin copolymer (COC): Topas 5013 L-10 produced by Topas Advanced Polymers, Frankfurt am Main, Germany. The viscosity and $pvT$ data of the material are shown in Fig. 6. The melt and mold temperature in the simulation were set to typical practical processing settings for COC of 280 °C and 110 °C, respectively. The part was supposed to be molded on the same aforementioned machine Arburg Allrounder 370 A 600-70. In this case, the filling was set to be velocity controlled with an injection speed of 200 mm/s.

The material choice for the conducted experimental short shots and simulation validation was the PP Sabic PP 579 S. The melt temperature was set to 230 °C, the mold temperature was set to 60 °C, and the injection speed of the machine was chosen as 40 mm/s. The same injection molding machine was deployed as for the gate investigations.

## Simulation Software and Models

###### Software Properties.

In this work, the commercially available software tool autodesk simulation moldflow insight® (ASMI) in the version of 2014 and 2015 made by Autodesk, San Rafael, CA, was used for carrying out the process simulations. The software enables to investigate the whole injection molding cycle with the filling, packing, and cooling phases, the mold and part behavior during the process, and also the quality of the resulting plastic part, e.g., with regard to the shrinkage and warpage behavior.

Due to the complexity of the process and the geometries of injection molding, the mathematical models describing the physics are impossible to be solved directly for an entire plastic part. Therefore, ASMI is an FEA-based software, like most of the commercial tools for the investigation and simulation of the injection molding process. The FEA breaks down the original geometry into smaller entities. This discretization of the geometry in elements is called meshing. The mesh consists of triangular elements given by three nodes in case of two-dimensional (2D) analyses. In 3D, on the contrary, the geometry is represented by tetrahedral elements given by four nodes. For each node, the mathematical models can be simplified and together with some reasonable approximations, the equations can be solved individually for every node. In sum, this yields a solution for the entire investigated geometry.

In general, the accuracy of the approximated solution given by the FEA depends on the density of the mesh. Hence, the finer the mesh, the more accurate the solution will be. However, the finer the mesh, the more equations have to be solved because of the higher number of nodes and thus the longer the computation time of the conducted simulation will be.

ASMI applies the meshing together with the Cross-WLF and Tait model to describe the viscosity and $pvT$ behavior of the plastics. The flow is modeled by the Navier–Stokes equations in 3D meshes and by the generalized Hele–Shaw model in 2D meshes. The flow of the plastic starts at one or several nodes which were chosen as the injection location. From there, the flow advances to more and more neighboring nodes in every time step until the entire meshed plastic part is completely full or the material flow freezes completely.

Regarding the Navier–Stokes equations, ASMI provides the option to turn on the effect of gravity and inertia which were enabled in this simulation study.

###### Simulation Models.

The used simulation models were related to the actual plastic part with the feed system. The meshing of both entities in ASMI was based on the original and imported CAD data and conducted in process with two successive steps. First, the meshing was done in the 2D domain, leading to a surface mesh of the part. Afterward, the surface mesh was maintained and the volume of the part was meshed in the 3D domain with tetrahedral elements. The meshing and simulation settings varied between the two products, but they were kept equal among the gate configurations of each study case.

Due to the large differences in size of the incorporated features (e.g., sprue and microchannels for the distributor or sprue and micropillars for the mixer), a so-called multiscale mesh was applied to both study cases, i.e., the mesh size can vary significantly between the various meshed entities, and also within one meshed part.

The mesh intensifies at the microstructures in order to capture the actual CAD geometry and to provide sufficient resolution to prevent from effects given by the mesh like a Boolean behavior of the filling where the structure is empty in one time step and in the next time step it is completely filled, but an intermediate step is not possible.

The mesh size for the microfluidic distributor ranged from 40 to 800 μm edge length of the tetrahedral elements for all three configurations (design A, design B, and all gate sizes of design C). This resulted in models with approximately 2.9–3.8 × 106 tetrahedrons. The model of gate design C is exemplary shown in Fig. 7. The remarkable difference in element count is caused by the very different volumes (compare to the previous section, Microfluidic Distributor System) and shapes of the three gate types.

