Energy balances applied to electrowetted systems

Wetting between a dielectric liquid and an insulated flat, over-coating a conducting surface, is analyzed using energy balances. The temperature and entropy, the wetted surface area and the interfacial surface energy, the voltage and charge are considered the conjugate pairs of state variables in the system. Reversible, equilibrium mechanics are used to obtain the voltage versus charge relations on lines of isothermal, constant interfacial surface energy. The voltage is generally considered linear with charge, i.e., a linear capacitor for most systems of interest. However, non-linear, charged systems are included in the general energy balances developed. The heat released during charging of an isothermal, aquatic dielectric is shown to be 140% larger than the electrical work in a linear capacitor system at room temperature. The stability of linear systems is studied in quite a bit of detail: it is shown that a parallel plate capacitor whose capacitance changes linearly with wetted surface area is neutrally stable (free energy curvature is zero) at constant voltage and absolutely stable (positive free energy curvature) at constant charge. It is again established experimentally in these systems that the voltage squared is proportional to the interfacial surface energyʹs driving force using charge control. The charge added to the system is proportional to the total wetted surface area so the current is proportional to the areal velocity of the interface. It is experimentally demonstrated that the second derivative of the wetted capacitance versus area is central to stability control for constant voltage systems; controlled wetting for constant charge and voltage systems in electro-capillary lines are investigated in some detail.