1. Stability in Film Casting
Olena Zavinska

2. Outline Problem Statement Project Goal Modeling Solution Method
Validation
Results
Conclusions

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

4. 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.

5. Outline Modeling Problem Statement Project Goal Solution Method
Validation
Results
Conclusions

6. 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.

7. 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

8. Outline Solution Method Problem Statement Project Goal Modeling
Validation
Results
Conclusions

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

10. Solution Procedure Scaled: Stationary Solution Method
+ inhomogeneous boundary conditions
Solution Method

11. 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

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

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

14. Comparison with literature reference
NEWTON: Method vs Literature

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

16. STABLE
UNSTABLE
LLDPE (eps=0.1) : Stability Curves

17. STABLE
UNSTABLE
LDPE (eps=0.01) : Stability Curves

18. 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.

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

20. the end