The spreading of volatile liquid droplets on heated surfaces

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Abstract
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.