phone +7 (3412) 91 60 92
mail imi@udsu.ru
ru-RU Russian
Home » Issues » Archive of Issues » 2014 - 3 issue » pp. 110-122

Archive of Issues

Russia Astrakhan
Year
2014
Issue
3
Pages
110-122
<<
>>
Section Mechanics
Title Comparing of a quasisteady and a nonsteady mathematical models of fluid flow in evaporating drop with regard to viscosity
Author(-s) Kolegov K.S.ab
Affiliations Astrakhan State Universitya, Caspian Institute of Sea and River Transport, Branch of the Volga State Academy of Water Transportb
Abstract Applicability limits of a quasisteady approach to modelling the fluid dynamics in evaporated drop on a substrate (with constant contact area) and in circular well are defined in this paper. A nonsteady model is considered for comparison. Quasisteady and nonsteady (with the full-form equation of motion) sets of equations have been solved numerically. The modeling is carried out at different values of evaporation rate and capillary number. Water and ethylene glycol drops were taken as examples. Analysis of calculated data shows that results obtained for the final stage of pure solvent evaporation by using two models differ from each other. Velocity of a radial flow calculated with the help of nonsteady model agrees with experimental data much better than the result obtained using a quasisteady approach at the final stage of process. This is because at the final stage of evaporation the quasisteady approach works poorly due to the rapid changes in the relative film thickness and high velocities.
Keywords evaporating drop, radial flow, drop on a substrate, pinning, circular well
UDC 532.511
MSC 76D45
DOI 10.20537/vm140310
Received 28 June 2014
Language Russian
Citation Kolegov K.S. Comparing of a quasisteady and a nonsteady mathematical models of fluid flow in evaporating drop with regard to viscosity, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 3, pp. 110-122.
References
  1. 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, no. 1, pp. 756-765.
  2. Yakhno T. Salt-induced protein phase transitions in drying drops, Journal of Colloid and Interface Science, 2008, vol. 318, no. 2, pp. 225-230.
  3. Tarasevich Y.Y., Vodolazskaya I.V., Bondarenko O.P. Modeling of spatial–temporal distribution of the components in the drying sessile droplet of biological fluid, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2013, vol. 432, pp. 99-103.
  4. 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.
  5. Takhistov P., Chang H.C. Complex stain morphologies, Industrial & Engineering Chemistry Research, 2002, vol. 41, no. 25, pp. 6256-6269.
  6. Ragoonanan V., Aksan A. Heterogeneity in desiccated solutions: implications for biostabilization, Biophysical Journal, 2008, vol. 94, no. 6, pp. 2212-2227.
  7. Layani M., Gruchko M., Milo O., Balberg I., Azulay D., Magdassi S. Transparent conductive coatings by printing coffee ring arrays obtained at room temperature, ACS Nano, 2009, vol. 3, no. 11, pp. 3537-3542.
  8. Lebedev-Stepanov P.V., Kadushnikov R.M., Molchanov S.P., Ivanov A.A., Mitrokhin V.P., Vlasov K.O., Rubin N.I., Yurasik G.A., Nazarov V.G., Alfimov M.V. Self-assembly of nanoparticles in the microvolume of colloidal solution: Physics, modeling, and experiment, Nanotechnologies in Russia, 2013, vol. 8, no. 3-4, pp. 137-162.
  9. Larson R.G. Transport and deposition patterns in drying sessile droplets, AIChE Journal, 2014, vol. 60, no. 5, pp. 1538-1571.
  10. Fischer B.J. Particle convection in an evaporating colloidal droplet, Langmuir, 2002, vol. 18, no. 1, pp. 60-67.
  11. Kolegov K.S., Lobanov A.I. Comparing of a quasisteady and nonsteady mathematical models of fluid flow in evaporating drop, Computer Research and Modeling, 2012, vol. 4, no. 4, pp. 811-825 (in Russian).
  12. Barash L.Y., Bigioni T.P., Vinokur V.M., Shchur L.N. Evaporation and fluid dynamics of a sessile drop of capillary size, Physical Review E, 2009, vol. 79, no. 4, p. 046301.
  13. Bartashevich M.V., Marchuk I.V., Kabov O.A. Numerical simulation of natural convection in a sessile liquid droplet, Thermophysics and Aeromechanics, 2012, vol. 19, no. 2, pp. 317-328.
  14. Dunn G.J., Wilson S.K., Duffy B.R., David S., Sefiane K. A mathematical model for the evaporation of a thin sessile liquid droplet: comparison between experiment and theory, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2007, vol. 323, no. 1-3, pp. 50-55.
  15. Hamamoto Y., Christy J.R.E., Sefiane K. Order-of-magnitude increase in flow velocity driven by mass conservation during the evaporation of sessile drops, Phys. Rev. E, 2011, vol. 83, p. 051602.
  16. Cachile M., Benichou O., Cazabat A.M. Evaporating droplets of completely wetting liquids, Langmuir, 2002, vol. 18, no. 21, pp. 7985-7990.
  17. Bhardwaj R., Attinger D. Non-isothermal wetting during impact of millimeter-size water drop on a flat substrate: numerical investigation and comparison with high-speed visualization experiments, International Journal of Heat and Fluid Flow, 2008, vol. 29, no. 5, pp. 1422-1435.
  18. 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.
  19. Hu H., Larson R.G. Analysis of the microfluid flow in an evaporating sessile droplet, Langmuir, 2005, vol. 21, no. 9, pp. 3963-3971.
  20. Masoud H., Felske J.D. Analytical solution for inviscid flow inside an evaporating sessile drop, Physical Review E, 2009, vol. 79, no. 1, p. 016301.
  21. Saverchenko V.I., Fisenko S.P., Khodyko Yu.A. Evaporation of a picoliter droplet on a wetted substrate at reduced pressure, Journal of Engineering Physics and Thermophysics, 2011, vol. 84, no. 4, pp. 723-729.
  22. Saverchenko V.I., Fisenko S.P., Khodyko J.A. Low pressure evaporation of binary picoliter droplet on substrate, 15-th International Symposium on Flow Visualization, June 25-28, 2012, Minsk, Belarus, pp. 12–17.
  23. Tarasevich Y.Y., Vodolazskaya I.V., Isakova O.P., Abdel Latif M.S. Evaporation-induced flow inside circular wells: analytical results and simulations, Microgravity Science and Technology, 2009, vol. 21, pp. 39-44.
Full text
/doc/issues-2014/14-03-10.pdf
<< Previous article
Next article >>