The optimal tap: three-dimensional nozzle design

Recent years have seen an increased interest in the physics of the generation of small liquid droplets from nozzles, largely motivated by the requirements of high-resolution inkjet printers and general microfluidic applications. Serious limitations on the desired downsizing are imposed by surface tension effects: the pressures encountered during droplet formation are inversely proportional to the length scale and tend to become unfeasibly large. With this in mind, and following upon the recent contribution of Chen and Brenner, we investigate the influence of the design of the micro-sized nozzle on the relationship between the encountered pressures and the volume of the attached droplet. Using numerical surface minimization techniques, we extend the previous work by showing that smaller droplets can be generated by employing nozzles with non-circular boundaries and that a further improvement is achieved by using nozzles with three-dimensional (3D) (i.e. non-planar) boundaries. For example, droplets formed from nozzles with a 3D curvilinear-triangular boundary can be 33% smaller than those formed from circular nozzles at the same maximum pressure.