Topographical evolution and simulation of SLE-fabricated fused silica surfaces in spray-burner nozzles during chemical etching

Selective laser-induced etching (SLE) enables the fabrication of complex three-dimensional micrometer-precise structures in transparent materials by combining laser modification and chemical etching. While numerical models, such as cellular automata (CA) simulations, have been proven effective in predicting etch front propagation and the use in compensating for loss of components during etching, they do not account for the evolution of surface roughness during etching. In this work, we present a method to incorporate measured surface roughness directly into a CA etching simulation. Using experimentally characterized SLE-surfaces in fused silica, we derive an exponential decay model describing the temporal evolution of surface roughness during KOH etching. This reduction of the surface roughness with etching time is incorporated into the CA rule set by including a surface roughness memory mechanism that propagates along the glass front as etching progresses. The method is then applied to the orifice region of a glass spray-burner nozzle, e.g., for liquid ammonia combustion, fabricated by SLE. Furthermore, the CA simulation couples the surface roughness prediction with form deviation prediction, enabling the identification of compensation strategies for the nozzle orifice diameter for targeted surface roughness values. This interplay between etching-induced geometry changes and surface smoothing provides a pathway towards process-aware design optimization in rapid prototyping of transparent materials.