Electrohydrodynamic deformation of a confined droplet in an alternating current electric field: An analytical study

An analytical solution is formulated for the mean and time-periodic deformation of a confined droplet in an alternating current electric field, assuming small deviations from its perfectly spherical shape. The deformation is influenced by the confinement ratio, defined as the ratio of the droplet radius to the radius of the surrounding spherical domain. As the confinement ratio increases, the critical frequency at which the mean deformation becomes zero and the phase difference between the time-periodic deformation and the applied field decrease. This study also examines the effect of confinement on key electrohydrodynamic parameters, including electric potential, free electric surface charge density, normal and tangential electric stress, and fluid flow at the droplet–medium interface. Furthermore, the variation of deformation with frequency and viscosity ratio for a confined droplet is systematically analyzed within this analytical framework. This study introduces a parametric space to fundamentally understand the impact of confinement on droplet electrohydrodynamic deformation in an oscillating electric field. These insights are crucial for the microfluidic manipulation of droplets in micro-confinement.