Spreading Law of Evaporative Droplets

Droplet spreading is ubiquitous and plays a significant role in applications such as spray cooling, inkjet printing, and micro-flow devices. While the spreading of non-volatile droplets can be described by the competition between capillary and viscous dissipation, namely the Tanner's law, R(t)~t1/10, the spreading and flow transition in volatile droplets remains elusive due to the complexity added by interfacial phase change. Here we show, using both theoretical modeling and experiments, that the wetting dynamics of volatile droplets can be scaled by the spatial temporal interplay between capillary, evaporation, and thermal Marangoni effects. We quantify these complex interactions using phase diagrams based on detailed theoretical and experimental analyses. We further illustrate the spreading law of droplets by generalizing the Tanner's law to a full range of liquids with saturation vapor pressure spanning from 101 to 104 Pa and on substrates with thermal conductivity spanning from 10-1 to 103W/m/K. Our conclusions enable a unifying explanation to a series of individual works including the criterion of flow reversal and the state of dynamic wetting, making it possible to control liquid transport in diverse application scenarios.