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Understanding the kinematics and dynamics of spreading, pinching, andcoalescence of drops is critically important for a diverse range ofapplications involving spraying, printing, coating, dispensing, emulsification,and atomization. Hence experimental studies visualize and characterize theincrease in size over time for drops spreading over substrates, or liquidbridges between coalescing drops, or the decrease in the radius of pinchingnecks during drop formation. Even for Newtonian fluids, the interplay ofinertial, viscous, and capillary stresses can lead to a number of scaling laws,with three limiting self-similar cases: visco-inertial (VI), visco-capillary(VC) and inertio-capillary (IC). Though experiments are presented as examplesof the methods of dimensional analysis, the lack of precise values or estimatesfor pre-factors, transitions, and scaling exponents presents difficulties forquantitative analysis and material characterization. In this tutorial review,we reanalyze and summarize an elaborate set of landmark published experimentalstudies on a wide range of Newtonian fluids. We show that moving beyond VI, VC,and IC units in favor of intrinsic timescale and lengthscale determined by allthree material properties (viscosity, surface tension and density), creates acomplementary system that we call the Ohnesorge units. We find that in spite oflarge differences in topological features, timescales, and material properties,the analysis of spreading, pinching and coalescing drops in the Ohnesorge unitsresults in a remarkable collapse of the experimental datasets, highlighting theshared and universal features displayed in such flows.

Spreading, pinching, and coalescence: the Ohnesorge units