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Modeling Reactive Wetting when Inertial Effects are Dominant



Daniel Wheeler, James A. Warren, William J. Boettinger


Recent experimental studies of molten metal droplets wetting and spreading on high temperature reactive substrates have established that the majority of triple-line motion occurs when inertial effects are dominant. In light of these studies, this paper investigates wetting, spreading and disolution when inertial effects are dominant using a thermodynamically derived, diffuse interface model of a binary, three-phase material. The liquid-vapor transition is modeled using a van der Waals diffuse interface approach, while the solid-fluid transition is modeled using a traditional phase field approach. The results from the model capture some of the main features of inertial spreading such as the 0 (t(Superscript -1/2) spreading rate and the triple-line oscillations that occur when the metal droplet adjusts from inertial to diffusive spreading. In addition, initial droplet conditions varying between fully saturated and dilute concentrations (within the limits permitted by numerical stability restrictions) are examined and demonstrate that dilute mixtures, which promote dissolution of the substrate, reduce spreading extent and rate. The results from the model exhibit good qualitative and quantitative agreement with a number of recent high temperature experimental studies, particularly experiments of pure and saturated copper on silicon. Analysis of the numerical data suggests that non-equilibrium surface tension evaluations can determine the extent of spreading in the inertial regime and controls the rate of spreading in the diffusive regime via a quasi-equilibrium dynamic contact angle. Furthermore, observations of the entropy production field determine that dissipation primarily occurs in the locality of the triple-line region during the inertial stage, but extends along the solid-liquid interface region during the diffusive stage.
Physical Review B


Wetting, spreading, diffusion, phase field modeling


Wheeler, D. , Warren, J. and Boettinger, W. (2010), Modeling Reactive Wetting when Inertial Effects are Dominant, Physical Review B, [online], (Accessed April 12, 2024)
Created June 30, 2010, Updated March 10, 2020