Electrohydrodynamic jet printing is a highly promising technology for the fabrication of three-dimensional micro/nanoscopic structures, but the advancement of this technology is hindered by the insufficient understanding of many aspects of its mechanisms. Here we conduct a numerical investigation on high-frequency (∼1 kHz) pulsating electrohydrodynamic jet at low electric Bond numbers (${Bo}_e$ = 0.15–0.7). By analyzing the entire jetting process using the voltage distribution, electric charge density, and flow field obtained from the numerical results, we overcome the limitations of experimental approach and demonstrate the influences of electric voltage ($\Phi$ ), nozzle-to-substrate distance ($H$ ), and liquid surface tension coefficient ($\gamma$ ) on the dynamic behaviors and durations of the three jetting stages: (1) cone formation, (2) jetting, and (3) meniscus oscillation. Furthermore, as a measure of the relative significance of the electric force to the surface tension force, the impacts of ${Bo}_e$ on the jetting process are also examined. Results show that some critical aspects of the pulsating jetting process are closely related to ${Bo}_e$ : (1) the transitional values of ${Bo}_e$ between the four observed jetting regimes on the variations of $\Phi$ , $H$ , and $\gamma$ apply to all three parameters; (2) the nondimensionalized Taylor cone length scales with ${Bo}_e$ according to a power law; (3) the jetting processes that have similar ${Bo}_e$ collapse onto a universal profile. These new findings of pulsating electrohydrodynamic jet provide a useful supplement to the currently inadequate comprehension of the complicated electrohydrodynamic jet printing process.

Electrohydrodynamic (EHD) jet printing is a highly effective technique for micro/nanoscale three-dimensional manufacturing. However, due to the complicated electrohydrodynamic mechanisms behind liquid deformation and jet emission, the printing process with remarkable droplet consistency and excellent controllability is still under investigation. In this work, a numerical analysis is conducted on EHD jet printing under constant and step change of electric voltages. We first examine constant-voltage-based pulsating EHD jet printing and explain the impacts of voltage on the regimes, deposited droplet volumes, and durations of the three key printing stages, namely, cone formation, jetting, and jet/meniscus retraction and oscillation. After that, we carry out a comprehensive investigation on EHD jet printing under various step changes of voltages while focusing on the jet behaviors at the voltage switch and after detaching from the Taylor cone. With the assistance of the electric field distribution, interface charge density, velocity fields, and very clear liquid motion images obtained from the numerical data, we fully inspect the pulsed printing processes and elucidate the influences of the pulse time, bias voltage, and peak voltage on the printing behaviors, durations of the three printing stages, and deposited droplet volumes. Finally, based on the obtained results, we make a comparison of the printing outcomes between these two techniques. The findings discovered in this work can be used for advancing the understanding and controlling methods of this complicated but very useful manufacturing technology.

When a charge neutral drop impacts on a flat solid substrate, a small air bubble is always trapped underneath due to the lubrication pressure coming from the viscous stress in the squeezed air film. Herein we find experimentally and numerically that the process of the air entrapment and the initial contact state of the drop with the substrate can be profoundly altered via an external electric field. In an electric field, the induced electric stresses at the bottom of the drop increase drastically right before the drop contacts the substrate, which acts against the lubrication pressure, resulting in reduced initial contact radius and air bubble size. When the external electric field reaches a critical value, the electrical stress accelerates the flow near the bottom of the drop and generates a conical tip quickly instead of a dimple, resulting in a centre contact and eliminating the air bubble entrapment. Based on the dipole mirror charge model, we find the dimensionless strength of critical electric field scales with the square root of capillary number based on the air viscosity. This scaling law of the critical electric field for eliminating the air bubble entrapment is verified experimentally and numerically. This work may offer a new way to mitigate defects caused by air bubble entrapment for inkjet printing and droplet-based additive manufacturing.

The toroidal vortex inside the Taylor cone is one of the most interesting features in electrohydrodynamic (EHD) jet printing. However, due to the considerable difficulty in capturing the microscopic internal fluid flow from the experiment, many aspects of the printing process are still not fully understood. Here we present a numerical study on the Taylor cone formation process of pulsating EHD jet printing under the variations of several key operational parameters and liquid properties, namely electric voltage, nozzle height, liquid surface tension coefficient, dynamic viscosity, and density. Besides the electrohydrodynamic motion of the liquid-gas interface, we focus our attention to the time evolution of the liquid flow and vortex inside the Taylor cone. The intensity of the vortex is evaluated by analyzing the absolute value of the swirling strength throughout the formation process. By virtue of examining the electric field distribution, interface charge density, velocity field, and the absolute value of the swirling strength from the numerical data, we elucidate the influences of the aforementioned parameters on Taylor cone formation and internal flow behaviors. Eventually, a scaling law of |λ²|_max∝Bo_e/Ca² between the absolute value of the maximum swirling strength and the dimensionless variables electric Bond number Boe and Capillary number Ca is proposed, which applies to all the parameters investigated in this work.

In this work, the post-impact drop motions of the rebound regime on inclined hydrophobic surfaces are investigated using a numerical technique. The effects of impact velocity ($V_i$ = 0.5–1.5 m/s), drop diameter ($D_0$ = 1.0–2.5 mm), surface wettability (${\theta }_{eq}$ = 120°–160°), and inclined angle ($\alpha$ = 0°–80°) on the post-impact regimes, contact time ($t_c$ ) and spreading time ($t_s$ ), nondimensionalized maximum spreading diameter (${D_{s\_\text{max}}}^{*}$ ), and drop displacement prior to the rebound ($l_{d\_\mathit{final}}$ ) are examined and analyzed, some of which exhibit markedly different outcomes at $\alpha$ = 80° compared to $\alpha \le$ 60°. It has been discovered that the rebound regime occurs in most impact conditions at ${\theta }_{eq}$ = 160° and 140° but transitions to sliding for all $\alpha$ = 80° cases at ${\theta }_{eq}$ = 120°. When $\alpha \le$ 60°, $t_c$ and $t_s$ of ${\theta }_{eq}$ = 160° and 140° are very close and hardly affected by $V_i$ and $\alpha$ , which are generally smaller than those of $\alpha$ = 80°, resulting from the rapid decline of the normal impact velocity that diminishes drop deformation and prolongs drop sliding motion. ${D_{s\_\text{max}}}^{*}$ is barely influenced by ${\theta }_{eq}$ but increases with $V_i$ and $D_0$ and decreases when $\alpha$ increases owing to a greater normal inertial force. $l_{d\_\mathit{final}}$ generally increases with $V_i$ , $D_0$ , and $\alpha$ but with different mechanisms. More importantly, the nondimensionalized parameters ${t_c}^{*}$ , ${D_{s\_\text{max}}}^{*}$ , and ${l_{d\_\mathit{final}}}^{*}$ are found to scale with the normal or tangential Weber numbers according to the power law, while the exponents vary with ${\theta }_{eq}$ and $\alpha$ .