Experiments and simulation of the growth of droplets on a surface (breath figures)

Detailed experiments are reported of the growth of droplets when water vapor condenses from a saturated carrier gas onto a hydrophobic plane substrate. We have investigated the effects of the carrier-gas flow velocity, the nature of the gas, the experimental geometry, and heat transfer through the substrate. Individual drops grow according to a power law with exponent μ=1/3. At high flow velocities, the temperature of the substrate can rise significantly, which lowers the condensation rate and leads to lower apparent growth-law exponents. A self-similar regime is reached when droplets interact by coalescences. The coalescences continuously rescale the pattern, produce spatial correlations between the droplets, and accelerate the growth, leading to a power law with an exponent ${\mathrm{\mu }}_0$=3μ. The experiments are compared to predictions of scaling laws and to simulations.