dThe accurate prediction of multiphase flow phenomena is associated with high computational costs. Among many different numerical approaches that have been employed to reduce computational resources is the so-called Viscous Potential Theory (VPT) pioneered by D.D. Joseph [Joseph (2006)]. The present method builds on this theory and extends it to include a generalized form of the viscous pressure correction for viscous potential flow, thereby providing more accurate results. In addition, an efficient and accurate numerical algorithm has been developed allowing for the analysis of complex flows with complex boundary conditions. The proposed method is based on a variant of the unsteady Bernoulli equation, which includes the full effect of viscosity through the VPT combined together with a boundary element formulation and a Runge-Kutta scheme to solve the governing equations. The method is currently implemented for two-dimensional (2D) flows and was previously shown to produce comparable results to those from general purpose multiphase simulation methods, such as volume of fluid or smoothed-particle-hydrodynamics, despite the underlying irrotationality assumption of the flow. Here, we use the new method to investigate the performance of a small-scale [microelectromechanical system (MEMS)-type], vibrating 2D slit-nozzle atomizer. Neglecting the edge effects of the discharging planar liquid film, its disintegration into cylindrical ligaments is fully resolved by the present method. To arrive at a droplet size prediction, breakdown of the 2D ligaments into droplets is simply modeled and estimated based on the Rayleigh-Plateau instability. The simulations provide preliminary insight into how frequency and amplitude of the imposed sinuous and/or dilation modulations affect nonlinear film rupture and droplet size distribution in the device.