Kriging-based multi-objective optimization of bubble path complexity under non-uniform electric fields in vertical channel

This article presents a multi-objective surrogate-based optimization study of electrohydrodynamically (EHD) controlled bubble trajectories in a vertical channel under a non-uniform electric field. This is achieved by coupling a Kriging surrogate model with a genetic algorithm search, building on our previous work. Optimization aims to make a trade-off between the complexity of the bubble trajectory, quantified by the relative path complexity, and the electrical energy input represented by the electric capillary number (CaE). Two parametric frameworks are evaluated: a four-parameter model (electrode length L, inter-electrode gap G, electric capillary number CaE, channel width w) and an extended five-parameter model that additionally includes bubble diameter Db as a design variable. Latin hypercube sampling generates an initial design space, and OpenFOAM-based volume of fluid simulations supply high-fidelity evaluations. The Kriging surrogate is adaptively updated via expected hypervolume improvement, producing a well-resolved Pareto front that spans CaE = 1.0–4.47 in the four-parameter study and CaE = 1.0–3.19 in the five-parameter study. The key findings reframe the design problem, highlighting Db as the most influential parameter in the system. The results confirm that surrogate-assisted optimization serves as a practical and efficient design framework for EHD systems.