Zeitschrift Kunststofftechnik Journal of Plastics Technology · 2015-09-01 · Juster, Steinbichler...

4Autor Titel (gegebenenfalls gekürzt)

© Carl Hanser Verlag Zeitschrift Kunststofftechnik / Journal of Plastics Technology 11 (2015) 5

11 (2015) 5 eingereicht/handed in: 05.03.2015 angenommen/accepted: 23.06.2015

Dipl.-Ing. Dipl.-Ing. Herwig Juster, Prof. Dr. Georg Steinbichler Institute of Polymer Injection Moulding and Process Automation, Johannes Kepler University Linz

Numerical design study of the shear conditions in the gate of an injection mold for drug delivery systems In this study, we used Computational Fluid Dynamics (CFD) methods to investigate the strain and shear behavior of a polymer-based drug-delivery fluid consisting of Soluplus® 90wt% - Fenofibrate 10wt% passing through the gate of an injection mold. For comparison, the behavior of Soluplus® alone was also analyzed. The largest strain rate observed for all systems appeared next to the inflow in the cavity due to the decrease in diameter of the gate. We found that the Active Pharmaceutical Ingredient (API) acts as a plasticizer, which results in higher strain rates and lower wall shear stresses. On the basis of the simulation results, we were able to predict how the design of the mold influences the shear rate. Our results indicate that the gate diameter in the inlet should be greater than 1 mm. A CFD approach can be used to improve the design of molds for drug delivery applications, enabling the development of tablets with new shapes and specified dissolution characteristics in the future.

Numerische Untersuchung der Scherbelastungen im Anguss eines Spritzgießwerkzeuges für pharmazeutische Darreichungsformen In dieser Studie wurden Computational Fluid Dynamics (CFD) Methoden für die Untersuchung von mechanischen Belastungen eines Polymer-Wirkstoff Systems, bestehend aus Soluplus® (90wt%) und Fenofibrat (10wt%) im Anschitt eines Spritzgießwerkzeuges verwendet. Als Vergleichsmaterial diente das Polymer Soluplus® ohne Wirkstoff. Es konnte ein weichmachender Effekt des Wirkstoffes auf das Polymer festgestellt werden. Durch diese Untersuchungen konnten Auslegungsprinzipien für Spritzgießwerkezuge für pharmazeutische Darreichungsformen abgeleitet werden.

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Juster, Steinbichler Numerical design study in gate of injection mold

Journal of Plastics Technology 11 (2015) 5 306

Numerical design study of the shear conditions in the gate of an injection mold for drug delivery systems

H.R. Juster, G. Steinbichler

1 INTRODUCTION

The poor solubility of pharmaceutical drugs has attracted the attention of academia and industry over the past few decades. Recent developments in this field have shown that solubility can be improved by using hydrophilic polymers as carrier matrices for Active Pharmaceutical Ingredients (APIs) to form so-called solid dispersion system [1]. Hot Melt Extrusion (HME) has been used to produce solid dispersions efficiently for over a decade [2]. HME is a way of creating dosage forms with better bioavailability in the pharmaceutical solution. Direct shaping after the extrusion process is possible, but requires downstream processing systems which incur increased production costs and time. The standard tableting process requires two steps: granulation followed by tablet pressing. In the granulating step, the API and the support material are transformed from powder particles into granules (by adding water or other fluids). The result is then ready to be pressed into a tablet shape. In HME, granulation is achieved by changing the thermo-physical state of the polymer and the API, resulting – in the ideal case – in an amorphous one-phase system. Injection molding (IM) is another processing technology that can may combine the advantages of HME (e.g., preparing a solid solution) with a direct shaping step under pressure, figure 1. IM is a versatile approach in the polymer processing industry, and is used, for instance, in manufacturing medical devices such as disposable syringes.

