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The spreading of volatile liquid droplets on heated surfaces D. M. Andersona) and S. H. Davis

Summary: The spreading of volatile liquid droplets on heated surfaces
D. M. Andersona) and S. H. Davis
Department of Engineering Sciences and Applied Mathematics, Northwestern University Evanston,
Illinois 60208
(Received 6 July 1994; accepted 11 October 1994)
A two-dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered.
Lubrication theory is used to describe the effects of capillarity, thermocapillarity, vapor recoil,
viscous spreading, contact-angle hysteresis, and mass loss on the behavior of the droplet. A new
contact-line condition based on mass balance is formulated and used, which represents a
leading-order superposition of spreading and evaporative effects. Evolution equations for steady and
unsteady droplet profiles are found and solved for small and large capillary numbers. In the steady
evaporation case, the steady contact angle, which represents a balance between viscous spreading
effects and evaporative effects, is larger than the advancing contact angle. This new angle is also
observed over much of the droplet lifetime during unsteady evaporation. Further, in the unsteady
case, effects which tend to decrease (increase) the contact angle promote (delay) evaporation. In the
"large" capillary number limit, matched asymptotics are used to describe the droplet profile; away
from the contact line the shape is determined by initial conditions and bulk mass loss, while near the
contact-line surface curvature and slip are important. 0 1995 American Institute of Physics.
Many processing systems involve trijunctions where


Source: Anderson, Daniel M. - Department of Mathematical Sciences, George Mason University


Collections: Mathematics