Time lag in nucleation: A variational treatment of relaxation times in the binary sulfuric acid–water system

A method for evaluating a lower bound to the time required for the establishment of steady state nucleation in binary mixtures of water and sulfuric acid vapors is described. The method is an extension of an earlier approach devised by Reiss and Katz for unary systems, and involves matrix algebra and the Rayleigh–Ritz variation principle. The mathematical development is described at some length. Application to laboratory-type mixtures of H2O and H2 SO4 indicate that times to the steady state may be very long and should seriously impede the measurements of critical supersaturations in both expansion cloud chamber and nozzle experiments.