Dynamics of Spherical Bubble Growth

Abstract

A model for the dynamics of spherical bubble growth in a quiescent viscous liquid is presented. The gas inside the bubble is a van der Waals fluid, and the viscous liquid outside the bubble is a Flory–Hugins solvent–polymer solution. The growth of the bubble in the viscous liquid is assumed to be controlled by momentum, heat and mass transfer. Using the integral method, the transport equations were transformed into ordinary differential equations, which were numerically solved. An analytical criterion of when it is justified to make the usual isothermal assumption is also derived. The relevance of this work to the processes of polymer melt devolatilization and the production of foamed plastics is discussed.

Get full access to this article

View all access options for this article.

References

1. Albalak, R. J. (Ed.) (1996). Polymer Devolatilization, Marcel Dekker, New York NY.

2. Lee, S.-T. (Ed.) (2000). Foam Extrusion, Technomic Publishing Co., Inc., Lancaster, PA.

3. Barlow, E. J. and Langlois, W. E. (1962). IBM J. Res. Dev., 6: 329–337.

4. Patel, R. D. (1980). Chem. Eng. Sci., 35: 2352–2356.

5. Han, C. D. and Yoo, H. J. (1981). Polym. Eng. Sci., 21: 518–533.

6. Yoo, H. J. and Han, C. D. (1982). AIChE J., 28:1002–1009.

7. Amon, M. and Denson, C. D. (1984). Polym. Eng. Sci., 24: 1026–1034.

8. Arefmanesh, A. , Advani, S. G. and Michaelides, E. E. (1990). Polym. Eng. Sci., 30: 1330–1337.

9. Arefmanesh, A. and Advani, S. G. (1991). Rheol. Acta, 30: 274–283.

10.

10. Ramesh, N. S. , Rasmussen, D. H. and Campbell, G. A. (1991). Polym. Eng. Sci., 31: 1657–1664.

11.

11. Arefmanesh, A. , Advani, S. G. and Michaelides, E. E. (1992). Int. J. Heat Mass Trans., 35: 1711–1722.

12.

12. Goel, S. K. and Beckman, E. J. (1994). Polym. Eng. Sci., 34: 1148–1156.

13.

13. Shafi, M. A. , Lee, J. G. and Flumerfelt, R. W. (1996). Polym. Eng. Sci., 36: 1950–1959.

14.

14. Shafi, M. A. and Flumerfelt, R. W. (1997). Chem. Eng. Sci., 52: 627–633.

15.

15. Shafi, M. A. , Joshi, K. and Flumerfelt, R. W. (1997). Chem. Eng. Sci., 52: 635–644.

16.

16. Venerus, D. C. and Yala, N. (1997). AIChE J., 43: 2948–2959.

17.

17. Kwak, H. Y. and Kim, Y. W. (1998). Int. J. Heat Mass Trans., 41: 757–767.

18.

18. Venerus, D. C. , Yala, N. and Bernstein, B. (1998). J. Non-New. Fluid Mech., 75: 55–75.

19.

19. Vrentas, J. S. and Vrentas, C. M. (1998). J. Appl. Polym. Sci., 67: 2093–2103.

20.

20. Ramesh, N. S. and Malwitz, N. (1999). J. Cell. Plas., 35: 199–209.

21.

21. Favelukis, M. , Zhang, Z. and Pai, V. (2000). Polym. Eng. Sci., 40: 1350–1359.

22.

22. Upadhyay, R. K. (1985). Adv. Polym. Tech., 5: 55–64.

23.

23. Arefmanesh, A. and Advani, S. G. (1995). Polym. Eng. Sci., 35: 252–260.

24.

24. Lee, S. T. , Ramesh, N. S. and Campbell, G. A. (1996). Polym. Eng. Sci., 36: 2477–2482.

25.

25. Street, J. R. , Fricke, A. L. and Reiss, L. P. (1971). Ind. Eng. Chem. Fund., 10: 54–64.

26.

26. Powell, K. G. and Denson, C. D. (1983). AIChE Ann. Meet.

27.

27. Tukachinsky, A. , Talmon, Y. and Tadmor, Z. (1994). AIChE J., 40: 670–675.

28.

28. Rosner, D. E. and Epstein, M. (1972). Chem. Eng. Sci., 27: 69–88.

29.

29. Pai, V. and Favelukis, M. (2000). SPE ANTEC 2000, 1: 518–522.

30.

30. Favelukis, M. and Albalak, R. J. (1996). In: Albalak, R. J. (Ed.), Polymer Devolatilization, Marcel Dekker, New York NY.

31.

31. Scriven, L. E. (1959). Chem. Eng. Sci., 10: 1–13.

32.

32. Wall, F. T. (1958). Chemical Thermodynamics–A Course Study, W.H. Freeman and Company, San-Francisco CA.