Modeling Reactive Wetting when Inertial Effects are Dominant

TL;DR

This paper develops a diffuse interface model to study inertial-dominated reactive wetting of metal droplets on substrates, revealing a specific spreading rate, oscillations, and dissipation mechanisms consistent with recent experiments.

Contribution

It introduces a thermodynamically derived diffuse interface model capturing inertial effects, oscillations, and dissipation mechanisms in reactive droplet wetting, aligning well with experimental observations.

Findings

Spreading rate follows an $O(t^{-1/2})$ law during inertial regime.

Oscillations occur in triple-line position during transition from inertial to diffusive spreading.

Dissipation mainly occurs at the triple-line during inertial stage and along the solid-liquid interface during diffusive stage.

Abstract

Recent experimental studies of molten metal droplets wetting 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 and spreading on reactive substrates 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 phase field approach. The results from the simulations demonstrate an $O \left( t^{-\nicefrac{1}{2}} \right)$ spreading rate during the inertial regime and oscillations in the triple-line position when the metal droplet transitions from inertial to diffusive spreading. It is found that the spreading extent is reduced by enhancing dissolution by manipulating the initial liquid composition. The results from the model exhibit good qualitative and quantitative agreement with a number of recent experimental studies of high-temperature droplet spreading, particularly experiments of copper droplets spreading on silicon substrates. Analysis of the numerical data from the model suggests that the extent and rate of spreading is regulated by the spreading coefficient calculated from a force balance based on a plausible definition of the instantaneous interface energies. A number of contemporary publications have discussed the likely dissipation mechanism in spreading droplets. Thus, we examine the dissipation mechanism using the entropy-production field and 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.