Figure 1: Joint assembly of an injection molding machine

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An injection molding machine consists of a plastification unit and a clamping unit with the mold. In the plastification unit, the polymer and the drug (in the form of pellets or a powder premix) are fed into the barrel. As the screw rotates, the polymeric system is converted from a solid phase into a melt phase. The melt is collected in the antechamber of the plasticization unit and then injected into a mold that has the negative shape of the product (e.g., tablets). During injection, the screw acts like a plunger and does not rotate, whereas during plasticization, the screw is in extrusion mode [3, 4]. The whole manufacturing process of a tablet takes place in a discontinuous production circle, which can be seen in figure 2. First, polymer and API are plasticized. Only the volume necessary for filling the part geometry is plasticized by means of the rotating screw. The melt is then injected, packed (compacted with pressure to avoid shrinkage), and cooled. After the cooling phase is finished, the part can be ejected.

Figure 2: The injection molding production circle: (1) Start plasticizing, (2) End plasticizing, (3) Injection of polymer – API system, (4) Packing and cooling, (5) Ejection of the tablet [5]

When designing molds for polymer applications, variations in gate diameter allow easy removal gates of the part from the runner. As a consequence, additional mechanical removal is in most cases not necessary. Industrial-scale design of tablet-shaped molds for drug delivery systems has not yet been explored, but may become feasible with the appropriate gate diameter. The geometry of the gate is critical due to the progressive diameter decrease (from 2 to 1 mm in this study) that promotes elevated flow velocities, which in turn lead to increased strain rates and stresses. These conditions in combination with temperature increases due to elevated shear rates, can lead

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to degradation of polymer and API. A positive side effect is that the melt is further mixed in this part, and viscosity decreases. However, viscous heating can also lead to degradation of the polymer matrices and/or of the API. The open-source methods currently used to design IM molds do not take into account degradation due to temperature or shear rate increase when using standard polymers, such as polyolefins. Apart of open-source fluid dynamic packages, commercially available mold design software packages which are able to make filling simulations have already more advanced methods implemented. The downside of commercial software packages is the high maintenance costs such as licenses and service costs. The design of injection molds for drug delivery applications must consider not only the rheological and thermal characteristics of the melt, but also its susceptibility to degradation. So far, no general method of predicting the stress and strain behavior of such melts has been published. Structure simulation is a powerful tool for analyzing the mechanical conditions of the mold. Flow simulations allow different geometries to be investigated and individually optimized in a step-by-step procedure. The aim of our study was to apply open source CFD methods to simulate the flow conditions during tablet filling. A standard gate design followed by a tablet mold shape was used to explore in detail the design space and to understand the shear rate effects of the selected polymer – API system. We present the results of combining experimentally obtained rheology data with open source CFD code for designing molds for drug delivery systems, validated using numerical methods.

2 MATERIALS AND METHODS

2.1 Materials

2.1.1 Solupus® Soluplus® polymer, figure 3, was obtained from BASF SE (Ludwigshafen, Germany). The backbone consists of a polyethylene-glycol intercalated with polyvinyl caprolactam-polyvinyl acetate [6]. Figure 3 shows the structure of the Soluplus® monomer.

Figure 3: Soluplus®-Polymer: Used as a drug carrier matrix system [7]

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The main purpose of polymeric Soluplus® is to enhance the bioavailability of poorly soluble drugs. Its glass transition temperature is around 70°C [7], which allows processing at lower temperatures.

2.1.2 Soluplus® 90 wt% – Fenofibrate 10 wt% To form a drug delivery system, Soluplus® was compounded with Fenofibrate as an example API, figure 4, at RCPE GmbH (Graz, Austria). Fenofibrate is used to reduce the concentration of the low-density lipoprotein in the human body. It was chosen as the example poorly soluble drug in this study due to its low cost. Fenofibrate melts at 80°C.

Figure 4: Fenofibrate: Used as a drug in the system investigated

2.1.3 Polystyrene type 145D Polystyrene (PS) 145 D was acquired from BASF SE (Ludwigshafen, Germany). We used it in this study as a benchmark material because its behavior as a high-flow fluid in injection molding applications is well understood [8]. This polystyrene type has its glass transition at 91°C.

2.2 Methods

2.2.1 Mold The mold used in this study can be seen in figure 5. It was designed with 6 cavities and 1 star-shaped runner for the melt inflow. The gate area of the mold was the main object of study in our work, since in this region stress and strain reach their maximum values. Each cavity has a diameter of 13 mm and a height of 4 mm to form tablets with the same dimensions.

