The Bateman-type variational formalism for an acoustically-driven drop

Authors

DOI:

https://doi.org/10.15407/dopovidi2023.03.017

Keywords:

Bateman variational principle, Clebsch potentials, acoustical levitation

Abstract

By employing the Clebsch potentials, the Bateman-type variational formulation for a drop levitating in an acoustic field is proposed when both fluids, liquid drop and external ullage gas, are barotropic, inviscid, compressible and admit rotational flows

Downloads

Download data is not yet available.

References

Lukovskii, I. A. & Timokha, A. N. (1993). Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields. Ukr. Math. J., 45, Iss. 12, pp. 1849-1860. https://doi.org/10.1007/BF01061355

Chernova, M. O, Lukovsky, I. A. & Timokha, A. N. (2015). Differential and variational formalism for acoustical-ly-levitating drops. J. Math. Sci., 220, No. 3, pp. 359-375. https://doi.org/10.1007/s10958-016-3189-z

Pandey, K., Prabhakaran, D. & Basu, S. (2019). Review of transport processes and particle self-assembly in acoustically levitated nanofluid droplets. Phys. Fluids, 31, Iss. 11, art. 112102. https://doi.org/10.1063/1.5125059

Chen, H., Li, A., Zhang, Y. & Xiaoqiang, Z. (2022). Evaporation and liquid-phase separation of etha-nol-cyclohexane binary drops under acoustic levitation. Phys. Fluids, 34, Iss. 9, art. 092108. https://doi.org/10.1063/5.0109520

Timokha, A. N. (2022). A note on the variational formalism for sloshing with rotational flows in a rigid tank with unprescribed motion. Ukr. Math. J., 73, No. 10, pp. 1580-1589. https://doi.org/10.1007/s11253-022-02015-3

Bateman, H. (1944). Partial differential equations of mathematical physics. New York: Dover Publications, 556 pp.

Faltinsen, O. M. & Timokha, A. N. (2009). Sloshing. Cambridge Univ. Press, 678 pp.

Downloads

Published

11.07.2023

How to Cite

Timokha, A. (2023). The Bateman-type variational formalism for an acoustically-driven drop. Reports of the National Academy of Sciences of Ukraine, (3), 17–22. https://doi.org/10.15407/dopovidi2023.03.017