Numerical modelling of thermocapillary deformation in a locally heated thin horizontal volatile liquid layer

Ella Barakhovskaya,Jean Claude Legros,Igor Marchuk,D.V Zaitsev,O.A Kabov

doi:10.1051/matecconf/20168400003

Ella Barakhovskaya, Jean Claude Legros + Show 3 more

Open Access

https://doi.org/10.1051/matecconf/20168400003

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Abstract

The thermocapillary flow in a thin horizontal layer of viscous incompressible liquid with 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 surface and ambient. Heat transfer in the substrate is also simulated. The deformation of the free surface has been calculated for different values of the heating power and thickness of the liquid layer. Initially the liquid layer has flat surface and uniform temperature. The model predicts the thermocapillary deformation of the liquid surface and the formation of the thin residual layer of the liquid.

Highlights

Problem statementHeat transfer in thin liquid layers with local heating is an important challenge for thermal stabilization technique of electronic equipment [1,2,3]
The thermocapillary flow in a thin horizontal layer of viscous incompressible liquid with free surface is considered
The model predicts the formation of the thin residual layer of the liquid and film breakdown at sufficiently intensive heating

Summary

Problem statement

Heat transfer in thin liquid layers with local heating is an important challenge for thermal stabilization technique of electronic equipment [1,2,3]. The problem consider a thin horizontal volatile liquid layer on the substrate with local heater, Figure 1. The liquid layer has flat surface and uniform constant temperature T0. At the time t0=0 the heater is activated and starts heating the substrate and liquid. Shear stress occurs on the liquid surface caused by the heterogeneity of its temperature. Thermocapillary flow and deformation of the liquid surface is developing. The mechanism of convective heat transfer in the liquid and deformation of surface in the heat problem is taken into account. Surface tension, thermocapillary effect, viscosity are included in the evolution equation for the liquid layer thickness

Basic equations

The evolution equation for liquid film thickness

The boundary conditions

Numerical modelling

Numerical results

Conclusions