Intricate Role of Thermal Properties and Volatility in Droplet Spreading: A Generalization to Tanner's Law

Droplet spreading is ubiquitous and plays a significant role in liquid-based energy systems, thermal management devices, and microfluidics. While the spreading of non-volatile droplets is quantitatively understood, the spreading and flow transition in volatile droplets remains elusive due to the complexity added by interfacial phase change and non-equilibrium thermal transport. Here we show, using both mathematical 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 elucidate and quantify these complex interactions using phase diagrams based on systematic theoretical and experimental investigations. A spreading law of evaporative droplets is derived by generalizing Tanner's law (valid for non-volatile liquids) to a full range of liquids with saturation vapor pressure spanning from 10^1 to 10^4 Pa and on substrates with thermal conductivity from 10^{-1} to 10^3 W/m/K. Besides its importance in fluid-based industries, the conclusions also 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.