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**Stability in Film Casting**

Olena Zavinska

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**Outline Problem Statement Project Goal Modeling Solution Method**

Validation Results Conclusions

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**Problem Statement 1. Early Film Breakage 2. Draw Resonance Air Gap**

Width Die Web Chill Roll Off-Set Thickness

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Project Goal Design and implement a method for analysis of stability of the film casting process Determine the tolerance values of system parameters to keep the process stable Reference: Silagy, D. et.al., Study of the Stability of the Film Casting Process, Polymer Engineering and Science, 36, no.21, 1996.

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**Outline Modeling Problem Statement Project Goal Solution Method**

Validation Results Conclusions

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**Assumptions Polymer flow: Isothermal Elongational**

Inertia, gravity, and surface tension are neglected Kinematics’ Hypothesis (Silagy) membrane approximation 1D model Coordinates (x,y,z) Width (L) Thickness (e) Velocity (u) Length (X) Reference: Silagy, D. et.al., Study of the Stability of the Film Casting Process, Polymer Engineering and Science, 36, no.21, 1996.

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**Governing Equations Solving Unknowns Modeling 1. Mass Conservation:**

2. Forces: 3. Constitutive Eq.: 5. Kinematics F.S. Condition: 4. Stress F.S. condition: 6. Boundary Conditions: Solving Unknowns Modeling

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**Outline Solution Method Problem Statement Project Goal Modeling**

Validation Results Conclusions

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**Step 1: Scaling Solution Method 1. Unknown Variables:**

2. Independent Variables: 3. Unknown Parameter: 4. Input Parameters: Solution Method

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**Solution Procedure Scaled: Stationary Solution Method**

+ inhomogeneous boundary conditions Solution Method

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**Step 2: Stationary Solution**

+ inhomogeneous b.c.’s 1. Shooting method is applied to find the parameter E 2. RK4 is applied to solve the system, when E is given Solution Method

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**Step 3: Dynamic Solution**

+ homogeneous b.c.’s Parameter indicates instability - process is stable - process is unstable Solution Method

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**Validation (Newtonian model)**

Outline Problem Statement Project Goal Modeling Solution Method Validation (Newtonian model) Results Conclusions

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**Comparison with literature reference**

NEWTON: Method vs Literature

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**Outline Results (PTT model) Problem Statement Project Goal Modeling**

Solution Method Validation Results (PTT model) Conclusions

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STABLE UNSTABLE LLDPE (eps=0.1) : Stability Curves

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STABLE UNSTABLE LDPE (eps=0.01) : Stability Curves

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Conclusions A numerical algorithm for the resolution of linear stability analysis was developed It shows excellent performance (precision, low calculation time) The material rheological model explains the stabilization effect of LDPE The algorithm can be applied to other similarly mathematical described processes.

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**Acknowledgment Angela Sembiring (TU/e) Hong Xu (TU/e)**

Andriy Rychahyvskyy (TU/e) Jerome Claracq (Dow) Stef van Eijndhoven (TU/e)

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