Droplet formation by rapid expansion of a liquid

Molecular dynamics of two- and three-dimensional liquids undergoing a homogeneous adiabatic expansion provides a direct numerical simulation of the atomization process. The Lennard-Jones potential is used with different force cutoff distances; the cluster distributions do not depend strongly on the cutoff parameter. Expansion rates, scaled by the natural molecular time unit (about a picosecond), are investigated from unity down to 0.01; over this range the mean droplet size follows the scaling behavior of an energy balance model which minimizes the sum of kinetic plus surface energy. A second model which equates the elastic stored energy to the surface energy gives better agreement with the simulation results. The simulation results indicate that both the mean and the maximum droplet size have a power-law dependence upon the expansion rate; the exponents are -2d/3 (mean) and -d/2 (maximum), where d is the dimensionality. The mean does not show a dependence upon the system size, whereas the maximum does increase with system size, and furthermore, its exponent increases with an increase in the force cutoff distance. A mean droplet size of 2.8/eta(2), where eta is the expansion rate, describes our high-density three-dimensional simulation results, and this relation is also close to experimental results from the free-jet expansion of liquid helium. Thus, one relation spans a cluster size range from one atom to over 40 million atoms. The structure and temperature of the atomic clusters are described.