Simulation of droplet detachment from hydrophobic and hydrophilic solid surfaces under the electric field using Lattice Boltzmann Method (LBM)

In this work, the dynamic behaviour of the droplet formation, deformation, breakup, and fragmentation is studied under the influence of the electric field using a potential model and leaky dielectric assumption via the lattice Boltzmann method (LBM). Through a lattice dependency analysis, the size ratio between the droplet and the channel conduit, as well as the lattice dimensions is optimized, by quantifying the changes in the pressure difference and surface tension at the droplet boundary, and variations of instantaneous and terminal Reynolds numbers. Effects of gravitational, surface tension, viscous and electric field forces are also studied in a range of dimensionless numbers: Eotvos number (6 ≤ Eo ≤ 24), capillary number (0 ≤ CaE ≤ 4) and at constant values of Ohnesorge number, conductivity and dielectric constant ratios respectively set to Ohd = 0.07, Rσ = 2 and Sε = 0.5. Hydrophobicity (θd > 90) and hydrophilicity (θd < 90) of the surface versus the positive and negative distinction functions are also taken into consideration. The morphology changes of the droplet into an oblate or prolate shapes under different dielectric constant ratios (0.5 < Sε < 2), and resulting streamlines and velocity vector fields are also investigated. It was shown that the electric field behaves differently under positive or negative distinction functions in terms of preventing or promoting the droplet detachment from the ceiling. Moreover, the balance between Eotvos and capillary numbers at different hydrophobicity and hydrophilicity conditions is discussed on the quality of droplet detachment, deformation, breakup and morphology change. It is also shown that droplet deforms to an oblate or prolate shape at various dielectric ratios. Simulation results also showed an acceptable agreement with the analytical and numerical solutions.