In this paper, the problem of a particle subjected to an acoustic field is addressed theoretically. Once the fundamental equation of motion is obtained, two nonlinearities are identified: one related to the drag law and one associated with the excitation. In order to face the nonlinearities, two cases are constructed: the first corresponds to the parametric numerical solution of a particle with nonlinear drag in an oscillating flow field (infinite wavelength) and the second refers to the particle submitted to an acoustic standing wave (finite wavelength). For the latter, an approximated analytical solution is formulated. The system is linearized around an equilibrium point and the parameters of the equation are grouped in three nondimensional numbers: the Stokes number (S t), the acoustic Mach number (M a), and the densities ratio (). Conditions of parametric resonance in the particle response are deduced for this system by means of the analytical method here proposed, based on Hill's determinants. Comparison with numerical solutions of the linearized and nonlinearized equations close to an equilibrium point corroborates the analysis for different combinations of parameters.

Multiple interactions may occur when a poly-disperse spray is exposed to an acoustic field. In the context of spray combustion instabilities, acoustic agglomeration, the formation of a droplet number density wave and the modulation of the droplet size distribution are interesting effects. A droplet number density wave, i.e. preferential concentration of droplets in space, may result from size-dependent, one-way momentum coupling between the acoustic field and the spray. The modulation of the droplet size distribution, which has been evidenced in the experimental work of Gurubaran and Sujith (AIAA 2008-1046), is thus a consequence of the droplet number density wave formation. In the present work, the mechanisms that produce these effects are simulated and analyzed in depth by means of computational fluid dynamics. The spray is modeled with both Lagrangian (particles mass-point approach) and Eulerian (continuous phase approach) descriptions. The particular Eulerian method used is a variant of the presumed density function method of moments, which allows to account for the effects of poly-dispersity, in particular the size-dependence of particle velocity. Both the Lagrangian and Eulerian models are validated against experimental data for spray dynamics and spray response to an acoustic field.