Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.

A microfluidic dispensing device that is capable of generating droplets with volumes varying between 1 nL and 50 pL at an ejection frequency of up to 6 kHz is presented. In this device, a piezoactuator pushes onto an elastic membrane via piston tips; the mechanical bending of the membrane generates a pressure pulse pushing droplets out. An analytical model was developed solving bending characteristics of a plate-actuated fluidic dispensing system and used to calculate the displaced volume. The model was extended to perform stress analysis to find the optimum piston tip radius by minimizing design stresses. The optimum piston tip radius was found to be 67% of the chamber radius. The actuation force estimated using the analytical model was then used as input to a finite element model of the dispenser. A detailed numerical analysis was then performed to model the fluid flow and droplet ejection process and to find critical geometric and operating parameters. Results from both models were used together to find the best design parameters. The device contains three layers, a silicon layer sandwiched between two polydimethylsiloxane (PDMS) polymer layers. Silicon dry etching, together with PDMS soft lithography, was used to fabricate the chip. PDMS oxygen plasma bonding is used to bond the layers. Prototypes developed were successfully tested to dispense same-sized droplets repeatedly without unwanted droplets. The design allows easy expansion and simultaneous dispensing of fluids.

Modeling of an air-fluid interface in an electric field is presented. Specifically, equilibrium of the interface under the dominant forces-electric stress, surface tension, and pressure-is investigated. Since interface shape and equilibrium are related, the shape of an electrified interface is also addressed. To determine the electric stress, an analytical expression for the electric field in the vicinity of the interface is determined. The operating point of the interface is shown to exist in a three-dimensional parameter space that is divided by a critical surface into equilibrium, quasiequilibrium, and nonequilibrium subdomains. The three parameters are applied voltage, electrode separation, and pressure difference. Interface size, counterelectrode size, and fluid properties are also considered. The subdomain in which the operating point resides defines the important characteristics of the interface. The operating point moves within, and transfers between, equilibrium subdomains, and points on the critical surface represent "rupture points" of the interface. The final shape of the interface is solved iteratively using this equilibrium model. Interfaces emitting an electrospray can have a range of apex angles, and it is shown that the magnitude of this angle impacts equilibrium. It is revealed that the excess pressure difference term is critical in determining the interface shape ͑specifically the cone generatrix͒ and that minimization of the potential energy of all forces can be used to predict the magnitude of the apex angle and pressure immediately after interface rupture. The equilibrium model is important from an operational and optimization perspective, as it is useful to predict the conditions required to break equilibrium and transfer to a quasiequilibrium state ͑i.e., an electrospray͒, and the conditions necessary to maintain quasiequilibrium once it is formed.

Transient modes of an electrified fluid interface are investigated, specifically, (a) intermittent or pulsed cone-jet mode and (b) smooth and abrupt transitions of the interface in response to a step voltage. These modes were studied experimentally by capturing the motion of the interface and measuring the emitted ion current (via electrospray) as they occur. The observed phenomena are described using an analytical model for the equilibrium of an electrified fluid interface, and the effect of operational parameters on the transient modes is discussed. Pressure, which is related to the supplied flow rate, significantly influences the behavior of the transient modes. It is useful to understand transient modes so they can be avoided in applications that require a stable electrospray. However, with improved knowledge, the modes studied here can assist in the development of specialized applications.