Condensation of saturated vapor on subcooled droplet

Consider the process of condensation of vapor on falling subcooled droplet in the stagnant saturated vapor (neglect the vapor drag on droplet). What can be said about the relation between the droplet diameter and the time for reaching saturation temperature for droplet?

I wanted to build a mathematical model to calcaulte the time versus diameter, but I couldn’t prepare enough heat transfer and dynamical arguments.

Maybe we can discuss the relation without modeling the situation, like using reynolds number, heat transfer coefficient and etc. Please share your ideas.