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Figure 5: Geometry of the molded product: (1) Star runner and tablet cavities and (2) gate with details (d = 13 mm, h = 4 mm, α = 1°, r = 0.5 mm, l = 1 mm, t = 0.5 mm) [9]

2.2.2 Numerical (CFD) methods - Governing equations To model the motions of the polymer melt, we used non-linear partial differential equations [10]. In general, such a system is divided into (I) the continuity equation, (II) the momentum equations, and (III) the energy equations. The general description of the continuity equation (Equation 1) is

𝜕𝜕𝜕𝜕

+ ∇ ∙ 𝜌𝜌 = 0. Equation 1

In Equation 1, ρ, t, and u are the density of the fluid, the time and the vector of velocity, respectively. The momentum equations (Equation 2) describe the conservation of the momentum properties of the fluid:

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𝜕𝜕𝜕𝜕𝜕

+ ∇ ∙ 𝜌𝜌𝜌 = − ∇𝑝 + ∇ ∙ 𝑆𝑣𝑣𝑣𝑣𝑣𝜕𝑣 + 𝐹, Equation 2

where p represents the pressure, Sviscous=ρν[∇u+(∇u)T- 2/3∇∙u] is the viscous stress tensor with the kinematic viscosity v, and F is a source term. If heat transfer is also to be considered, the energy equation (Equation 3) can be written in the form

𝜕𝜕𝜕𝜕

+ ∇ ∙ (𝜌𝑢) = 1𝑣𝑝𝜕

∇ ∙ 𝑘∇𝑢 + 𝑄𝑝, Equation 3

where T stands for the transported temperature, cp and k are the heat capacity and the thermal conductivity of the fluid, and Qp is a source term. Since in our simulation setup the density of the polymer melt does not change, it is assumed to be an incompressible fluid. This leads to a reduction of the continuity equation to ∇∙u=0, and of the momentum equations to 𝜕𝜕𝜕𝜕

+ ∇ ∙ 𝜌𝜌 = − 1𝜕∙ ∇𝑝 + 1

𝜕∇ ∙ 𝑆𝑣𝑣𝑣 + 𝐹′.

Generally, in injection molding the assumption of incompressible flow during the filling phase can only be a first approximation. The filling of a cavity is accompanied by high pressure levels which lead to remarkably density changes. In this study, a stationary flow field for the gate region is computed and analysed. The same is valid for temperature changes. Inlet and outlet temperatures are identical and considered as isothermal.

2.2.3 Material models Polymers generally exhibit anisotropic material behavior. The viscosity of the polymer is a function of temperature, pressure, time, shear rate, and chemical structure of the sample (Equation 4):

𝜂(𝛾,̇ 𝑢,𝑝, 𝑡) = 𝜏�̇� Equation 4

where 𝜂 is the viscosity in relation to shear rate �̇�, temperature T, pressure p and time t. The shear stress is represented by 𝜏. Since high shear rates occur in the molding process, the change in viscosity as a function of shear rate must be taken into account. Hence, a model that properly describes the material behavior is required. We use the Cross-Power-Law (Equation 5) to model the shear thinning behavior of the polymer-API system:

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𝜂(�̇�) = 𝐴1+(𝐵∙�̇�)𝐶

Equation 5

Here, A represents the zero-shear viscosity at a given temperature, B is the reciprocal transition shear rate, and C is the gradient of the viscosity curve. Table 1 lists the numerical values of A, B and C for all materials used. We fit the material parameters, which were obtained using a Rheograph 25 (Göttfert, Germany) high-pressure capillary rheometer, for T equal to the processing temperature. The material parameters were obtained using a Rheograph 25 (Göttfert, Germany) high-pressure capillary rheometer.