The multiscale mesh of the microfluidic mixer (shown in Fig. 8) comprised mesh sizes in the order of 65–800 μm for all gate thicknesses, resulting in models with 4.0–4.2 × 106 tetrahedral elements. The volume difference of the three gate configurations was negligible. However, the necessity for decreasing mesh size with decreasing film gate thickness led to the difference in element count.

## Results and Discussion

For both plastic products, the simulations showed that all examined gate designs provided complete filling of the respective part. No short shots were detected. The important simulation results for both parts are summarized in Tables 1 and 2.

###### Microfluidic Distributor System.

Regarding the microfluidic distributor and as listed in Table 1, all three gate designs result in similar injection times of about 0.4 s and thus go in accordance with the demanded optimum injection time.

Moreover, the pin gate requires as expected the highest maximum injection pressure with about 95 MPa because of its narrow cross section. Still, it is clearly within the limits of the machine capability, the maximum clamping force likewise. On the other hand, design A requires the lowest injection pressure with about 51 MPa due to the large cross section of the long fan gate.

The filling behavior of the polymer is illustrated in Fig. 9 for one single time step during the filling phase. Design A shows clearly the most inhomogeneous filling, whereas B and C yield more even flow fronts. When looking at the entire filling phase design C is slightly in favor over design B regarding the flow front.

The reason for this inhomogeneous filling in design A is the flow length from the sprue to the actual cavity. It is much smaller in the center of the gate than at the outer flanks, so that the flow reaches the cavity much earlier in the center. Design B shows however that a fan gate provides an even distribution of the material flow in the center and at the flanks leading to an even flow front entering the cavity.

The observed flow disturbances in the cavity, which lead to the uneven flow front, are caused by the ribbing and coring out and thus the significant thickness variation of the part. All ribs are introduced in the first place to minimize the warpage of the part and provide stabilization. The ribs are thinner than the actual bulky body, and therefore they act as flow restrictors where the flow front lags behind, as it is illustrated in Fig. 10.

The thickness variation along the part (depicted in Fig. 10) has a similar effect. The plastic flow will be restricted in thinner areas and flow more quickly where the party is thicker. The depressions between the ribs show only about one-third of the total part thickness and restrict the flow. In contrast, the fluidic channel areas exhibit more than three-quarters of the total thickness and thus act as flow leader in direct comparison.

The inhomogeneity in the flow front and the difference in flow direction between the three investigated designs also affect the warpage of the plastic part which can be predicted by the simulations. The warpage of this part is crucial, as the flatness is directly connected to it and one of the major part quality criteria at the same time. The results for the warpage prediction of the simulations for all three gate designs are shown in Fig. 11.

Design A shows the worst warpage behavior which is best seen in z direction (Fig. 12). The inverse “U-shape” is very distinct and the warpage level is also highest indicated by the quite strong red area in the center.

Design B shows worse warpage than design C which is best seen by looking at the deflection of the lower left corner in z direction. It bent up more significantly when compared to design C. In addition, the warpage in y direction (Fig. 11) for design B was the most unsymmetrical.

With regard to the average shrinkage, design B gives the lowest value. The maximum shear rate of gate design C exceeds plainly the recommended limit for the chosen polymer. Thus, there is a risk for material degradation. However, only design C fulfills the requirement of a flatness value below 10 μm. Altogether, gate C seems the most favorable choice.

As a first option, the shear stress can be lowered by modifying the cross section of the pin gate. Derived from runners, a full round or trapezoidal shape is more efficient, i.e., causing lower pressure drop and shear. The excessive shear stress was counteracted in this work alternatively by simply increasing the width of the pin gate which was the reason for the second iteration of the microfluidic distributor.

The maximum shear rate decreased from the aforementioned 104,000 s−1 for the 0.50-mm thick gate (compare to Table 1) to values of 54,000 s−1 and 20,000 s−1 for the 0.75 mm and 0.90 mm, respectively. The two latter values are fairly below the permitted maximum level of 50,000 s−1.

The warpage results in z direction for the three different gate sizes are shown in Fig. 12. The thinnest gate with 0.50 mm diameter shows the greatest warpage, the thickest gate with 0.90 mm diameter shows the smallest warpage. This can be noticed especially at the upper left corner in red and the lower right corner in green which are much more emphasized for the thin gate. The reason for this is probably the better packing performance of the thick gate which freezes later than the thin and medium-sized one, allowing for larger and longer shrinkage compensation.

