Effect of acoustic streaming on the mass transfer from a sublimating sphere

Abstract

The effect of the acoustic streaming on the mass transfer from the surface of a sphere positioned in an ultrasonic acoustic levitator is studied both experimentally and theoretically. Acoustic levitation using standing ultrasonic waves is an experimental tool for studying the heat and mass transfer from small solid or liquid samples, because it allows an almost steady positioning of a sample at a fixed location in space. However, the levitator introduces some difficulties. One of the main problems with acoustic levitation is that an acoustic streaming is induced near the sample surface, which affects the heat and mass transfer rates, as characterized by increased Nusselt and Sherwood numbers. The transfer rates are not uniform along the sample surface, and the aim of the present study is to quantify the spatial Sherwood number distribution over the surface of a sphere. The experiments are based on the measurement of the surface shape of a sphere layered with a solid substance as a function of time using a charge-coupled device (CCD) camera with backlighting. The sphere used in this research is a glass sphere layered with a volatile solid substance (naphthalene or camphor). The local mass transfer from the surface both with and without an ultrasonic acoustic field is investigated in order to evaluate the effect of the acoustic streaming. The experimental results are compared with predictions following from the theory outlined [A. L. Yarin, M. Pfaffenlehner, and C. Tropea, J. Fluid Mech. 356, 65 (1998); A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, ibid. 399, 151 (1999)] which describes the acoustic field and the resulting acoustic streaming, and the mass transfer at the surface of particles and droplets located in an acoustic levitator. The results are also compared with the experimental data and with the theoretical predictions of Burdukov and Nakoryakov [J. Appl. Mech. Tech. Phys. 6, 51 (1965)], which are valid only in the case of spherical particles much smaller than the sound wavelength. Good agreement between experiment and the theory of Yarin et al. is demonstrated. The time-averaged heat and mass transfer rates over a sphere surface are greatest at the sphere’s equator and least at its poles in the experiment as predicted by the theory (the ultrasonic standing wave spans the vertical axis passing through the poles). The measured distribution of the mass transfer rate over the sphere surface also agrees with the theoretical predictions, which shows that in strong acoustic fields sublimation (or evaporation) results from the acoustic streaming.