Self-similarity problem of thermal convection averaged over a thin layer
https://doi.org/10.12737/22161
Abstract
Three types of self-simulated replacements for the problem of thermal convection averaged over a thin layer of the vaporizing liquid are presented. It is a model of the drying non-viscous extended droplet specified by the non-thermal diffusivity. For the construction of self-simulated solutions, a transition to the Riemann invariants is performed. Self-simulated solutions are functions of time and position determining the drop height, the mass-transfer rate and the heat flow averaged over the drop thickness. The found self-simulated solutions are classified on the basis of the behavior of the function that describes the drop height under the evaporation-condensation. The domains of applicability of various self-simulated solutions to the simulation of different situations of drying drops and films are identified.
References
1. Golbraykh, Е.О., Rapis, E.G., Moiseev, S.S. O formirovanii uzora treshchiny v svobodno vysykhayushchey plenke vodnogo rastvora belka. [On the formation of the crack pattern in a free drying film of aqueous protein solution. ] Technical Physics, 2003, vol. 73, iss. 10, pp. 116–121 (in Russian).
2. Yushchenko, A.A., Daudova, A.D., Ayupova, A.K., Urlyapova, N.G., Shatokhina, S.N. Sposob otsenki obshchetoksicheskogo deystviya lekarstvennykh sredstv na organizm: patent 2232387 Ros. Federatsiya : G01N33/15, G01N33/49. [A method of estimating general toxical action of drugs on the body.] Patent RF, no. 2232387, 2004 (in Russian).
3. Rapis, E. Belok i zhizn' (samosborka i simmetriya nanostruktur belka). [Protein and life (self-assembly and symmetry of protein nanostructures.)] Jerusalem; Moscow: ZL. Milta-PKP GIT, 2002, 257 p. (in Russian).
4. Abramchuk, S.S., Khokhlov, A.R., Iwataki, T., Oana, H., Yoshikawa, K. Direct observation of DNA molecules in a convection flow of a drying droplet. Europhys. Lett., 2001, vol. 55, pp. 294–300.
5. Harris, D. J., Hu, H., Conrad, J. C., Lewis, J. A. Patterning Colloidal Films via Evaporative Lithography. Physical Review Letters, 2007, vol. 98, no. 14, p. 148301.
6. Xu J., Xia J., Hong S.W., et al. Self-Assembly of Gradient Concentric Rings via Solvent Evaporation from a Capillary Bridge. Physical Review Letters, 2006, vol. 96, no. 6, p. 066104.
7. Helseth, L. E., Fischer, T. M. Particle interactions near the contact line in liquid drops. Physical Review E, 2003, vol. 68, no. 4, p. 042601.
8. Rieger, B., van den Doel, L. R., van Vliet, L. J. Ring formation in nanoliter cups: Quantitative measurements of flow in micromachined wells. Physical Review E, 2003, vol. 68, no. 3, p. 036312.
9. Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten, T.A. Contact line deposits in an evaporating drop. Physical Review E, 2000, vol. 62,pp. 756–765.
10. Maki, K. L., Kumar, S. Fast Evaporation of Spreading Droplets of Colloidal Suspensions. Langmuir, 2011, vol. 27, no. 18, pp. 11347– 11363.
11. Widjaja, E., Harris, M. Particle deposition study during sessile drop evaporation. AIChE J., 2008, vol. 54, no. 9, pp. 2250– 2260.
12. Tarasevich, Y. Y., Vodolazskaya, I.V., Sakharova, L.V. Mathematical modeling of pattern formation caused by drying of colloidal film under a mask. Eur. Phys. J. E, 2016, vol. 39, no. 2.
13. Zhukov, М.Y., Shiryaeva, E.V., Polyakova, N.M. Modelirovanie ispareniya kapli zhidkosti. [Simulation of the liquid drop evaporation.] Rostov-on-Don: SFU Press, 2015, 208 p. (in Russian).
14. Barenblatt, G.I. Podobie, avtomodel'nost', promezhutochnaya asimptotika. Teoriya i prilozheniya k geofizicheskoy gidrodinamike. [Similarity, self-similarity, intermediate asymptotics. Theory and applications to geophysical hydrodynamics .] Leningrad: Gidrometioizdat, 1982, 257 с. (in Russian).
15. Rozhdenstvenskiy, B.L., Yanenko, N.N. Sistemy kvazilineynykh uravneniy i ikh prilozheniya k gazovoy dinamike. [Systems of quasilinear equations and their applications to gas dynamics.] Moscow: Nauka, 1978, 687 p. (in Russian).
Review
For citations:
Sakharova L.V. Self-similarity problem of thermal convection averaged over a thin layer. Vestnik of Don State Technical University. 2016;16(4):17-28. (In Russ.) https://doi.org/10.12737/22161
Views:
430
Email this article 