Research output: Contribution to journal › Article › peer-review
Numerical modeling of thermocapillary deformations in locally heated liquid layer. / Barakhovskaia, E. V.; Marchuk, I. V.; Fedorets, A. A.
In: Eurasian Journal of Mathematical and Computer Applications, Vol. 5, No. 4, 2017, p. 4-13.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Numerical modeling of thermocapillary deformations in locally heated liquid layer
AU - Barakhovskaia, E. V.
AU - Marchuk, I. V.
AU - Fedorets, A. A.
PY - 2017
Y1 - 2017
N2 - The problem of thermocapillary deformation of the locally heated horizontal liquid layer is considered. The numerical solution of the problem has been obtained in the lubrication approximation theory for two-dimensional axisymmetric thermocapillary flow. The model takes into account surface tension, viscosity, gravity and heat transfer in the substrate and liquid. Evaporation is neglected. The numerical algorithm for the joint solution of the energy equation and the evolution equation for the liquid layer thickness has been developed. Stationary solutions have been obtained by the establishment method. There have been measured and numerically calculated deformations in locally heated horizontal layers of silicone oils of different types and thickness. The dependencies of the depth of thermocapillary deformations on the layer thickness have been obtained for silicone oils of different viscosities. It has been found that the value of the relative deformation of the layer decreases nonlinearly with increasing the layer thickness, when other conditions being equal. It has been found a good qualitative agreement of numerical results and experimental data.
AB - The problem of thermocapillary deformation of the locally heated horizontal liquid layer is considered. The numerical solution of the problem has been obtained in the lubrication approximation theory for two-dimensional axisymmetric thermocapillary flow. The model takes into account surface tension, viscosity, gravity and heat transfer in the substrate and liquid. Evaporation is neglected. The numerical algorithm for the joint solution of the energy equation and the evolution equation for the liquid layer thickness has been developed. Stationary solutions have been obtained by the establishment method. There have been measured and numerically calculated deformations in locally heated horizontal layers of silicone oils of different types and thickness. The dependencies of the depth of thermocapillary deformations on the layer thickness have been obtained for silicone oils of different viscosities. It has been found that the value of the relative deformation of the layer decreases nonlinearly with increasing the layer thickness, when other conditions being equal. It has been found a good qualitative agreement of numerical results and experimental data.
KW - Deformations of the liquid surface
KW - Energy equation
KW - Lubrication approximation theory
KW - Method of fractional steps
KW - Silicone oil
KW - Thermocapillary effect
UR - http://www.scopus.com/inward/record.url?scp=85037112151&partnerID=8YFLogxK
U2 - 10.32523/2306-3172-2017-5-4-4-13
DO - 10.32523/2306-3172-2017-5-4-4-13
M3 - Article
AN - SCOPUS:85037112151
VL - 5
SP - 4
EP - 13
JO - Eurasian Journal of Mathematical and Computer Applications
JF - Eurasian Journal of Mathematical and Computer Applications
SN - 2306-6172
IS - 4
ER -
ID: 9080104