Skip to main content Accessibility help

Thermocapillary migration of a two-dimensional liquid droplet on a solid surface

  • Marc K. Smith (a1)


A two-dimensional liquid droplet placed on a non-uniformly heated solid surface will move towards the region of colder temperatures if the temperature gradient in the solid surface is large enough. Such behaviour is analysed for a thin viscous droplet using lubrication theory to develop an evolution equation for the shape of the droplet. For the small mobility capillary numbers examined in this work, the contact-line motion is controlled by a dynamic relationship posed between the contact-line speed and the apparent contact angle. Results are obtained numerically and also approximately using a perturbation technique for small heating. The initial spreading or shrinking of the droplet when placed on the heated solid is biased toward the direction of decreasing temperature on the solid. Possible steady-state responses are either a motionless droplet or one moving at a constant velocity down the temperature gradient without change in shape. These behaviours are the result of a thermocapillary recirculation cell inside the droplet that distorts the free surface and alters the apparent contact angles. This change in the apparent contact angles then modifies the contact-line speed.



Hide All
Boyd, J. P. 1989 Chebyshev & Fourier Spectral Methods. Lecture Notes in Engineering, Vol. 49. Springer.
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1990 Steady themocapillary flows of thin liquid layers. II. Experiment. Phys. Fluids A 2, 322333.
Chaudhury, M. K. & Whitesides, G. M. 1992 How to make water run uphill. Science 256, 15391541.
Chen, J. 1988 Experiments on a spreading drop and its contact angle on a solid. J. Colloid Interface Sci. 122, 6072.
Dussan, V. E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371400.
Dussan, V. E. B., Ramé, E. & Garoff, S. 1991 On identifying the appropriate boundary condition at a moving contact line: an experimental investigation. J. Fluid Mech. 230, 97116.
Ehrhard, P. 1993 Experiments on isothermal and non-isothermal spreading. J. Fluid Mech. 257, 463483.
Ehrhard, P. & Davis, S. H. 1991 Non-isothermal spreading of liquid drops on horizontal plates. J. Fluid Mech. 229, 365388.
Gennes, P. G. DE 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.
Greenspan, H. P. 1978 On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125143.
Haley, P. J. & Miksis, M. J. 1991 The effect of the contact line on droplet spreading. J. Fluid Mech. 223, 5781.
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Maths 36, 5569.
Hocking, L. M. 1992 Rival contact-angle models and the spreading of drops. J. Fluid Mech. 239, 671681.
Hocking, L. M. & Rivers, A. D. 1982 The spreading of a drop by capillary action. J. Fluid Mech. 121, 425442.
Marsh, J. A., Garoff, S. & Dussan, V. E. B. 1993 Dynamic contact angles and hydrodynamics near a moving contact line. Phys. Rev. Lett. 70, 27782781.
Ngan, C. G. & Dussan, V. E. B. 1989 On the dynamics of liquid spreading on solid surfaces. J. Fluid Mech. 209, 191226.
Rosenblat, S. & Davis, S. H. 1985 How do liquid drops spread on solids? In Frontiers in Fluid Mechanics (ed. S. H. Davis & J. L. Lumley), pp. 171183. Springer.
Tan, M. J., Bankoff, S. G. & Davis, S. H. 1990 Steady thermocapillary flows of thin liquid layers. I. Theory. Phys. Fluids A 2, 313321.
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 14731484.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

Thermocapillary migration of a two-dimensional liquid droplet on a solid surface

  • Marc K. Smith (a1)


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.