Electromechanical model for actuating liquids in a two-plate droplet microfluidic device

Both conducting and insulating liquids can be actuated in two-plate droplet (digital'') microfluidic devices. Droplet movement is accomplished by applying a voltage across electrodes patterned beneath the dielectric-coated top and bottom plates. This report presents a general electromechanical model for calculating the forces on insulating and conducting liquids in two-plate devices. The devices are modeled as an equivalent circuit in which the dielectric layers and ambient medium (air or oil) are described as capacitors, while the liquid being actuated is described as a resistor and capacitor in parallel. The experimental variables are the thickness and dielectric constant of each layer in the device, the gap between plates, the applied voltage and frequency, and the conductivity of the liquid. The model has been used to calculate the total force acting on droplets of liquids that have been studied experimentally, and to explain the relative ease with which liquids of different conductivities can be actuated. The contributions of the electrowetting (EW) and dielectrophoretic (DEP) forces to droplet actuation have also been calculated. While for conductive liquids the EW force dominates, for dielectric liquids, both DEP and EW contribute, and the DEP force may dominate. The general utility of the model is that it can be used to predict the operating conditions needed to actuate particular liquids in devices of known geometry, and to optimize the design and operating conditions to enable movement of virtually any liquid.