The natural breakup length of a steady capillary jet

Despite their fundamental and applied importance, a general model to predict the natural breakup length of steady capillary jets has not been proposed yet. In this work, we derive a scaling law with two universal constants to calculate that length as a function of the liquid properties and operating conditions. These constants are determined by fitting the scaling law to a large set of experimental and numerical measurements, including previously published data. Both the experimental and numerical jet lengths conform remarkably well to the proposed scaling law. This law is explained in terms of the growth of perturbations excited by the jet breakup itself.