Geodesic
Comparison of quasisteady and nonsteady mathematical models of fluid flow in evaporating drop with due regard for the viscosity
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2014), pp. 110-122

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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. 
@article{VUU_2014_3_a9,
     author = {K. S. Kolegov},
     title = {Comparison of quasisteady and nonsteady mathematical models of fluid flow in evaporating drop with due regard for the viscosity},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {110--122},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2014_3_a9/}
}
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K. S. Kolegov. Comparison of quasisteady and nonsteady mathematical models of fluid flow in evaporating drop with due regard for the viscosity. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2014), pp. 110-122. http://geodesic.mathdoc.fr/item/VUU_2014_3_a9/