This paper takes the advantage of the elemental enriched finite element method to provide a comprehensive analysis of the factors influencing the electrohydrodynamics of droplets confined within microspaces. Specifically, the impact of electrical property ratios (permittivity and conductivity) and eccentricities along the x- and y-axes on droplet deformation is investigated. A critical confinement size is revealed based on the findings of the paper: below this threshold, droplet deformation exhibits a transition, in contrast to the observations made in unbounded domains. Furthermore, the numerical results demonstrate a strong deformation dependence on both the electrical properties ratios and the confinement ratio itself. It is found that the deformation parameter shows a monotonic decrease as the conductivity ratio increases relative to the permittivity ratio. The study further reveals that droplet location within the domain plays a crucial role. When centered, pressure forces become relevant at high confinement ratios, primarily affecting prolate droplets, while electric forces dominate the shaping of oblate droplets. For off-center droplets (with geometric eccentricity), the pressure force becomes even more critical.

"This work was performed in the framework of the DIDRO project (Towards establishing a Digital twin for manufacturing via drop-on-demand inkjet printing, Proyectos Estratégicos Orientados a la Transición Ecológica y a la Transición Digital 2022-2024, reference TED2021–130471B-I00) financed by Ministry of Spain MCIN/AEI 10.13039/501100011033 and by European Union Next GenerationEU/ PRTR, and DECIMA project, PID2022–137472OBI00 financed by MCIN/AEI/10.13039/501100011033/ FEDER, UE. The work of C. Narvaez-Muñoz was supported by the “Severo Ochoa Scholarship” Reference: PRE2020–096632, granted by the above-mentioned Ministry."

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1140/epjs/s11734-025-01683-z

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