Droplet pattern and condensation gradient around a humidity sink

We describe the evolution of a water drop saturated with NaCl and the growth of pure water droplets in a breath figure pattern (BF) condensing around it. This salty drop acts as a humidity sink, inhibiting the BF inside a ring at a distance r=δ from the sink center and slowing down BF growth outside the ring. The initial salty drop is taken either from a salt-saturated solution (type I experiment) or by placing an NaCl crystal on the substrate (type II experiment). The results are similar, provided that the initial time for type II evolution is taken at the end of the crystal dissolution. The evolution of the salty drop radius R is deduced from the establishment of a three-dimensional hyperbolic concentration profile around the salty drop. This profile scales with r/δ. Accounting for the salt concentration decrease with salty drop growth, R is seen to grow as t5. In the region r>δ, water droplets nucleate and grow. The rate of evolution of the water droplets at constant r/δ can be used to determine the local water pressure. The corresponding data reasonably agree with a hyperbolic water vapor profile around the salty drop. These results can be applied to the growth of BF patterns to determine whether hyperbolic or linear water vapor profiles apply.