Material A [Pa s] B [s] C [/]

Soluplus 100 wt% 3,145.6 0.269 0.372

Soluplus 90 wt% Feonfibrate 10 wt% 747.6 0.010 0.463

Polysytrene 1,174.8 0.034 0.766

Table 1: Material parameters for the Cross-Power-Law

3 SIMULATING ISOTHERMAL FLOW OF A NON-NEWTONIAN FLUID

The geometry of the injection gate was created and meshed using the Pointwise V17R2 program [11]. We applied a mapping scheme for meshing, which means that in our case we had a hexahedral structure throughout the whole system. The geometries of the flow inlet and flow outlet were simplified and the area of the gate was accurately rebuilt. Therefore, it was possible to create the geometry of the injection gate in Pointwise without importing data from other design software. The cells were hexahedral and oriented in the flow direction, since the discretization scheme is typically more accurate on structured grids aligned to the flow. The geometry consisted of a 27 mm long cylindrical melt distributor, followed by a 1 mm long gate and the 6.5 mm long tablet mold. The diameter of the gate changed from 2 mm at the end of the melt channel to 1 mm at the beginning of the tablet.

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For quality control, the maximum skewness was taken into account. At the end of the melt channel, where it connects to the gate, we obtained a maximum skewness value of 1.43, which is acceptable. A cross-section of the 3D mesh decomposition is illustrated in fgure 6.

Figure 6: Mesh decomposition for the fluid simulation: (1) cross-sectional

view; (2) decomposition for mesh study

3.1 Mesh dependency study

In order to know which decomposition of the mesh influences the simulation results (mainly pressure and velocity gradients in filling direction), a mesh study was carried out. This ensures that the velocity gradient is accurately calculated and the results are independent of the mesh used. Table 2 shows the parameters of the three meshes which were designed for the study.

Mesh 1 Mesh 2 Mesh 3

Amount of cells 32745 92391 140047

Cell layers in gate area (flow direction) 3 7 16

Cell layers in runner area (flow direction) 9 21 45

Table 2: Information of the mesh study in OpenFOAM

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Simulations with all the material systems were performed and figure 7 shows the results of the velocity and the kinematic viscosity changes in the gate as a function of the mesh configurations: mesh 1, mesh 2 and mesh 3. Mesh 1 has only 3 cell layers in the flow direction in the gate area. Consequently, the calculation of the velocity gradient is not sufficiently accurate. Furthermore, mesh 2 and mesh 3 already do not have a significant deviation of the velocity profile. Figure 8 shows the error plot of the mesh comparisons. The error between mesh 2 and mesh 3 is no greater than 5% (maximum velocity in gate), but the computational time is disproportionate. More than 25% error was found in the comparison of mesh 1 to mesh 2. As a result of this study, mesh 2 was chosen to further proceed with the investigations in the gate.

Figure 7: Results of the comparison of mesh study for Soluplus 100%wt

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Figure 8: Error comparison (%) of mesh study for Soluplus 100%wt

3.2 Boundary conditions After creating the mesh, we imported it to the OpenFOAM open-source CFD package. OpenFOAM – short for Open source Field Operation and Manipulation – is a C++ toolbox for developing customized numerical solvers for solving continuum problems such as CFD [12]. In our study, we used OpenFOAM version 2.1.1. This program package has the advantage of providing full access to the source code, so solvers can be created or adapted for specific purposes. The simulation parameters and the solver settings can be found in Table 3.

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Boundary Domain Physics Solver settings

Inlet velocity flow 1 30 cm3/s Type Pressure-based

Inlet velocity flow 2 60 cm3/s Time Steady

Inlet velocity flow 3 90 cm3/s

Outlet pressure 0 Pa

Walls Stationary; no slip

Models Materials

Energy equation

solving Off Density

Constant (900 g

/cm)

Model Viscous-laminar Viscosity

model

Cross-Power-

Law

Solution

Solver name simpleFOAM

Pressure-velocity

coupling SIMPLE

Discretization of

momentum

Second order

upwind

Table 3: Boundary conditions for the simulation in OpenFOAM

4 RESULTS AND DISCUSSION

4.1 Residuals of the simulations The residuals in a numeric simulation indicate whether the simulation has reached a converged solution or whether further iterations are necessary [13]. It is possible to compute the residuals of the pressure and of the velocity for each iteration step of the simulation. We investigated the residual plots for all

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material systems and for different injection flow settings and confirmed converged solutions. This ensured the accuracy of the results obtained.

