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 -