Stability in Film Casting Olena Zavinska Outline Problem

Stability in Film Casting Olena Zavinska

Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

Problem Statement 1. Early Film Breakage 2. Draw Resonance Width Thickness Die Air Gap Web Chill Roll Off-Set

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.

Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

Assumptions • Polymer flow: – Isothermal – Elongational • Inertia, gravity, and surface tension are neglected • Kinematics’ Hypothesis (Silagy) – membrane approximation – 1 D 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.

Governing Equations 5. Kinematics F. S. Condition: 1. Mass Conservation: 4. Stress F. S. condition: 2. Forces: Solving Unknowns 6. Boundary Conditions: 3. Constitutive Eq. : Modeling

Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

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

Solution Procedure Scaled: + inhomogeneous boundary conditions Stationary Solution Method

Step 2: Stationary Solution + inhomogeneous b. c. ’s 1. Shooting method is applied to find the parameter E 2. RK 4 is applied to solve the system, when E is given Solution Method

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

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

Comparison with literature reference NEWTON: Method vs Literature

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

STABLE UNSTABLE LLDPE (eps=0. 1) : Stability Curves

STABLE UNSTABLE LDPE (eps=0. 01) : Stability Curves

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.

Acknowledgment • Angela Sembiring (TU/e) • Hong Xu (TU/e) • Andriy Rychahyvskyy (TU/e) • Jerome Claracq (Dow) • Stef van Eijndhoven (TU/e)