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Stability in Film Casting Olena Zavinska

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Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions Outline

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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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Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions Outline

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Assumptions Velocity (u)Velocity (u) Length (X)Length (X) Polymer flow:Polymer flow: –Isothermal –Elongational Inertia, gravity, and surface tension are neglectedInertia, gravity, and surface tension are neglected Kinematics Hypothesis (Silagy)Kinematics Hypothesis (Silagy) –membrane approximation –1D model Coordinates (x,y,z)Coordinates (x,y,z) Width (L)Width (L) Thickness (e)Thickness (e) Reference: 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 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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Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions Outline

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Step 1: Scaling Solution Method 1. Unknown Variables: 2. Independent Variables: 4. Input Parameters: 3. Unknown Parameter:

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Solution Procedure Solution Method Scaled: Stationary + inhomogeneous boundary conditions

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

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Step 3: Dynamic Solution Solution Method + homogeneous b.c.s Parameter - indicates instability - process is stable - process is unstable

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

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Comparison with literature reference NEWTON: Method vs Literature

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

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LLDPE (eps=0.1) : Stability Curves STABLE UNSTABLE

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LDPE (eps=0.01) : Stability Curves STABLE UNSTABLE

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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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