4.2 Comparison of shear rates and wall shear stresses in the gate

The distributions of wall shear stresses and strain rates of the different flows through the gate were determined by simulation using OpenFOAM in order to find their maximum values, figure 9 and 10.

30 60 900

10

20

30

40

50

60

70

80

90

100

110

120

shea

r rat

e [s

-1] x

103

injection flow rate [cm3 s-1] Figure 9: Shear rates (1/s); Soluplus® 100 wt% and Soluplus® 90

wt%-Fenofibrate 10 wt%; Polystyrene; Injection flow rates: 30, 60 and 90 cm3/s

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30 60 90

2

3

200

400

600

800

1000wa

ll she

ar s

tress

[Pa]

x 1

03

injection flow rate [cm3/s] Figure 10: Wall shear stress (Pa); Soluplus® 100 wt%, Soluplus® 90

wt%-Fenofibrate 10 wt% and Polystyrene; Injection flow rates: 30, 60 and 90 cm3/s

The strain rate increases with increasing melt flow rate through the gate for all systems. Further, higher shear rates were found for the Soluplus-Fenofibrate system in comparison to pure Soluplus®, figure 9, which evidences the plasticizing effect of the API on the polymer. Thus, lowering the zero-shear viscosity level led to higher shear rates in the area of the gate. Polystyrene showed the strongest shear rate increase with increasing flow velocity. Chain orientation in the injection flow direction is easier for polystyrene than for Soluplus®, resulting in an improved shear thinning behavior for the former (=polystyrene) system. The results obtained for the wall shear stresses, figure 10f were similar. With higher flow rates, the mechanical impact on the walls around the gate increases. Inlet velocity variations due to geometry changes along the gate also contribute to increased wall shear stresses. Extremely high wall shear stresses were observed for pure Soluplus® (4x103 Pa for �̇�=90 cm3/s) in comparison to the other systems studied. We believe that this may by a direct consequence of the bulky molecular structure of Soluplus®, which hinders the polymer chains in aligning with the flow. However, this effect becomes less pronounced in the presence of the API. Introduction of 10 wt% API led to a reduction in wall shear stresses form 461972 m²/s2 to 114399 m²/s2 at 90 cm3/s injection flow rate, figure 11.

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Figure 11: Comparison of the wall shear stresses at the highest injection flow rate (90 cm3/s) for (a) polystyrene, (b) Soluplus® 90 wt%-Fenofibrate 10 wt%, and (c) Soluplus® 100 wt%

4.3 Dynamic viscosity analysis Injection molding is facilitated when lower levels of dynamic viscosity in the melt can be attained. In Figure 12, it can be seen that the addition of 10 wt% API to Soluplus ® results in a reduction of the dynamic viscosity of the polymer-drug system by 30% for all injection flow rates.

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Figure 12: Dynamic viscosities (m2/s) of the systems investigated (

Soluplus® 100 wt%, Soluplus® 90 wt%-Fenofibrate 10 wt% and Polystyrene)

4.4 Comparison of simulation and analytical-rheological calculation

In order to determine whether the numerical results are in the correct range, we additionally performed analytical calculations. The shear rate was determined using the method of apparent viscosity [14] according to

𝛾 ̇ = 3𝑛+14𝑛

∙ 4 ∙ 𝑄𝜋∙𝑅3

, Equation 6

where R is the radius of the gate, Q is the volume flow rate through the gate and n is the power-law coefficient (n=0.4). As can be seen in Figure 13 and Figure 14, the simulated shear rate values were underpredictions for both systems involving Soluplus®, and underpredictions for polystyrene too, figure 15. The ratios of analytical overprediction of the shear rate for Soluplus® 100 wt and Soluplus® 90 wt%-Fenofibrate 10 wt% are in the same range for all injection flow rates.

