Study of Path Selection of a Droplet in a Symmetric Y-Microchannel Using a Uniform Electric Field

The droplet dynamics in a symmetric bifurcating Y-microchannel under the influence of a direct current (DC) electric field imposed across only one daughter channel are investigated. The interface of the droplet has been captured using Cahn–Hilliard equation, while the effect of electric force at the droplet interface has been incorporated by modelling it as a body force term in the momentum equation. Two different sorting behaviours of the droplet have been observed depending on the relative permittivity ratio ( \(\varepsilon_{{\text{r}}}\) ) of the droplet and carrier fluid and the choice of daughter channel where electric field is imposed. The droplet chooses the path of the channel where the electric field is applied if its permittivity is higher than that of the carrier fluid. The reverse phenomenon is seen to take place when droplet electrical permittivity is lower than that of the carrier. Furthermore, it is also observed that by altering the intensity of the electric field, it is possible to accurately regulate the daughter droplet breakup ratio in a Y junction and reach droplet of any size. We have also identified a critical electric Capillary number (Cae) at which the droplet completely transcends from breakup to no-breakup regime and gets sorted in any one branch channel depending on \(\varepsilon_{{\text{r}}}\) and the branch channel where the electric field is imposed. The increase in Cae beyond its critical value doesn’t affect the no-breakup regime but increases droplet velocity and facilitates a bit faster sorting than the previous droplet.