Capacitive detection of nanoliter droplets on the fly - investigation of electric field during droplet formation using CFD-simulation

Recently we presented a capacitive droplet sensor that enables the characterization of volume and velocity of dispensed nanoliter liquid droplets on the fly in a contact free manner. In this work we perform a multi-physics simulation study to understand the physical effects behind the sensor signal. We combine a two-phase fluid dynamics model for droplet generation and droplet flight with an electrostatic model for analyzing the electric field distribution inside an open plate capacitor while the droplet is passing through. Beside droplet volume and velocity, also droplet tear-off point as well as droplet oscillations are reflected in the electric field distribution. The characteristic negative dip of the transient sensor signal which was observed in experiments can be explained by capacitive coupling of the liquid column with the sensor and is correctly reflected by the model. The detected changes in charge on the sensor capacitor, are in the range of 2 - 28 fC and correspond to droplet volumes in the range of 5 nl <; V_drop <; 100 nl. This is in good agreement with experimental findings and analytical approximations.