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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 two-component alloy system with three (vapor, liquid and solid) phases. The method naturally includes time dependent chemical interactions between substrate and liquid and also non-classical (diffuse interface) effects. (The latter are important for applications where the system size approaches nanometer dimensions).
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 Navier-Stokes 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 solid-fluid 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 Bi-20 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, 2007
End Date:September 30, 2009
Lead Organizational Unit:mml
Project Summary (PDF)
William J. Boettinger
100 Bureau Drive, M/S 8554