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A MODEL FOR A SPREADING AND MELTING DROPLET ON A HEATED SUBSTRATE
 

Summary: A MODEL FOR A SPREADING AND MELTING DROPLET
ON A HEATED SUBSTRATE
D. M. ANDERSON, M. G. FOREST, AND R. SUPERFINE§
SIAM J. APPL. MATH. c 2001 Society for Industrial and Applied Mathematics
Vol. 61, No. 5, pp. 1502­1525
Abstract. We develop a model to describe the dynamics of a spreading and melting droplet on
a heated substrate. The model, developed in the capillary-dominated limit, is geometrical in nature
and couples the contact line, trijunction, and phase-change dynamics. The competition between
spreading and melting is characterized by a single parameter KT that represents the ratio of the
characteristic contact line velocity to the characteristic melting (or phase-change) velocity. A key
component of the model is an equation of motion for the solid. This equation of motion, which
accounts for global effects through a balance of forces over the entire solid­liquid interface, including
capillary effects at the trijunction, acts in a natural way as the trijunction condition. This is in
contrast to models of trijunction dynamics during solidification, where it is common to specify a
trijunction condition based on local physics alone. The trijunction dynamics, as well as the contact
angle, contact line position, and other dynamic quantities for the spreading and melting droplet, are
predicted by the model and are compared to an isothermally spreading liquid droplet whose dynamics
are controlled exclusively by the contact line. We find that in general the differences between the
dynamics of a spreading and melting droplet and that of an isothermally spreading droplet increase
as KT increases. We observe that the presence of the solid phase in the spreading and melting

  

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

 

Collections: Mathematics