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Summary:
Description:From fundamental physical considerations, we have derived a set of partial differential equations describing wetting and spreading. These equations are derived using a variational thermodynamic principle applied to a twocomponent alloy system with three (vapor, liquid and solid) phases. The method naturally includes time dependent chemical interactions between substrate and liquid and also nonclassical (diffuse interface) effects. (The latter are important for applications where the system size approaches nanometer dimensions).
Major Accomplishments:We have implemented a numerical solution scheme to solve these equations and are examining the predictions. Four coupled partial differential equations comprise the model: a mass balance equation, a modified NavierStokes equation for the velocity of the matter in the various phases, a modified diffusion equation for the concentration field, and an equation to treat the dynamics of the solidfluid interface (phase field). Solving this system of coupled equations accurately with appropriate parameters requires sophisticated numerical solution techniques and long simulation times. Our approach thus far has yielded a complete solution of the equations in two dimensions with a slightly nonrealistic parameter set to enable the solution of the equations in a practical time frame. To date we have been able to develop: The first test of the model will be a comparison to simple experiment in a metallurgical context. One such experiment is the spreading of a liquid metal droplet of tin on a bismuth substrate. Here wetting is accompanied by dissolution of the substrate so that the triple junction motion is governed by solute diffusion as well as capillary processes.
A reactive wetting experiment of liquid Bi20 wt%Sn spreading on solid Bi. To date, we cannot match the physical parameters of this experiment in a reasonable computation time, and considerable effort is being devoted to improving our solution methods. However below are shown two time slices from a calculation of the change in shape, composition and accompanying fluid flow pattern when the temperature of a droplet is reduced. The first slice shows the droplet at equilibrium for the high temperature (shown by the black lines). The droplet contracts and dissolves the substrate at a later time and lower temperature. These results show promise for the approach.

Start Date:October 1, 2007End Date:September 30, 2009Lead Organizational Unit:mmlStaff:James Warren Associated Products:Project Summary (PDF) Contact
William J. Boettinger General Information: 100 Bureau Drive, M/S 8554 