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30 60 900

20

40

60

80

100

120

140

160sh

ear r

ate

[1/s

] x10

3

injection flow rate [cm3/s] Figure 13: Comparison of simulation results with analytical results:

Soluplus® 100 wt% numercial, Soluplus® 100 wt% analytical

30 60 900

20

40

60

80

100

120

140

160

shea

r rat

e [1

/s] x

103


Soluplus® 90wt%-Fenofibrate-10wt% numerical, Soluplus® 90wt%-Fenofibrate 10 wt% analytical

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For polystyrene, figure 15, the underprediction is closer to the simulation results. The change of viscosity within the length of the gate leads to a high maximum peak at an injection flow rate, for example, of 15 cm3/s. The analytical calculation takes viscosity changes using the power-law approach into account. No such extreme changes in viscosity occur in the Soluplus systems, figure 16.

30 60 900

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120

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/s] x

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Polystyrene numerical, Polystyrene analytical

Figure 16: Comparison of dynamic viscosity of the Soluplus® 100%wt system

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This analytical validation indicates that the OpenFOAM simulation of shear rates and shear stresses results in underprediction. Possible reasons are:

• High-pressure capillary rheometry may not be a suitable means of characterizing the viscous behaviour of the polymer-API system.

• The Cross-Power-Law may be insufficiently accurate as a material model (influence of temperature is neglected due to isothermal simulations).

• A strong simplification in the simulation model.

• A combination of these errors and others may have occurred. However, the results are within the boundary conditions set for this study. From this point of view, numerical simulations are a good means of gaining insights into the design of injection molds.

5 CONCLUSIONS

This study used open source CFD code to investigate the shear rate conditions in an injection mold gate. We conclude that: • It is possible to investigate the flow conditions using OpenFOAM. The material models provided by the program itself are able to predict shear thinning behavior, but only as a function of shear rate and without considering the relation to pressure and temperature. The models need to be adapted to incorporate such relations. • The largest strain rate occurs next to the cavity inflow. • The velocity levels found there were high, which resulted in high strain rates and low wall shear stresses. We expected this outcome, and recommend taking this into account in the production process in order to prevent jetting situations in the tablet cavity. • The high strain rate peaks in processing must be reduced either by lowering the injection speed or by changing the design of the gate in the mold. At the beginning, a number of important simulation prerequisites, such as the meshing strategy and the quality of the final mesh, need to be considered. In this regard, some improvements in the area of the gate could be achieved. Now that the critical meshing areas are known, a denser cell structure and number of cells as well, can be generated there to yield more accurate results in the future. Another important quality issue is the material data used. The rheological system behavior must be characterized experimentally. Consequently, the final simulation can only deliver results that are within the experimental error range. As part of future work, we intend to perform simulations of a hot-runner gate system and compare them to real-world results. We believe that hot-runner

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systems decrease stress in the polymer-API melt, but the temperature load on the material will increase. Additionally, it will also be important to understand the impact of the shear conditions on the degradation of the polymeric system. We expect this new approach based on open source computational methods to be helpful in designing injection molds for drug delivery systems.

ACKNOWLEDGMENTS

The authors wish to express their thanks to Dr. Koscher (RCPE GmbH) and Dr. Eggenreich (RCPE GmbH) for supplying the material, and to the Austrian Research Fund (FFG) for financial support.

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LITERATURE

[1] Dhirendra, K. Lewis, S. Udupa, N. et al.

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[2] Breitenbach, J.

Melt extrusion: from process to drug delivery technology European Journal of Pharmaceutics and Biopharmaceutics, 54, p. 107-117, 2002 DOI: 10.1016/S0939-6411(02)00061-9

[3] Michaeli, W. Greif,H. Kretzschmar, G. et al.

Technologie des Spritzgießens Carl Hanser Verlag, 2009

[4] Rees, H. Catoen, B.

Selecting Injection Molds Carl Hanser Verlag, 2006 DOI: 10.3139/9783446413023

[5] Juster, H.R. Distlbacher, T. Steinbichler, G.

Investigation of polymer- API systems distribution behavior in the mold during injection molding process by numerical (CFD) methods At: 9th World Meeting on Pharmaceutics, Biopharmaceutics and Pharmaceutical Technology, Lisbon, Portugal, 2014

[6] Kolter, K. Karl, M. Gryczke, A.

Hot-Melt Extrusion with BASF Pharma Polymers BASF SE, 2012

[7] Reintjes,T.

