Lifshitz–van der Waals forces in aerosol particle collisions. I. Introduction: Water droplets

Abstract

Collision rates among water droplets are computed by the application of results of a current paper which gives a rigorous expression for free-molecular collisions between aerosol particles with a singular, attractive contact potential and the extension of that expression throughout the transition regime via Fuchs’ interpolation method. An expression for the Lifshitz–van der Waals attractive potential recently derived by Kiefer et al. is modified to include a physically motivated, frequency-dependent retardation factor and is used with experimental data for water’s frequency-dependent dielectric susceptibility. This expression is employed in the computation of the ratio of the collision rate incorporating the interaction potential to the collision rate omitting the potential for various pairs of water particles of 1, 10, 100, and 1000 nm radii at 0.1, 1.0, and 10.0 atm. pressures. A graph of this ratio for a pair of 200 nm radius particles as a function of pressure is given and shown to display similar pressure-dependent behavior to recent experimental results by Wagner and Kerker on the coagulation rates of DEHS particles of the same size. This appears to be the first explanation of the systematic deviations near to and beyond experimental error of their experimental data from the predictions of Fuchs’ unmodified formula. The ratio is also calculated by dividing the integral over the electromagnetic frequency spectrum in the van der Waals energy into long and short wavelength parts. This is used to estimate the relative importance of these components upon aerosol particle collision rates. By inference they suggest broader patterns of behavior for other particles. Specifically, an explanation is tendered for the source of the large discrepancy between experimental data taken by Graham and Homer and those authors’ theoretical treatment of their data on the coagulation rates of high temperature, free-molecular regime lead aerosol particles. The spectral decomposition of the collision rates also displays interesting behavior, apparently originating from the retardation damping of the modes, which shows that the frequency dependence of the collision rate enhancement by van der Waals forces is strongly dependent upon size. The role of retardation upon the collision rates is computed and shown to increase from unimportance for 1 nm particles to dominance for 100 nm particles, suggesting the need for further work on computational methods which rigorously incorporate retardation in readily computed van der Waals energy formulas.