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Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations

Published online by Cambridge University Press:  28 March 2007

HANG DING  and
PETER D. M. SPELT
HANG DING
Affiliation:
Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK
PETER D. M. SPELT
Affiliation:
Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK
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Abstract

Axisymmetric droplet spreading is investigated numerically at relatively large rates of spreading, such that inertial effects become important. Results from two numerical methods that use different means to alleviate the stress singularity at moving contact lines (a diffuse interface, and a slip-length-based level-set method) are shown to agree well. An initial inertial regime is observed to yield to a regime associated with Tanner's law at later times. The spreading rate oscillates during the changeover between these regimes. This becomes more significant for a fixed (effective) slip length when decreasing the value of an Ohnesorge number. The initial, inertia-dominated regime is characterized by a rapidly extending region affected by the spreading, giving the appearance of a capillary wave travelling from the contact line. The oscillatory behaviour is associated with the rapid collapse that follows the point at which this region extends to the entire droplet. Results are presented for the apparent contact angle as a function of dimensionless spreading rate for various values of Ohnesorge number, slip length and initial conditions. The results indicate that there is no such universal relation when inertial effects are important.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 287 - 296
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Biance, A.-L., Clanet, C. & Queré, D. 2004 First steps in the spreading of a liquid droplet. Phys. Rev. E 69, 016301.Google ScholarPubMed
Cox, R. G. 1998 Inertial and viscous effects on dynamic contact angles. J. Fluid Mech. 357, 249–278.CrossRefGoogle Scholar
Dussan, V. E. B., 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371–400.CrossRefGoogle Scholar
Eggers, J. & Stone, H. A. 2004 Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle. J. Fluid Mech. 505, 309–321.CrossRefGoogle Scholar
deGennes, P. G. Gennes, P. G. Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827.Google Scholar
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Maths 36, 55–69.CrossRefGoogle Scholar
Hocking, L. M. & Davis, S. H. 2002 Inertial effects in time-dependent motion of thin films. J. Fluid Mech. 467, 1–17.CrossRefGoogle Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.CrossRefGoogle Scholar
Jacqmin, D. 1999 Calculation of two-phase Navier-Stokes flows using phase-field modelling. J. Comput. Phys. 155, 96–127.CrossRefGoogle Scholar
Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57–88.CrossRefGoogle Scholar
Marsh, J. A., Garoff, S. & DussanV., E. B. V., E. B. 1993 Dynamic contact angles and hydrodynamics near a moving contact line. Phys. Rev. Lett. 70, 2778–2781.CrossRefGoogle Scholar
Renardy, M., Renardy, Y. & Li, J. 2001 Numerical simulation of moving contact line problems using a volume-of-fluid method. J. Comput. Phys. 171, 243–263.CrossRefGoogle Scholar
Shikhmurzaev, Y. D. 1997 Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech. 334, 211–249.CrossRefGoogle Scholar
Spelt, P. D. M. 2005 A level-set approach for simulations of flows with multiple moving contact lines with hysteresis. J. Comput. Phys. 207, 389–404.CrossRefGoogle Scholar
Spelt, P. D. M. 2006 Shear flow past two-dimensional droplets pinned or moving on an adhering channel wall at moderate Reynolds numbers: a numerical study. J. Fluid Mech. 561, 439–463.CrossRefGoogle Scholar
Stoev, K., Ramé, E. & Garoff, S. 1999 Effects of inertia on the hydrodynamics near moving contact lines. Phys. Fluids 11, 3209–3216.CrossRefGoogle Scholar
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D 12, 1473–1483.Google Scholar
Villanueva, W. & Amberg, G. 2006 Some generic capillary-driven flows. Intl J. Multiphase Flow 32, 1072–1086.CrossRefGoogle Scholar
Yarin, A. L. 2006 Droplet impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar