Propagation of Acoustic Waves in a Two-Phase Vaporizing Mixture

Nomenclature a; a0 = speeds of sound in the droplet–gas mixture and in the pure gas Cl;C p = speciŽ c heats of liquid and gas d = droplet diameter h = enthalpy per unit mass K = complex wave number, k1 C ik2 k = gas thermal conductivity L = length of the domain lv = latent heat of vaporization Np = droplet number per unit volume of the mixture Pr = Prandtl number p = pressure of the mixture T = temperature t = time u = velocity component in the x direction ®; = spatial coefŽ cients of attenuation and dispersion of acoustic energy ° = speciŽ c heat ratio of gas · = mass ratio of liquid to gas per unit volume of the mixture (loading) 1 = gas dynamic viscosity 1⁄2 = mass concentration (equal to density for the gas) 1⁄2l = droplet density ?u ; ?t ; ?m = dynamic, thermal, and mass exchange response times in the Stokes regime ! = angular frequency