Langmuir, Vol.9, No.12, 3724-3727, 1993
The Aging of a Liquid-Drop
The aging of a liquid drop is made evident when any surface property, eg. surface tension, surface density, or surface concentration, is modified in the course of time. In the present study, the diffusion of solute inside the drop will be considered the only agent which produces these changes. The surface mass conservation law is derived in spherical geometry. This law links the time variation of the surface mass density with the gradient of the solute concentration in the drop. The solute concentration inside the drop is found by solving the diffusion equation; in the gas phase, the solute concentration is assumed to be constant. In the dilute case, the surface density changes with time following an integrodifferential equation of Volterra type. The solution of this equation, obtained as a Fourier series, together with a two-dimension equation of state, makes it possible to find the surface tension variation with time. The present result is compared with those obtained for a plane interface in refs 1 and 3. While the latter works predict a diminution proportional to t1/2 and t, respectively, the present model indicates an exponential decay of surface tension with time. Also the theory is tested with experimental dynamic measurement obtained by the pendant-drop technique and with data gathered from the oscillating jet method.