Theory for shock dynamics in particle-laden thin films

Physical Review Letters

Volumn 94, Issue 11, 2005, Pages

  Zhou, Junjie ^a   Dupuy, B ^a   Bertozzi, A L ^b   Hosoi, A E ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIGITAL CAMERA; FLUID FILMS; LUBRICATION THEORY; SHOCK DYNAMICS;

COMPUTER SIMULATION; CONCENTRATION (PROCESS); FLUID DYNAMICS; LUBRICATION; PARTICLE SIZE ANALYSIS; REYNOLDS NUMBER; SUSPENSIONS (FLUIDS); THERMOANALYSIS; TRANSPORT PROPERTIES;

THIN FILMS;

DRUG;

CHEMISTRY; PARTICLE SIZE; THEORETICAL MODEL;

MODELS, THEORETICAL; PARTICLE SIZE; PHARMACEUTICAL PREPARATIONS;

EID: 18044398982     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.94.117803     Document Type: Article

References (23)

1. T. G. Myers, SIAM Rev. 40, 441 (1998).
2. H. E. Huppert, Nature (London) 300, 427 (1982).
3. S. M. Troian, E. Herbolzheimer, S. A. Safran, and J. F. Joanny, Europhys. Lett. 10, 25 (1989).
4. A. Oron, S. H. Davis, and S. G. Bankoff, Rev. Mod. Phys. 69, 931 (1997).
5. Y. Ye and H.-C. Chang, Phys. Fluids 11, 2494 (1999).
6. L. Kondic and J. Diez, Phys. Fluids 13, 3168 (2001).
7. O. Pouliquen, J. Delour, and S. B. Savage, Nature (London) 386, 816 (1997).
8. S. B. Savage and K. Hutter, J. Fluid Mech. 199, 177 (1989).
9. J. E. Simpson, Gravity Currents in the Environment and the Laboratory (Cambridge University Press, Cambridge, England, 1997), 2nd ed.
10. R. M. Iverson, Rev. Geophys. 35, 245 (1997).
11. R. H. Davis and A. Acrivos, Annu. Rev. Fluid Mech. 17, 91 (1985).
12. L. Xianfan and C. Pozrikidis, Philos. Trans. R. Soc. London A 361, 847 (2003).
13. A. L. Bertozzi, A. Münch, X. Fanton, and A. M. Cazabat, Phys. Rev. Lett. 81, 5169 (1998).
14. J. Sur, A. L. Bertozzi, and R. P. Behringer, Phys. Rev. Lett. 90, 126105 (2003).
15. A. Münch, Phys. Rev. Lett. 91, 016105 (2003).
16. M.F.G. Johnson, R. A. Schluter, M. J. Miksis, and S. G. Bankoff, J. Fluid Mech, 394, 339 (1999).
17. J. M. Jerrett and J. R. de Bruyn, Phys. Fluids A 4, 234 (1992).
18. J. F. Richardson and W. N. Zaki, Trans. Inst. Chem. Eng. 32, 35 (1954).
19. For a single particle settling near a vertical wall, the settling speed correction can be calculated analytically via the method of images [see, e.g., J. Happel and H. Brenner. Low Reynolds Number Hydrodynamics (Prentice-Hall Inc., Englewood Cliffs, NJ, 1965)].
20. J. F. Brady, J. Chem. Phys. 99, 567 (1993).
21. A. L. Bertozzi and M. P. Brenner, Phys. Fluids 9, 530 (1997).
22. max at z = 0 and 0 at z = h. However, we restrict our analysis to the high angle, high concentration regime where the φ = φ(x, t) assumption is valid.
23. P. D. Lax, Hyperbolic Systems of Conservation Laws and Mathematical Theory of Shock Waves, CBMS-NSF Regional Conference Series in Applied Mathematics Vol. 11 (SIAM, Philadelphia, 1973).