In conclusion, the increase in gate diameter does not only enable to push the maximum shear rate to an acceptable level, but it is even beneficial for further improvement of the flatness of the microfluidic distributor.

The design of the prototype was finalized including the pin gate at the long side of the part with a diameter of 0.9 mm and indeed realized as actual cavity in a steel mold. Hence, the insight coming from the simulation could be applied in practice. The final mold, which was used for part production and the short shots, is depicted in Fig. 13.

###### Flow Pattern Validation of Microfluidic Manifold.

The comparison between the actual flow front given by short shots molded in PP and the predicted flow front given by the simulation is done on a qualitative basis. The comparison of the flow fronts on part level is illustrated in Fig. 14. The overlay of the simulated and real flow front shows good agreement between the flow fronts. Hence, the simulation can forecast the actual flow front behavior. However, there is some small deviation to observe: the flow front given by the simulation is slightly ahead in the lower half of the cavity, whereas it lags slightly behind in upper half of the cavity compared to the short shots.

The comparison of the flow fronts on feature level looking closer at the microfeatures of the microfluidic manifold is shown in Fig. 15. Also, time steps can be found in the simulation which show good agreement to the actual part shape. Nevertheless, the simulation predicts falsely the filling of the microfeatures. None of the real parts shows complete filling of the microfeatures which most likely happens later at the end of the filling phase or in the packing phase. The simulation on the other hand shows complete filling already at an early stage of the filling phase.

Moreover, it should be noted that for the single short shots the time step for the best fit of the flow front on part level often differs from the time step for best fit on feature level. The differences are in the range of up to about 3% of the individual filling time. This divergence might be explained by the fact that the simulation assumes perfect venting, since the mold is not modeled. In reality, the air has to escape from the microfeatures of the cavity and the built up counterpressure holds the plastic flow back.

###### Microfluidic Mixer System.

The film gate is in general well suited for the part, as the polymer flow enters the cavity rather uniformly across the gate width, as depicted in Fig. 16. Additionally, the simulation identifies hesitation of the polymer flow at the micropillars which is illustrated in Fig. 16. It is characterized by the easier flow into the bulky substrate (in the actual main flow direction) than into the micropillars. The hesitation effect is a common phenomenon for cavities of different thicknesses, as it is pronouncedly the case for microstructures on substrates [22].

This leads to the flow actually reaching the end of the cavity before the micropillars are completely filled which has to be considered for setting up the packing phase when producing the part.

The volumetric shrinkage for all three gates is depicted in Fig. 17 and listed in Table 2. The thickest gate proved to achieve the lowest volumetric shrinkage, highest part mass (mass increase due to larger gate thickness is negligible), and thus the best packing performance. In addition, the shrinkage is also quite homogeneous compared to the thinnest gate. Even and low shrinkage is important, as the part will be assembled to another part by means of the four holes. Any displacement or misalignment will make the assembly more difficult.

As shown in Table 2, the shear rate is at an acceptable level for the thickest gate only, whereas for the small and medium gates the risk of polymer degradation exists. On the other hand, it also needs the highest clamping force which can however be delivered by a typical injection molding machine without problems.

The injection pressure yields no such clear and simple trend. With values of 35.5 MPa and 35.1 MPa, the gates sizes of 280 μm and 560 μm do not show a significant pressure difference. For the medium-sized gate, however, the predicted injection pressure of 30.8 MPa is noticeably lower (about 12%) in comparison.

In general, it can be assumed that the injection molding exhibits high pressure domains. At very high pressures, the bulk compression of the polymer melt decreases the free volume which again leads to a reduction of the mobility of the polymer chains. This effect is known as that the so-called pressure-induced viscosity increase [28].

The nonlinear behavior of the injection pressure could thus be explained by taking three effects into consideration: the pressure drop to drive the flow, the pressure-induced viscosity increase, and the shear thinning effect of polymers.

At the small gate, the pressure drop is large; the pressure-induced viscosity increase counteracts the shear thinning effect. In total, the injection pressure is hence high. In case of the medium-sized gate, the pressure drop and the pressure-induced increase in viscosity get less. The shear thinning becomes visible, and the total injection pressure is thus lower. The injection pressure rises again for the large gate, because the shear thinning effect disappears. In the aggregate, the pressure drop and pressure induced viscosity are more pronounced.

