Applicability of the approximation of Stokes for calculating the velocity of a steam-air jet over a locally heated water surface

About the authors:

Nurken E. Aktaev, Cand. Sci. (Phys.-Math.), Microhydrodynamic Technology Research Laboratory, University of Tyumen; n.e.aktaev@utmn.ru; ORCID: 0000-0002-9750-2183

Tatiana A. Penkina, Assistant, Department of Record Management and Document Management Support, University of Tyumen; t.a.penkina@utmn.ru

Abstract:

This paper presents a mathematical model of an air steam flow arising above a locally heated water surface. The model is based on the system of equations of free convection in the Boussinesq approximation and is implemented as a computer program in C language. Numerical simulation aided in obtaining the velocity fields of the jet are obtained at various values of the water surface temperature. The values of the flow velocities obtained in the framework of the Stokes approximation are compared with the calculated values based on the results of experiments on the levitation of water droplets. As a result of the comparison, the condition of the applicability of the approximation of Stokes to estimate the velocity of an air steam flow is formulated.

References:

1. Agresti J. J., Antipov E., Abate A. R., Ahn K., Rowat A. C., Baret J. C., Marquez M., Klibanov A. M., Griffiths A. D., Weitz D. A. 2010. “Ultrahigh-throughput screening in drop-based microfluidics for directed evolution”. Proceedings of the National Academy of Sciences of the United States of America, vol. 107, no. 9, pp. 4004-4009.

2. Aktaev N. E., Fedorets A. A., Bormashenko E. Y., Nosonovsky M. 2018. “Langevin approach to modeling of small levitating ordered droplet clusters”. Journal of Physical Chemistry Letters, vol. 9, no. 14, pp. 3834-3838.

3. Chowdhury M. S., Zheng W., Kumari S., Heyman J., Zhang X., Dey P., Weitz D. A., Haag R. 2019. “Dendronized fluorosurfactant for highly stable water-in-fluorinated oil emulsions with minimal inter-droplet transfer of small molecules”. Nature Communications, vol. 10, no. 1, art. 4546.

4. Fedorets A. A., Dombrovsky L. A. 2017. “Generation of levitating droplet clusters above the locally heated water surface: a thermal analysis of modified installation”. International Journal of Heat and Mass Transfer, vol. 104, pp. 1268-1274.

5. Fedorets A. A. 2012. “Mechanism of stabilization of location of a droplet cluster above the liquid-gas interface”. Technical Physics Letters, vol. 38, no. 11, pp. 988-990.

6. Fedorets A. A., Aktaev N. E., Gabyshev D. N., Bormashenko E. Yu., Dombrovsky L. A., Nosonovsky M. 2019. “Oscillatory motion of a droplet cluster”. Journal of Physical Chemistry, vol. 123, pp. 23572-23576.

7. Fedorets A. A., Aktaev N. E., Dombrovsky L. A. 2018. “Suppression of the condensational growth of droplets of a levitating cluster using the modulation of the laser heating power”. International Journal of Heat and Mass Transfer, vol. 127, pp. 660-664.

8. Jiao L., Chen R., Zhu X., Liao Q., Wang H., An L., Zhu J., He X., Feng H. 2019. “Highly flexible and ultraprecise manipulation of light-levitated femtoliter/picoliter droplets”. Journal of Physical Chemistry Letters, vol. 10, no. 5, pp.1068-1077.

9. Kabov O. A., Lyulin Yu. V., Marchuk I. V., Zaitsev D. V. 2007. “Locally heated shear-driven liquid films in microchannels and minichannels”. International Journal of Heat and Fluid Flow, vol. 28, no. 1, pp. 103-111.

10. Nightingale A. M., Leong C. L., Burnish R. A., Hassan S. U., Zhang Y., Clough G. F., Boutelle M. G., Voegeli D., Niu X. 2019. “Monitoring biomolecule concentrations in tissue using a wearable droplet microfluidic-based sensor”. Nature Communications, vol. 10, no. 1, art. 2741.

11. Scheeline A., Behrens R. L. 2012 “Potential of levitated drops to serve as microreactors for biophysical measurements”. Biophysical Chemistry, vols. 165-166, pp. 1-12.

12. Song H., Tice J. D., Ismagilov R. F. 2003. “A Microfluidic system for controlling reaction networks in time”. Angewandte Chemie, vol. 42, no. 7, pp. 768-772.

13. Stone H. A., Stroock A. D., Ajdari A. 2004. “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip”. Annual Review of Fluid Mechanics, vol. 36, pp. 381-411.