DROPLET DISTORTION IN ACCELERATING FLOW

Several commercial instruments size particles based on their acceleration in a highvelocity flow field. Previous work suggested that droplet distortion in these instruments resulted in inaccurate sizing. Liquid aerosol droplet shape distortion produced in an accelerating flow field was therefore computed through analytical solution of the Navier-Stokes equation for comparison to experiment. A high-Reynolds-number empirical approximation to the pressure external to the droplet was used in these calculations. Within the droplet, the longest-lived excitations correspond to a quadrupolar distortion of shape. Droplet excitations were obtained in terms of aerosol diameter, viscosity, surface tension and density. At the largest viscosities considered (as in many oils), only a damped relaxation was found, whereas at lower viscosities and high surface tension (as in water) damped capillary oscillations were predicted as possible, given rapid shifts in the surrounding air flow. In order to compute the effect of airflow varying in time, an approximate Greenʹs function was used. The Greenʹs function in the frequency domain was approximated using only a pair of poles, thereby accounting for only the longest-lived excitations. In application of the theory to compute aerosol distortion on passage through an aerodynamic particle sizer (APS) acceleration nozzle, the change in air velocity was found to be so gradual that no oscillations were induced for droplets as small as 20-µm diameter. Measurements of droplet undersizing in the APS compared favorably with the theoretical predictions. The theoretical results were also consistent with photographs of distorted oleic acid and only slightly distorted water droplets emerging from a nozzle.