Eventually, the mold of the prototype was realized and one of the mold inserts used for the actual part production and the short shots is shown in Fig. 18. Implementing the findings of the simulations in the tooling, the final design incorporates the film gate with 560 μm thickness.

###### Flow Pattern Validation of Microfluidic Mixer.

Similar to the microfluidic manifold, the comparison between the actual flow front given by short shots in PP and the predicted flow front given by the simulation is done on a qualitative basis. The comparison of the flow fronts on part level is illustrated in Fig. 19. The overlay of the simulated and real flow front shows also in this case good agreement between the flow fronts with minimal deviations. The simulation can forecast the actual flow front behavior more accurately than in case of the manifold. The reason is possibly that the mixer exhibits a lower thickness variation which distorts the flow.

The comparison of the flow fronts on feature level looking closer at the micropillars of the microfluidic mixer is shown in Fig. 20. First, the effect of a depression at the base of the pillars should be noted in the plastic samples. Probably, they are caused by air in the cavity which creates a counterpressure and leaves an imprint. This effect could be seen for all pillars. Although the simulation assumes perfect venting, the plastic flow also showed narrow depressions at the base shortly before flowing into the pillars.

Despite the fact that the match for the flow front on part level was better, the filling of the micropillars was predicted with less accuracy than in case of the microfluidic manifold. In the simulation, the pillars fill too early; likely for the same reason mentioned before for the manifold: the simulation assumes an evacuated mold, whereas in reality the air might cause a counterpressure in the pillars which holds back the plastic flow. Additionally, the time steps in the simulation giving the best fit on part level or, respectively, on the feature level (considering pillars and walls, since the filling of the pillars were not predicted correctly) show differences of up to about 1%.

## Conclusion

The simulation-aided optimization of the gate design and the gate layout of two microfluidic plastic components was successfully conducted by using autodesk moldflow. The investigations included the behavior of the polymer flow during the filling phase and several part quality criteria, e.g., shrinkage and warpage. The simulation of the parts was based on the application of a multiscale mesh with a large span of mesh element size with 3D tetrahedral elements to the part and the entire feed system. The decision on the final gate for both parts was based on comparison between the simulated performances of the different given gate layouts.

Three different gate types were evaluated for the microfluidic distributor. For this device, the first design iteration of the gate optimization yielded the gate type and the gate size. The pin gate proved to be the best gate choice. However, the gate size had to be increased to 0.9 mm according to the second design iteration, as the maximum shear stress of the polymer was easily exceeded with the default size.

The thickness of the film gate of the microfluidic mixer was investigated, and the results showed that the thickest gate provides superior performance. The simulation proved the suitability of the film gate and the hesitation of the polymer flow at the micropillars as the most challenging features of the part.

Nonetheless, the simulation results showed in case of the microfluidic mixer also some inconsistency regarding the injection pressure. Their cause is not entirely clear, possibly the limited capability of the simulation software to handle microplastic parts and microscale phenomena. It is important to keep in mind that such limitations do exist and simulation results of micro-injection molding should always be critically analyzed. The quantitative comparison of the simulations with further experiments is subject to planned future work.

With this work, it was furthermore shown that the simulation of the injection molding process is a supportive and effective tool for micromanufacturing and the design of microplastic components. It was used for the part validation by checking, if the required part quality and possible tolerances are reached. Besides, the part and tool design was assisted by finding the most suitable gate type and size without spending lots of effort on prototyping and molding trials with different gate geometries. Finally, the insight of the simulations was in fact applied in practice by machining the cavities for both devices based on the findings in the simulation.

Simultaneously, it could be checked whether the given process parameters were suitable for reaching the required part quality as well as for successful molding or if problems or defects were to be expected.

The presented work also included the validation of the simulation by cross-checking with the actually molded plastic components made out of PP in order to find out how good the prediction actually was. It was observed that the simulation could predict the flow fronts on the global part level well, but the flow prediction on the local feature level showed some divergence to reality. In general, the simulation yielded an unproblematic and too early filling of the microfeatures of both prototypes.

