Evaporation of acoustically levitated droplets

The rate of heat and mass transfer at the surface of acoustically levitated pure liquid droplets is predicted theoretically for the case where an acou stic boundary layer appears near the droplet surface resulting in an acoust ic streaming. The theory is based on the computation of the acoustic held a nd squeezed droplet shape by means of the boundary element method developed in Yarin, Pfaffenlehner & Tropea (1998). Given the acoustic field around t he levitated droplet, the acoustic streaming near the droplet surface was c alculated. This allowed calculation of the Sherwood and Nusselt number dist ributions over the droplet surface, as well as their average values. Then, the mass balance was used to calculate the evolution of the equivalent drop let radius in time. The theory is applicable to droplets of arbitrary size relative to the soun d wavelength lambda, including those of the order of lambda, when the compr essible character of the gas how is important. Also, the deformation of the droplets by the acoustic field is accounted for, as well as a displacement of the droplet centre from the pressure node. The effect of the internal c irculation of liquid in the droplet sustained by the acoustic streaming in the gas is estimated. The distribution of the time-average heat and mass tr ansfer rate over the droplet surface is found to have a maximum at the drop let equator and minima at its poles. The time and surface average of the Sh erwood number was shown to be described by the expression Sh = KB/root omeg a D-0, where B = A(0e)/(rho(0)rho(0)) is a scale of the velocity in the sou nd wave (A(0e) is the amplitude of the incident sound wave, rho(0) is the u nperturbed air density, c(0) is the sound velocity in air, omega is the ang ular frequency in the ultrasonic range, D-0 is the mass diffusion coefficie nt of liquid vapour in air, which should be replaced by the thermal diffusi vity of air in the computation of the Nusselt number). The coefficient K de pends on the governing parameters (the acoustic field, the liquid propertie s), as well as on the current equivalent droplet radius a. For small spherical droplets with a << lambda, K = (45/4 pi)(1/2) = 1.89, i f A(0e), is found from the sound pressure level (SPL) defined using A(0e). On the other hand, if A(0e) is found from the same value of the SPL, but de fined using the root-mean-square pressure amplitude (p(rms) = A(0e)/root 2) , then Sh = KrmsBrms/root omega D-0, with B-rms = root 2B and K-rms = K/roo t 2 = 1.336. For large droplets squeezed significantly by the acoustic held , K appears always to be greater than 1.89. The evolution of an evaporating droplet in time is predicted and compared with the present experiments and existing data from the literature. The agreement is found to be rather goo d. We also study and discuss the effect of an additional blowing (a gas jet im pinging on a droplet) on the evaporation rate, as well as the enrichment of gas at the outer boundary of the acoustic boundary layer by liquid vapour. We show that, even at relatively high rates of blowing, the droplet evapor ation is still governed by the acoustic streaming in the relatively strong acoustic fields we use. This makes it impossible to study forced convective heat and mass transfer under the present conditions using droplets levitat ed in strong acoustic fields.