Solubility Enhancement with BASF Pharma Polymers BASF SE, 2011

[8] N,N. Product Information: PS 145D, 800-BC-RESIN (973-426-3923), BASF SE, 2004

[9] Juster, H. R. Steinbichler, G.

Tablets from the Injection Molding Machine: Certain Pharmaceutical Dosage Forms Can Be "Effectively" Injection Molded in a Single Step Kunststoffe International, 4, p. 24 – 28, 2015

[10] Ferziger, J.H. Peric, M.

Computational Methods for Fluid Dynamics Springer Verlag, 2002 DOI: 10.1007/978-3-642-56026-2

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http://ijpsr.com/?action=download_pdf&postid=7733

http://www.sciencedirect.com/science/article/pii/S0939641102000619

http://www.hanser-elibrary.com/doi/book/10.3139/9783446413023

http://link.springer.com/book/10.1007%2F978-3-642-56026-2



[11] Steinbrenner, J. P. Michal, T. Abelanet, J.P.

An Industry Specification for Mesh Generation Software At: AIAA 17th CFD Conference, Toronto, Ontario, 2005; DOI: 10.2514/6.2005-5239

[12] OpenCFD Ltd. ESI Group

User Guide, Version 2.1 OpenFOAM: The Open Source CFD Toolbox, 2012

[13] Schwarze, R. CFD-Modellierung: Grundlagen und Anwendungen bei Strömungsprozessen Springer Verlag, 2013 DOI: 10.1007/978-3-642-24378-3

[14] Macosko, C.W. Rheology: Principles, Measurements, and Applications, Wiley, 1994

Bibliography DOI 10.3139/O999.01052015 Zeitschrift Kunststofftechnik / Journal of Plastics Technology 11 (2015) 5; page 305–327 © Carl Hanser Verlag GmbH & Co. KG ISSN 1864 – 2217

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http://link.springer.com/book/10.1007%2F978-3-642-24378-3



Stichworte: Werkzeugkonstruktion, Darreichungsformen, OpenFOAM Keywords: Mold Design, Drug Delivery Systems, OpenFOAM Autor / author: DI DI Herwig Juster DI Dr. Georg Steinbichler Institut für Polymer-Spritzgießtechnik und Prozessautomatisierung Johannes Kepler Universität Linz Altenbergerstraße 69 4040 Linz, Österreich

E-Mail: [email protected] Webseite: www.jku.at/ipim Tel.: +43 732 / 2468 6601 Fax: +43 732 / 2468 6733

Herausgeber / Editors: Editor-in-Chief Prof. em. Dr.-Ing. Dr. h.c. Gottfried W. Ehrenstein Lehrstuhl für Kunststofftechnik, Universität Erlangen-Nürnberg Phone: +49 (0)9131/85 – 29701; Fax.: +49 (0)9131/85 – 29709, E-Mail: [email protected] Europa / Europe Prof. Dr.-Ing. Dietmar Drummer, verantwortlich Lehrstuhl für Kunststofftechnik Universität Erlangen-Nürnberg Am Weichselgarten 9 91058 Erlangen Deutschland Tel.: +49 (0)9131/85 - 29701 Fax: +49 (0)9131/85 - 29709 E-Mail: [email protected]

Amerika / The Americas Prof. Prof. hon. Dr. Tim A. Osswald, responsible Polymer Engineering Center, Director University of Wisconsin-Madison 1513 University Avenue Madison, WI 53706 USA Tel.: +1/608 263 9538 Fax: +1/608 265 2316 E-Mail: [email protected]

Verlag / Publisher: Carl Hanser Verlag GmbH & Co. KG Wolfgang Beisler Geschäftsführer Kolbergerstraße 22 D-81679 München Tel.: +49 (0)89 99830-0 Fax: +49 (0)89 984809 E-Mail: [email protected]

Redaktion / Editorial Office: Dr.-Ing. Eva Bittmann Christopher Fischer, M.Sc. E-Mail: [email protected] Beirat / Advisory Board: Experten aus Forschung und Industrie, gelistet unter www.kunststofftech.com

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Zeitschrift Kunststofftechnik Journal of Plastics Technology · 2015-09-01 · Juster, Steinbichler...

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