Numerical Analysis of an Electroless Plating Problem in Gas–Liquid Two-Phase Flow

Po-Yi Wu,Chengheng Robert Kao,Olivier Pironneau,Po-Shao Shih

doi:10.3390/fluids6110371

Abstract

Electroless plating in micro-channels is a rising technology in industry. In many electroless plating systems, hydrogen gas is generated during the process. A numerical simulation method is proposed and analyzed. At a micrometer scale, the motion of the gaseous phase must be addressed so that the plating works smoothly. Since the bubbles are generated randomly and everywhere, a volume-averaged, two-phase, two-velocity, one pressure-flow model is applied. This fluid system is coupled with a set of convection–diffusion equations for the chemicals subject to flux boundary conditions for electron balance. The moving boundary due to plating is considered. The Galerkin-characteristic finite element method is used for temporal and spatial discretizations; the well-posedness of the numerical scheme is proved. Numerical studies in two dimensions are performed to validate the model against earlier one-dimensional models and a dedicated experiment that has been set up to visualize the distribution of bubbles.

Highlights

The numerical simulation predicts that most bubbles are generated at an early stage and near the inlet
The numerical simulation of electroless plating is difficult for two reasons: multi-phase modeling and nonlinearities
The nonlinearities being similar to those of the Navier–Stokes equations, we have used a semi-Eulerian time discretization leading to a generalized Stokes operator for the two-velocity/one-pressure system; the inf-sup saddle point theorem has lead to a proof of stability and well-posedness of the discretized system by the Hood–Taylor finite element method

Summary

Introduction

Electroless plating is an industrial chemical process aimed at forming a thin film or layer on a base substrate by reducing complex metal cations in a liquid solution [1,2,3]. This technique has been widely applied in various industries. There are several works on the simulation of electroless processes that study the convection or migration of chemical species under a single-phase flow (e.g., [8,9]). For the simulation, we chose a system that includes a gas–liquid two-phase flow, chemical species transport, surface reaction, and moving boundary due to deposition.

Methods

Results

Discussion

Conclusion