Numerical investigation of electrowetting-based droplet splitting in closed digital microfluidic system: Dynamics, mode, and satellite droplet

Abstract

In this paper, the splitting of microdroplet in a closed electrowetting-based digital microfluidic system has been studied via a numerical model. The governing equations for the fluid flow are solved by a finite volume formulation with a two-step projection method on a fixed computational domain. The free surface of the liquid is tracked by a coupled level-set and volume-of-fluid method, with the surface tension at the free surface computed by continuum surface force scheme. Contact angle hysteresis is implemented as an essential component of electrowetting modeling, and a simplified viscous force model is adopted to evaluate the viscous stress based on the Hele-Shaw model. Excellent agreement has been achieved between the numerical and published experimental results. A parametric study has been performed in which the effects of viscous stress, channel height, static contact angles, contact angle hysteresis, and electrode size on the splitting process have been analyzed. Three distinct splitting modes, which are “splitting with satellite droplet,” “normal splitting,” and “splitting cessation,” have been discussed. Based on the competition between the curvature in the z-direction (κz) and that on the x-y plane (κxy), the physical mechanism that separates the splitting into these three modes has been revealed. More importantly, a dimensionless parameter κ̃ has been proposed, which can be used for (a) determining the splitting mode and (b) estimating satellite droplet volume for electrowetting-induced droplet splitting process.