Fig. 1

Origin, evolution and regulation of two-dimensional (2D) nano-nets during direct electronetting. a Schematic showing the collector inductively coupled direct electronetting strategy. Four designed collectors trigger the assembly of four different architectures. b Competition between the two main forces (Coulomb repulsion F_e and hydrostatic pressure F_γ) on the Taylor cone apex. c Electric field optimization by customizing the collectors in terms of conductivity and configuration. Left, flat conductive collector. Right, concave dielectric collector. d Forces acting on the charged droplet flying across a concave collector. Electrostatic force F_E and air drag F_f. e Profiles of the potential vs distance of electric fields generated using the two collectors in (c). The X- and Y-axis directions are shown using the horizontal and vertical arrows at the left of (c), respectively