Simulations easily allow changing the material of the part in order to see whether other plastics could be deployed for the study cases, as the chosen polymers are rather expensive. Possible improvements and enhancements of the simulations comprise the implementation of a more comprehensive model including the actual steel mold block and different layouts of the heating/cooling system. In general, the final influence of the mold and cooling on the part quality can be investigated by doing so. The cooling circuit can be optimized still in the design phase before the actual production of the mold starts. Finally, simulation results can benefit also from taking into account the effect of mold venting in connection with the clamping force, the surface finish of the plates, and the actual air gap at the mold closure parting plane.

## Acknowledgements

This paper reports work undertaken in the framework of the project “Hi-MICRO” (High Precision Micro Production Technologies),2 Task 1.2: Micro Injection-Moulding Oriented Product Design. Hi-MICRO is a collaborative project supported by the European Commission in the 7th Framework Programme (Grant Agreement No: 314055). Contribution from the Hi-MICRO consortium which provides the study cases for the application of the simulations in the presented work is acknowledged.

## References

Attia, U. M. , and Alcock, J. R. , 2011, “ A Review of Micro-Powder Injection Moulding as a Microfabrication Technique,” J. Micromech. Microeng., 21(4), p. 043001.
Giboz, J. , Copponnex, T. , and Mélé, P. , 2007, “ Microinjection Molding of Thermoplastic Polymers: A Review,” J. Micromech. Microeng., 17(6), pp. R96–R109.
Zhiltsova, T. V. , Oliveira, M. S. A. , and Ferreira, J. A. , 2013, “ Integral Approach for Production of Thermoplastics Microparts by Injection Moulding,” J. Mater. Sci., 48(1), pp. 81–94.
Tada, K. , Fukuzawa, D. , Watanabe, A. , and Ito, H. , 2010, “ Numerical Simulation for Flow Behaviour on Micro- and Nanomoulding,” Plast. Rubber Compos., 39(7), pp. 321–326.
Yang, C. , Yin, X.-H. , and Cheng, G.-M. , 2013, “ Microinjection Molding of Microsystem Components: New Aspects in Improving Performance,” J. Micromech. Microeng., 23(9), p. 093001.
Nguyen-Chung, T. , Loser, C. , Juttner, G. , Pham, T. , Obadal, M. , and Gehde, M. , 2011, “ Simulation of the Micro-Injection Moulding Process: Effect of the Thermo-Rheological Status on the Morphology,” Proc. Inst. Mech. Eng., Part E, 225(4), pp. 224–238.
Drummer, D. , and Messingschlager, S. , 2014, “ Ceramic Injection Molding Material Analysis, Modeling and Injection Molding Simulation,” Proceedings of the 29th International Conference of the Polymer Processing Society (PPS), Nuremberg, Germany, July 15–19, pp. 582–586.
Griffiths, C. A. , Dimov, S. S. , Scholz, S. , Hirshy, H. , and Tosello, G. , 2011, “ Process Factors Influence on Cavity Pressure Behavior in Microinjection Moulding,” ASME J. Manuf. Sci. Eng., 133(3), p. 031007.
Drummer, D. , Ehrenstein, G. W. , Hopmann, C. , Vetter, K. , Meister, S. , Fischer, T. , Piotter, V. , and Prokop, J. , 2012, “ Innovative Prozesstechnologien für die Herstellung thermoplastischer Mikrobauteile—Analyse und Vergleichende Bewertung,” Z. Kunststofftech. (J. Plast. Technol.), 8(5), pp. 440–467.
