MATHEMATICAL MODELING OF THROUGH-HOLE-PLATING IN ELECTROCHEMICAL MICROFABRICATION I. AXISYMMETRIC TWO-DIMENSIONAL FLUID FLOW

A mathematical model to simulate the current distribution in a through-hole plating process is developed to account for fluid mechanics, mass transfer mechanism and electrochemical kinetics. The first phase of the study involved the calculation of the flow pattern of a viscous fluid in an axisymmetric through-hole geometry. Numerical calculations were conducted for various degrees of contraction and expansion and for several values of Reynolds numbers. Results indicated that the extend of fluid separation depends linearly on the Reynolds number. The expected adverse pressure gradient during separation was evaluated quantitatively. It was also demonstrated that the axial velocity profile could be approximated satisfactorily by a modified Hagen-Poiseuille distribution with one parameter.