A smoothed particle hydrodynamics study on the electrohydrodynamic deformation of a droplet suspended in a neutrally buoyant Newtonian fluid

Abstract

In this paper, we have presented a 2D Lagrangian two-phase numerical model to study the deformation of a droplet suspended in a quiescent fluid subjected to the combined effects of viscous, surface tension and electric field forces. The electrostatics phenomena are coupled to hydrodynamics through the solution of a set of Maxwell equations. The relevant Maxwell equations and associated interface conditions are simplified relying on the assumptions of the so-called leaky dielectric model. All governing equations and the pertinent jump and boundary conditions are discretized in space using the incompressible Smoothed Particle Hydrodynamics method with improved interface and boundary treatments. Upon imposing constant electrical potentials to upper and lower horizontal boundaries, the droplet starts acquiring either prolate or oblate shape, and shows rather different flow patterns within itself and in its vicinity depending on the ratios of the electrical permittivities and conductivities of the constituent phases. The effects of the strength of the applied electric field, permittivity, surface tension, and the initial droplet radius on the droplet deformation parameter have been investigated in detail. Numerical results are validated by two highly credential analytical results which have been frequently cited in the literature. The numerically and analytically calculated droplet deformation parameters show good agreement for small oblate and prolate deformations. However, for some higher values of the droplet deformation parameter, numerical results overestimate the droplet deformation parameter. This situation was also reported in literature and is due to the assumption made in both theories, which is that the droplet deformation is rather small, and hence the droplet remains almost circular. Moreover, the flow circulations and their corresponding velocities in the inner and outer fluids are in agreement with theories.