Electrohydrodynamics of a pair of leaky dielectric droplets on the solid substrate: A lattice Boltzmann study

In this work, the electrohydrodynamics of a pair of leaky dielectric droplets on a solid substrate is investigated by the phase-field-based lattice Boltzmann method. Different from a pair of suspended droplets that may coalesce or separate, two leaky dielectric droplets on the substrate exhibit more complex modes due to the effects of wettability and electric force. The results show that when a horizontal electric field is applied, five different modes with electrostatic attractive force are observed, including attraction without coalescence, attraction with coalescence, coalescence with bubble entrapment, coalescence followed by suspension, and suspension followed by coalescence. Particularly, if the droplets are in a hydrophilic state, the coalescence mode is usually observed, while for droplets in a neutral or hydrophobic state, the permittivity ratio has an important effect on the droplet modes. Additionally, during the coalescence process, two droplets in a hydrophobic state not only capture bubbles, but may also exhibit suspension at a large permittivity ratio or contact angle. On the other hand, when a vertical electric field is applied, there are three different modes with repulsive electrostatic force, including non-coalescence, coalescence, and suspension followed by repulsion. Specially, a small permittivity ratio or a large contact angle can suppress the horizontal deformation of droplets, preventing their coalescence. Moreover, under superhydrophobic conditions, both horizontal and vertical electric fields suspend the droplets. However, the vertical electric field induces repulsion between the suspended droplets, driving them apart, whereas the horizontal electric field promotes their coalescence.