Skip to main content Accessibility help

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

  • ILIA V. ROISMAN (a1)


This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.


Corresponding author

Email address for correspondence:


Hide All
Amon, C. H., Schmaltz, K. S., Merz, R. & Prinz, F. B. 1996 Numerical and experimental investigation of interface bonding via substrate remelting of an impinging molten metal droplet. J. Heat Trans. 118, 164172.
Attinger, D., Zhao, Z. & Poulikakos, D. 2000 An experimental study of molten microdroplet surface deposition and solidification: transient behaviour and wetting angle dynamics. J. Heat Trans. 122, 544556.
Aziz, S. D. & Chandra, S. 2000 Impact, recoil and splashing of molten metal droplets. Intl J. Heat Mass Trans. 43, 28412857.
Bakshi, S., Roisman, I. V. & Tropea, C. 2007 Investigations on the impact of a drop onto a small spherical target. Phys. Fluids 19, 032102.
Bico, J., Marzolin, C. & Quéré, D. 1999 Pearl drops. Europhys. Lett. 47, 220.
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. Wiley.
Carey, V. P. 2007 Liquid Vapour Phase Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment. Pergamon.
Dhiman, R. & Chandra, S. 2005 Freezing-induced splashing during impact of molten metal droplets with high Weber numbers. Intl J. Heat Mass Trans. 48, 56255638.
Dijksman, J. F. & Pierik, A. 2008 Fluid dynamical analysis of the distribution of ink jet printed biomolecules in microarray substrates for genotyping applications. Biomicrofluidics 2, 044101.
Fauchais, P., Fukumoto, M., Vardelle, A. & Vardelle, M. 2004 Knowledge concerning splat formation: an invited review. J. Therm. Spray Technol. 13 (3), 337360.
Kellay, H. 2005 Impact of drops on a water-covered sand bed: erosion, entrainement and pattern formation. Europhys. Lett. 71 (3), 400406.
Manzello, S. L. & Yang, J. C. 2002 On the collision dynamics of a water droplet containing an additive on a heated solid surface. Proc. R. Soc. Lond. A 458, 24172444.
Miller, D. R., Lynch, J. & Tate, P. A. 2002 Overview of high speed close-up imaging in an icing environment. Tech. Mem. TM 2004-212925. NASA, Paper 2004-0407, Forty-second Aerospace Sciences Meeting and Exhibit, AIAA.
Mock, U., Michel, T., Tropea, C., Roisman, I. V. & Rühe, J. 2005 Drop impact on chemically structured arrays. J. Phys.: Condens. Matter 17, S607S622.
Orme, M. 1993 A novel technique of rapid solidification net-form materials synthesis. J. Mater. Engng Perform. 2 (3), 399405.
Pepper, R. E., Courbin, L. & Stone, H. A. 2008 Splashing on elastic membranes: the importance of early-time dynamics. Phys. Fluids 20, 082103.
Range, K. & Feuillebois, F. 1998 Influence of surface roughness on liquid drop impact. J. Colloid Interface Sci. 203, 1630.
Rein, M. (Ed.) 2000 Drop-Surface Interactions. Springer.
Roisman, I. V. 2009 Inertia dominated drop collisions. Part II. An analytical solution of the Navier–Stokes equations for a spreading viscous film. Phys. Fluids 21, 052104.
Roisman, I. V., Berberović, E. & Tropea, C. 2009 Inertia dominated drop collisions. Part I. On the universal flow in the lamella. Phys. Fluids 21, 052103.
Roisman, I. V. & Tropea, C. 2002 Impact of a drop onto a wetted wall: description of crown formation and propagation. J. Fluid Mech. 472, 373397.
Senda, J., Yamada, K., Fujimoto, H. & Miki, H. 1988 The heat transfer characteristics of a small droplet impinging upon a hot surface. JSME Intl J. II 31, 105111.
Steirer, K. X., Berry, J. J., Reese, M. O., van Hest, M. F. A. M., Miedaner, A., Liberatore, M. W., Collins, R. T. & Ginley, D. S. 2009 Ultrasonically sprayed and inkjet printed thin film electrodes for organic solar cells. Thin Solid Films 517, 27812786.
Tropea, C. & Roisman, I. V. 2005 Droplet breakup and coalescense. In Multiphase Flow Handbook (ed. Crowe, C.), Mechanical Engineering Series, vol. 27, ch. 12.3. CRC Press.
Ukiwe, C. & Kwok, D. Y. 2005 On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21, 666673.
Worster, M. G. 2000 Solidification of fluids. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffat, H. K. & Worster, M. G.), pp. 393446. Cambridge University Press.
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159192.
Yarin, A. L. & Weiss, D. A. 1995 Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J. Fluid Mech. 283, 141173.
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed