Instability development of a viscous liquid drop impacting a smooth substrate

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 2, 2010, Pages

  Xu, Lei ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

AIR PRESSURES; DIFFERENT MECHANISMS; INSTABILITY DEVELOPMENT; LIQUID VISCOSITY; ONSET-TIME; REAL-TIME DYNAMICS; SMOOTH SUBSTRATES; VISCOUS LIQUID DROP;

ATMOSPHERIC PRESSURE; HIGH SPEED PHOTOGRAPHY; STABILITY; SURFACE TENSION; VISCOSITY OF LIQUIDS;

LIQUIDS;

EID: 77957196118     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.025303     Document Type: Article

References (17)

1. A. L. Yarin, Annu. Rev. Fluid Mech. 38, 159 (2006). 10.1146/annurev. fluid.38.050304.092144
2. C. Mundo, M. Sommerfeld, and C. Tropea, Int. J. Multiphase Flow 21, 151 (1995). 10.1016/0301-9322(94)00069-V
3. R. Rioboo, M. Marengo, and C. Tropea, Atomization Sprays 11, 155 (2001).
4. D. Richard, C. Clanet, and D. Quéré, Nature (London) 417, 811 (2002). 10.1038/417811a
5. N. Z. Mehdizadeh, S. Chandra, and J. Mostaghimi, J. Fluid Mech. 510, 353 (2004). 10.1017/S0022112004009310
6. Tsai, Langmuir 25, 12293 (2009). 10.1021/la900330q
7. R. D. Deegan, P. Brunet, and J. Eggers, Nonlinearity 21, C1 (2008). 10.1088/0951-7715/21/1/C01
8. L. Xu, W. W. Zhang, and S. R. Nagel, Phys. Rev. Lett. 94, 184505 (2005). 10.1103/PhysRevLett.94.184505
9. L. Xu, Phys. Rev. E 75, 056316 (2007). 10.1103/PhysRevE.75.056316
10. S. Mandre, M. Mani, and M. P. Brenner, Phys. Rev. Lett. 102, 134502 (2009). 10.1103/PhysRevLett.102.134502
11. M. Mani, S. Mandre, and M. P. Brenner, J. Fluid Mech. 647, 163 (2010). 10.1017/S0022112009993594
12. R. D. Schroll, C. Josserand, S. Zaleski, and W. W. Zhang, Phys. Rev. Lett. 104, 034504 (2010). 10.1103/PhysRevLett.104.034504
13. S. T. Thoroddsen, J. Fluid Mech. 545, 203 (2005). 10.1017/ S0022112005006919
14. S. T. Thoroddsen, K. Takehara, and T. G. Etoh, Phys. Fluids 22, 051701 (2010). 10.1063/1.3407654
15. We note that Σ μ 1 / t while Σ L 1 / d 1 / √ t. Thus Σ μ always dominates for small t. However, Σ μ decreases more rapidly with t and can drop below Σ L soon after the impact, for the case of small μ. Therefore, Σ L can be dominant for most period of the impact in the inviscid regime.
16. Due to the discreteness of the measured d values, we use the calculated d value at t = t o n from the best fitting function such as the solid line shown in Fig. lower inset.
17. Actually V e also depends on μ. But the dependence is much weaker than √ μ (unpublished data), and qualitatively our argument is not affected. We also note that in Eq., V e cancels out, thus its dependence on μ does not affect the derivation of Eq..