This paper describes a sample digitization method that generates tens of thousands of nanoliter-sized droplets in a high-density array in a matter of minutes. We show that the sample digitization depends on both the geometric design of the microfluidic device and the viscoelastic forces between the aqueous sample and a continuous oil phase. Our design avoids sample loss: Samples are split into tens of thousands of discreet volumes with close to 100% efficiency without the need for any expensive valving or pumping systems. We envision this technology will have broad applications that require simple sample digitization within minutes, such as digital polymerase chain reactions and single-cell studies.