Costa, F. S. , Tosello, G. , and Whiteside, B. R. , 2009, “ Best Practice Strategies for Validation of Micro Moulding Process Simulation,” Polymer Process Engineering 2009 Conference, pp. 259–261.
Vietri, U. , Sorrentino, A. , Speranza, V. , and Pantani, R. , 2011, “ Improving the Predictions of Injection Molding Simulation Software,” Polym. Eng. Sci., 51(12), pp. 2542–2551.
Khalilian, S. A. , Park, S. S. , and Freiheit, T. I. , 2013, “ The Application of Commercial Injection Molding Software to Micro-Component Design and Process Development,” 8th International Conference on Micro Manufacturing (ICOMM 2013 No. 59), pp. 50–56.
Marhöfer, D. M. , Tosello, G. , Hansen, H. N. , and Islam, A. , 2013, “ Advancements on the Simulation of the Micro Injection Moulding Process,” 10th International Conference on Multi-Material Micro Manufacture (4M 2013), Research Publishing Services, San Sebastian, Spain, pp. 77–81.
Tosello, G. , Gava, A. , Hansen, H. N. , Reinecke, H. , Lucchetta, G. , and Schoth, A. , 2009, “ Experimental Validation of Micro Molding Simulations Using Different Process Setting Conditions,” 67th Annual Technical Conference (ANTEC) of the Society of Plastics Engineers 2009, Chigago, IL, pp. 1787–1793.
Chen, L. , Kietzmann, C. , Astbury, D. , and Shao, L. , 2014, “ Advanced Cooling Simulation Technologies for the Injection Molding Process,” Autodesk, San Rafael, CA.
Cramer, A. , Michaeli, W. , Friesenbichler, W. , and Duretek, I. , 2007, “ Simulation des Spritzgießprozesses von Mikrobauteilen,” Z. Kunststofftech. (J. Plast. Technol.), 3(1), pp. 1–26.
Young, W. B. , 2005, “ Simulation of the Filling Process in Molding Components With Micro Channels,” Microsyst. Technol., 11(6), pp. 410–415.
Tosello, G. , Costa, F. S. , and Hansen, H. N. , 2011, “ Micro Injection Moulding High Accuracy Three-Dimensional Simulations and Process Control,” Polymer Process Engineering 11: Enhanced Polymer Processing, Bradford, UK, p. 14.
Islam, A. , Hansen, H. N. , Marhöfer, D. M. , Angel, J. , Dormann, B. , and Bondo, M. , 2012, “ Two-Component Micro Injection Moulding for Hearing Aid Applications,” Int. J. Adv. Manuf. Technol., 62(5–8), pp. 605–615.
Kennedy, P. , and Zheng, R. , 2013, Flow Analysis of Injection Molds, Carl Hanser Verlag, Munich, Germany.
Wang, J. , 2012, Some Critical Issues for Injection Molding, InTech, Rijeka, Croatia.
Attia, U. M. , Marson, S. , and Alcock, J. R. , 2009, “ Micro-Injection Moulding of Polymer Microfluidic Devices,” Microfluid. Nanofluid., 7(1), pp. 1–28.
Autodesk, 2015, “ Autodesk Simulation Moldflow Insight®,” Software Material Data Base, Autodesk, San Rafael, CA.
Menges, G. , Michaeli, W. , and Mohren, P. , 2001, How to Make Injection Molds, Carl Hanser Verlag, Munich, Germany.
Beaumont, J. P. , 2004, Runner and Gating Design Handbook—Tools for Successful Injection Molding, Carl Hanser Verlag, Munich, Germany.
Goodship, V. , 2004, Practical Guide to Injection Moulding, Rapra Technology Limited, Shawbury, UK.
DSM Engineering Plastics, 2005, Design Guide—Performance And Value With Engineering Plastics, Technical Guide, Evanston, IN.
Lenk, R. S. , 2012, Polymer Rheology, Springer Science & Business Media, New York.
View article in PDF format.

