Abstract
The problem of thermocapillary deformation and film breakdown in a thin horizontal layer of viscous incompressible liquid with a free surface is considered. The deformable liquid layer is locally heated. The problem of thermocapillary deformation of the locally heated horizontal liquid layer has been solved numerically for two-dimensional unsteady case. The lubrication approximation theory is used. Capillary pressure, viscosity and gravity are taken into account. Evaporating rate is supposed to be proportional to the temperature difference between the liquid and ambient. Heat transfer in the substrate is also simulated. The numerical algorithm for the joint solution of the energy equation and the evolution equation for the thickness of liquid layer has been developed. The model predicts the thermocapillary deformation of the liquid surface and the formation of dry spots. The dynamics of liquid surface, the dry spots formation and the velocity of the contact line have been calculated. The deformation of the free surface has been calculated for different values of the heating power and thickness of the liquid layer. The effect of surface tension coefficient and wetting contact angle on the velocity of the contact line motion has been analyzed. It has been obtained that the velocity of the contact line increases with the increase of the wetting contact angle value and of the surface tension coefficient.
Highlights
Heat transfer and film breakdown in thin liquid layer with local heating is an important challenge of thermal stabilization technique of electronic equipment [1,2,3]
Boundary conditions for this problem are set naturally: hr t, 0 0 the condition of the axial symmetry is given in the center of the cuvette hr t, R 0 the contact angle is given on the border of the cuvette q t, 0 0 flow rate is equal to 0 in the center q t, R 0 the condition of impermeability of liquid through the walls it is necessary to set boundary conditions in case of occurrence of film breakdown and formation of dry spots: hr (t, rDry Spot ) r tanT q(t, rDry Spot ) 0
The numerical calculations with given model of thin horizontal liquid layer with local heating have shown that local heating of a horizontal liquid layer causes deformation of the liquid surface and thermocapillary flow
Summary
Heat transfer and film breakdown in thin liquid layer with local heating is an important challenge of thermal stabilization technique of electronic equipment [1,2,3]. The study of thermocapillary effects in the thin locally heated liquid layer is demanded problem in the field of technological processes as the thin films provide a high intensity of heat and mass transfer. The problem of thermocapillary breakdown of the locally heated horizontal liquid layer has been solved numerically in axisymmetric statement, fig.. Proportional to the temperature difference between temperatures of the liquid surface and ambient. Heat transfer in the substrate is simulated. The liquid layer has flat surface and uniform temperature. The local heating of the liquid occurs from the substrate side. Deformations of the liquid surface are determined by the properties of the liquid, substrate and heater
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