On the mitigation of shock waves by exciting vibrational modes in water droplets

The vibrational energy of water droplets has been investigated. Viscosity was neglected and only the lowest order symmetrical vibration, the quadrupole mode with m=0, was considered. An approximative solution was given by Rayleigh in 1879: w_vib=2a^2 ??r_0?^2 where ? is the relative vibration amplitude, ? is the surface tension, and r0 is the droplet radius at equilibrium, that is the radius of the spherical droplet. It was found that this solution agrees with the exact solution within a few percent for moderate values of the relative amplitude ?. The rationale of this study was to investigate whether dissipation of energy from a shock wave, e.g. from an explosion, into vibrational energy of droplets is a mechanism that needs to be considered on order to accurately model explosion mitigation using water mists. Traditionally droplet vibrations are not considered in such models whereas other mechanisms such as translational energy, heating, evaporation, and droplet breakup are considered. A useful parameter for quantifying the relative importance of vibrations as compared to linear acceleration of droplets is the ratio between vibrational and translational kinetic energy. This ratio is given by 3a^2 ?/(?p?r_0 v?_transl^2 ) where vtransl is the translational velocity to which the droplet has been accelerated by the shock front. This ratio is negligible for a particular severe explosion scenario where information on vtransl was available in the literature. For other cases vibrations might be of some significance but detailed information about the specific scenarios is needed to obtain detailed results. More work is needed in order to understand the effect of viscosity and higher order vibrations. Furthermore a model for the excitation of droplet vibrations by shock waves is required for modelling. Finally there is a lack of experimental knowledge on droplet size distribution for water mist interacting with a shock wave