## References

Attia, U. M. , and Alcock, J. R. , 2011, “ A Review of Micro-Powder Injection Moulding as a Microfabrication Technique,” J. Micromech. Microeng., 21(4), p. 043001.
Giboz, J. , Copponnex, T. , and Mélé, P. , 2007, “ Microinjection Molding of Thermoplastic Polymers: A Review,” J. Micromech. Microeng., 17(6), pp. R96–R109.
Zhiltsova, T. V. , Oliveira, M. S. A. , and Ferreira, J. A. , 2013, “ Integral Approach for Production of Thermoplastics Microparts by Injection Moulding,” J. Mater. Sci., 48(1), pp. 81–94.
Tada, K. , Fukuzawa, D. , Watanabe, A. , and Ito, H. , 2010, “ Numerical Simulation for Flow Behaviour on Micro- and Nanomoulding,” Plast. Rubber Compos., 39(7), pp. 321–326.
Yang, C. , Yin, X.-H. , and Cheng, G.-M. , 2013, “ Microinjection Molding of Microsystem Components: New Aspects in Improving Performance,” J. Micromech. Microeng., 23(9), p. 093001.
Nguyen-Chung, T. , Loser, C. , Juttner, G. , Pham, T. , Obadal, M. , and Gehde, M. , 2011, “ Simulation of the Micro-Injection Moulding Process: Effect of the Thermo-Rheological Status on the Morphology,” Proc. Inst. Mech. Eng., Part E, 225(4), pp. 224–238.
Drummer, D. , and Messingschlager, S. , 2014, “ Ceramic Injection Molding Material Analysis, Modeling and Injection Molding Simulation,” Proceedings of the 29th International Conference of the Polymer Processing Society (PPS), Nuremberg, Germany, July 15–19, pp. 582–586.
Griffiths, C. A. , Dimov, S. S. , Scholz, S. , Hirshy, H. , and Tosello, G. , 2011, “ Process Factors Influence on Cavity Pressure Behavior in Microinjection Moulding,” ASME J. Manuf. Sci. Eng., 133(3), p. 031007.
Drummer, D. , Ehrenstein, G. W. , Hopmann, C. , Vetter, K. , Meister, S. , Fischer, T. , Piotter, V. , and Prokop, J. , 2012, “ Innovative Prozesstechnologien für die Herstellung thermoplastischer Mikrobauteile—Analyse und Vergleichende Bewertung,” Z. Kunststofftech. (J. Plast. Technol.), 8(5), pp. 440–467.
Costa, F. S. , Tosello, G. , and Whiteside, B. R. , 2009, “ Best Practice Strategies for Validation of Micro Moulding Process Simulation,” Polymer Process Engineering 2009 Conference, pp. 259–261.
Vietri, U. , Sorrentino, A. , Speranza, V. , and Pantani, R. , 2011, “ Improving the Predictions of Injection Molding Simulation Software,” Polym. Eng. Sci., 51(12), pp. 2542–2551.
Khalilian, S. A. , Park, S. S. , and Freiheit, T. I. , 2013, “ The Application of Commercial Injection Molding Software to Micro-Component Design and Process Development,” 8th International Conference on Micro Manufacturing (ICOMM 2013 No. 59), pp. 50–56.
Marhöfer, D. M. , Tosello, G. , Hansen, H. N. , and Islam, A. , 2013, “ Advancements on the Simulation of the Micro Injection Moulding Process,” 10th International Conference on Multi-Material Micro Manufacture (4M 2013), Research Publishing Services, San Sebastian, Spain, pp. 77–81.
Tosello, G. , Gava, A. , Hansen, H. N. , Reinecke, H. , Lucchetta, G. , and Schoth, A. , 2009, “ Experimental Validation of Micro Molding Simulations Using Different Process Setting Conditions,” 67th Annual Technical Conference (ANTEC) of the Society of Plastics Engineers 2009, Chigago, IL, pp. 1787–1793.
Chen, L. , Kietzmann, C. , Astbury, D. , and Shao, L. , 2014, “ Advanced Cooling Simulation Technologies for the Injection Molding Process,” Autodesk, San Rafael, CA.
Cramer, A. , Michaeli, W. , Friesenbichler, W. , and Duretek, I. , 2007, “ Simulation des Spritzgießprozesses von Mikrobauteilen,” Z. Kunststofftech. (J. Plast. Technol.), 3(1), pp. 1–26.
Young, W. B. , 2005, “ Simulation of the Filling Process in Molding Components With Micro Channels,” Microsyst. Technol., 11(6), pp. 410–415.
Tosello, G. , Costa, F. S. , and Hansen, H. N. , 2011, “ Micro Injection Moulding High Accuracy Three-Dimensional Simulations and Process Control,” Polymer Process Engineering 11: Enhanced Polymer Processing, Bradford, UK, p. 14.
Islam, A. , Hansen, H. N. , Marhöfer, D. M. , Angel, J. , Dormann, B. , and Bondo, M. , 2012, “ Two-Component Micro Injection Moulding for Hearing Aid Applications,” Int. J. Adv. Manuf. Technol., 62(5–8), pp. 605–615.
Kennedy, P. , and Zheng, R. , 2013, Flow Analysis of Injection Molds, Carl Hanser Verlag, Munich, Germany.
Wang, J. , 2012, Some Critical Issues for Injection Molding, InTech, Rijeka, Croatia.
Attia, U. M. , Marson, S. , and Alcock, J. R. , 2009, “ Micro-Injection Moulding of Polymer Microfluidic Devices,” Microfluid. Nanofluid., 7(1), pp. 1–28.
Autodesk, 2015, “ Autodesk Simulation Moldflow Insight®,” Software Material Data Base, Autodesk, San Rafael, CA.
Menges, G. , Michaeli, W. , and Mohren, P. , 2001, How to Make Injection Molds, Carl Hanser Verlag, Munich, Germany.
Beaumont, J. P. , 2004, Runner and Gating Design Handbook—Tools for Successful Injection Molding, Carl Hanser Verlag, Munich, Germany.
Goodship, V. , 2004, Practical Guide to Injection Moulding, Rapra Technology Limited, Shawbury, UK.
DSM Engineering Plastics, 2005, Design Guide—Performance And Value With Engineering Plastics, Technical Guide, Evanston, IN.
Lenk, R. S. , 2012, Polymer Rheology, Springer Science & Business Media, New York.

