Analysis of an Electroless Plating Problem

Vivette Girault (1) , Olivier Pironneau (1) , Po-Yi Wu (2, 3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 NTU - National Taiwan University [Taiwan]

Electroless plating in microfluidic channels is a novel technology at the micrometer scale. As the microchannel depth varies with the flow of the chemicals, care must be taken for the channel not to run dry. Owing to the deposited chemical species the physical domain of the flow changes with time, leading to a free boundary problem. As the motion of the free boundary is small it is modeled by a transpiration approximation. With this simplification, the mathematical model, consists of a Navier-Stokes flow and an equation for the concentration of the plating chemical coupled by non standard and nonlinear boundary conditions. Existence and uniqueness are proven for the concentration equation. Numerical analysis is carried out and justifies the proposed numerical schemes and nonlinear algorithms. A numerical study is performed, in the two dimensional case, with the finite element method and an implicit Euler time-scheme.

Mots clés: Electroless process; Free boundary; Finite Element Method

Domaines: Analyse numérique [cs.NA]; Génie chimique

Vivette Girault, Olivier Pironneau, Po-Yi Wu. Analysis of an Electroless Plating Problem. 2019. ⟨hal-02361746⟩