A lumped parameter model to describe the electromechanics of mesoscale droplets

Abstract

An understanding of droplet electromechanics will advance the development of droplet-based technologies, such as lab-on-chip platforms, precision additive manufacturing tools, and fluid property sensors. To describe the electromechanics of mesoscale droplets, a simplified mathematical model is derived by treating the droplet as a spring–mass–damper system and validated with finite-element simulation and experiments. Through the model and experiments, the role of fluid properties on droplet electromechanics is investigated using different fluids—with over three orders of magnitude in dynamic viscosity—for a range of actuation voltage amplitudes V¯ and frequencies f. Despite the simplified modeling approach, the lumped model predicts two important droplet characteristic parameters: coalescence time tc and critical electric field Ecr with less than 30% error. Three observations are reported here: (1) applying the scaling laws to the electric field–time E–t relation for E≫Ecr shows that the coalescence time tc is proportional to the droplet length scale characterized in terms of radius r; (2) at lower voltage actuation frequencies f≤ 10 Hz and sub-critical electric fields E≪Ecr, the droplet dynamics is strongly dependent on the surface tension, while at higher voltage actuation frequencies f > 10 Hz, the droplet dynamics is dictated by all the three fluid properties, namely, surface tension, viscosity, and density; and (3) droplets of different fluids exhibit characteristics of a second-order system—validating our approach of modeling the droplet as the spring–mass–damper system.