A level set methodology for predicting the surface evolution of inclined masked micro-channels resulting from abrasive jet micro-machining at oblique incidence

Abstract

A novel implementation of narrow band level set methods (LSM) was used to predict the surface evolution of inclined masked micro-channels in glass and poly-methyl-methacrylate (PMMA) made using abrasive jet micro-machining (AJM) at oblique incidence. The resulting inclined PMMA channels had straight walls and rectangular bottoms, while the glass profiles had curved walls and rounded bottoms. The inclined micro-channels rapidly become multi-valued, and the Hamilton–Jacobi type partial differential equation describing their evolution cannot be solved using traditional analytical or numerical techniques. To predict the decrease in particle flux at the mask edge, a previously developed analytical model was generalized from the normal to the oblique incidence case. The local surface velocity function was non-convex, necessitating the development of a modified extension velocity methodology to address the problem of grid ‘visibility’ of the particle flux. The agreement between LSM-predicted and measured surface evolution was fair. Since in its current form the model ignores particle ‘second-strike effects’ and mask wear, it is best suited to predict AJM surface evolution in ductile targets where mask wear is minimal, and not for brittle targets (e.g. glass). Since AJM at oblique incidence can be used to machine three-dimensional suspended micro-structures, the work has important implications for the micro-fabrication of novel MEMS and microfluidic devices.