DYNAMICS OF THE CONDENSATION OF A SATURATED VAPOR INTO DROPLETS

A fluid-dynamic model of condensation is presented here. Under proper thermodynamic conditions a saturated vapor condenses into tiny droplets. This nonequilibrium process is characterized by a transfer of mass from the vapor to the incipient liquid, a thermal gradient at interface, and a release of heat from the gas to the interface (heat of condensation). These three fundamental physical aspects of the problem are taken into account in the present description. First, the thermal boundary condition for a spherical interface is derived. This surface equation, together with the balance mass equation and the thermal distribution of each bulk phase, results in a first-order nonlinear differential equation. For single noninteracting drops condensing onto a substrate (heterogeneous condensation) the equation predicts an exponent of 1/3 for the time evolution of the droplet radius. But, for an assembly of interacting drops, the power-law exponent changes to one. For the homogeneous case of single noninteracting droplets, the equation gives a power exponent of 1/2 and for an assembly of interacting drops, for small values of time, the radius of the drop grows linearly with time. These results are discussed and compared with experiment.