Direct numerical simulations of electrospinning and electrospraying are computationally demanding due to the large-scale separation between the needle and the tip-to-collector distance. The cone–jet mode that occurs in the vicinity of the needle arises from a delicate balance between surface tension, viscous stresses, inertia, and electric stresses. This mode has a central role in determining the subsequent instabilities of the jet and the eventual outcomes on the collector. Truncated-domain simulations offer a viable alternative but depend critically on the accuracy of far-field electrostatic boundary conditions. Existing truncated-domain approaches based on analytical expressions for the electric potential systematically underestimate the electric field near the needle tip and require empirical tuning informed by prior experiments or full-domain simulations, thereby limiting their predictive capability. Here, we present a general truncated-domain framework for electrohydrodynamic (EHD) simulations of the cone–jet mode that avoids these limitations. Our approach exploits inexpensive full-domain electrostatic simulations to obtain the exact electric field and potential distributions near the needle, which are then imposed as boundary conditions in an EHD simulation carried out on a truncated domain. Comparisons with full-domain EHD simulations and experimental data demonstrate that the proposed approach accurately reproduces cone–jet shapes as well as key physical quantities, including electric currents, charge distributions, velocity fields, and Maxwell stresses, while converging at substantially smaller domain sizes. The formulation eliminates tunable parameters, does not require prior knowledge of the cone–jet configuration, and significantly reduces computational cost, providing a reliable and predictive framework for studying electrohydrodynamic cone–jet flows.
C. et al. (Mon,) studied this question.