## Figures

Fig. 1

CAD model of the first investigated microplastic part with highlighted treelike structure for the distribution of fluid

Fig. 2

CAD models of the microfluidic distributor with three different gate designs

Fig. 3

Viscosity versus shear rate at different temperatures (left) and pvT data at different pressure levels (right) of the PEI Ultem 1000 which was used for the microfluidic manifold [23]

Fig. 4

CAD model of the second investigated microplastic part which acts as microfluidic mixer

Fig. 5

CAD model of the second investigated microplastic part with feed system (film gate, runner, sprue)

Fig. 6

Viscosity versus shear rate at different temperatures (left) and pvT data at different pressure levels (right) of the COC Topas 5013-L10 which was used for the microfluidic mixer [23]

Fig. 7

Meshed microdistributor with closer view on some details (microwalls at outlets). Range of mesh edge length of the entire model: 40–800 μm.

Fig. 8

Meshed micromixer with closer view on some details (micropillars and rim). Range of mesh edge length of the entire model: 65–800 μm.

Fig. 9

Filling behavior for the three configurations of the fluidic distributor

Fig. 10

Top: Example of a rib acting as flow restrictors and causing the flow to lag behind compared to the bulk of the microfluidic distributor. Bottom: Thickness variation in the part which contributes to the disturbance of the flow front in the cavity during the filling phase of the microfluidic distributor.

Fig. 11

Warpage prediction of the simulation in x and y direction for the microfluidic distributor

Fig. 12

Warpage prediction of the simulation in z direction for the microfluidic distributor. Left: different gate designs. Right: Different sizes of gate design C (pin gate).

Fig. 13

Actual steel mold of the microfluidic manifold with stationary half (left) and the movable half (right). The cavity wasmachined according to the optimized design based on simulation results applying the insight from the simulations in practice.

Fig. 14

Comparison on part level by overlay of the actual flow front given by short shots molded in PP and the simulated flow front for the microfluidic manifold

Fig. 15

Comparison on feature level between scanning electron microscopy (SEM) picture of the actual flow front given by short shots in PP (left) and the simulated flow front (right) for the microfluidic manifold

Fig. 16

Left: film gate of the microfluidic mixer with quite even flow front when the plastic is entering the actual part cavity. Right: cross-sectional view of the flow in the microfluidic mixer with indication of the distinct hesitation effect at the micropillars: the filling in bulk direction is faster than in the direction of the micropillars, i.e., the flow length a in bulk direction is larger than the flow length b in direction of the micropillars.

Fig. 17

Average volumetric shrinkage for the three film gates of the microfluidic mixer

Fig. 18

Finished mold insert of the microfluidic mixer. The cavity design was machined accordingly to the findings about the design in the simulations.

Fig. 19

Comparison on part level by overlay of the actual flow front given by short shots molded in PP and the simulated flow front for the microfluidic mixer

Fig. 20

Comparison on feature level between SEM picture of the actual flow front given by short shots molded in PP (left) and the simulated flow front (right) for the microfluidic mixer

## Tables

Table 1 Simulation results for the three investigated gate types of the microfluidic distributor
Table 2 Simulation results for the three investigated film gate thicknesses of the micromixer

## Errata

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