600 Electrowetting and hence a reduced flow rate in the pressure-drop direc- tion. This reduced flow rate seems to suggest that the liquid have an apparent higher viscosity. The apparent viscosity is called the electro-viscosity. Cross References  Streaming Current and Electroviscosity Electrowetting LESLIE YEO 1 ,HSUEH-CHIA CHANG 2 1 Micro/Nanophysics Research Laboratory Department of Mechanical Engineering, Monash University, Clayton, VIC, Australia 2 Center for Microfluidics and Medical Diagnostics Department of Chemical & Biomolecular Engineering, University of Notre Dame, Notre Dame, IN, USA leslie.yeo@eng.monash.edu.au Synonyms Electrocapillary effect; Electrowetting on dielectric (EWOD); Electrowetting on insulator coated electrodes (EICE); Electrowetting on line electrodes (ELE) Definition Electrowetting concerns the use of an externally applied electric field to actuate or manipulate small volumes of liq- uid by altering its interfacial tension and hence the macro- scopic contact angle or by inducing bulk liquid motion through an interfacial electric stress. Chemical and Physical Principles Electrowetting derives its roots from early observations of electrocapillary phenomena by Gabriel Lippmann in 1875, who noted variations in interfacial tension as an electric potential is applied between an electrolyte solu- tion in direct contact with a metal, in this case, mercury. This culminated in the classical Lippmann equation: ∂γ ∂ V     T,p,μ = - CV A , (1) where γ is the interfacial tension (between the metal and electrolyte), V the applied potential, T the temperature, p the pressure and μ the chemical potential. The right hand side of Eq. (1) is the surface charge density, where C is the capacitance with cross sectional area A and separation d. Since C = ε 0 ε l A/d, where ε 0 is the permittivity of free space and ε l the liquid dielectric constant, Eq. ( 1) can be written as γ = - ε 0 ε l 2d V 2 . (2) The term on the right hand side of Eq. ( 2) is hence the electrocapillary force per unit length (linear force density) in the solid plane along the contact line. Strictly, the term electrocapillarity therefore refers to the change in the solid or liquid metal–electrolyte interfacial tension, as shown in Fig. 1a. For the principle to be prac- tical, however, it was necessary to avoid electrolysis of the aqueous solution. This was later overcome by coating the electrode surface with a thin dielectric layer (e. g., poly- mer substrate) several microns to millimeters in thickness, from which the term electrowetting-on-dielectric (EWOD) or electrowetting on insulator coated electrodes (EICE) arises [1], as shown in Figs. 1b and 1c. In cases where the insulating layer is not hydrophobic (e. g., parylene), a very thin hydrophobic layer such as a fluoropolymer of order nanometers in thickness, is coated onto the insulator. In general, the term electrowetting, at least for EWOD or EICE configurations in which spontaneous spreading does not occur and hence the contact angles are static (we shall deal with the case of spontaneous electrowetting below), has traditionally been associated with the change in the macroscopic liquid–solid wetting angle θ subtended at the three-phase contact line where the vapor, liquid and solid phases converge [ 2]. Henceforth, we shall delineate the distinction between static and spontaneous electrowetting . A force balance at the contact line (Fig. 2) yields Young’s equation, γ LV cos θ = γ SV - γ SL , (3) where γ LV , γ SV and γ SL are the vapor–liquid, vapor–solid and liquid–solid interfacial tensions, respectively. Substi- tuting Eq. (3) into Eq. (1) with γ = γ SL gives d cos θ V dV = C γ LV , (4) which then leads to the equivalent Lippmann condition for electrowetting: cos θ = cos θ 0 + ε 0 ε l V 2 2dγ LV , (5) where θ 0 is the contact angle in the absence of an electric field. The electric field has changed the vapor–liquid sur- face force and hence altered the static contact angle when all three surface forces balance.