Evaporation of acoustically levitated droplets

Abstract

The rate of heat and mass transfer at the surface of acoustically levitated pure liquid droplets is predicted theoretically for the case where an acoustic boundary layer appears near the droplet surface resulting in an acoustic streaming. The theory is based on the computation of the acoustic field and squeezed droplet shape by means of the boundary element method developed in Yarin, Pfaffenlehner & Tropea (1998). Given the acoustic field around the levitated droplet, the acoustic streaming near the droplet surface was calculated. This allowed calculation of the Sherwood and Nusselt number distributions over the droplet surface, as well as their average values. Then, the mass balance was used to calculate the evolution of the equivalent droplet radius in time.

The theory is applicable to droplets of arbitrary size relative to the sound wavelength λ, including those of the order of λ, when the compressible character of the gas flow 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 circulation of liquid in the droplet sustained by the acoustic streaming in the gas is estimated. The distribution of the time-average heat and mass transfer rate over the droplet surface is found to have a maximum at the droplet equator and minima at its poles. The time and surface average of the Sherwood number was shown to be described by the expression Sh = KB/√ω[Dscr ]₀, where B = A_0e/(ρ₀c₀) is a scale of the velocity in the sound wave (A_0e is the amplitude of the incident sound wave, ρ₀ is the unperturbed air density, c₀ is the sound velocity in air, ω is the angular frequency in the ultrasonic range, [Dscr ]₀ is the mass diffusion coefficient of liquid vapour in air, which should be replaced by the thermal diffusivity of air in the computation of the Nusselt number). The coefficient K depends on the governing parameters (the acoustic field, the liquid properties), as well as on the current equivalent droplet radius a.

For small spherical droplets with a[Lt ]λ, K = (45/4π)^1/2 = 1.89, if 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 defined using the root-mean-square pressure amplitude (p_rms = A_0e/√2), then Sh = K_rmsB_rms/ √ω[Dscr ]₀, with B_rms = √2B and K_rms = K/√2 = 1.336. For large droplets squeezed significantly by the acoustic field, 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 good.

We also study and discuss the effect of an additional blowing (a gas jet impinging on a droplet) on the evaporation rate, as well as the enrichment of gas at the outer boundary of the acoustic bondary layer by liquid vapour. We show that, even at relatively high rates of blowing, the droplet evaporation 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 levitated in strong acoustic fields.