Numerical Simulation of Thermocapillary Convection with Evaporation Induced by Boundary Heating

The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.

Bifurcation of thermocapillary convection in a shallow annular pool of silicon melt

In order to understand the nature of surface patterns on silicon melts in industrial Czochralski furnaces, we conducted a series of unsteady threedimensional numerical simulations of thermocapillary convections in thin silicon melt pools in an annular container. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The results show that the flow is steady and axisymmetric at small temperature difference in the radial direction. When the temperature difference exceeds a certain threshold value, hydrothermal waves appear and bifurcation occurs. In this case, the flow is unsteady and there are two possible groups of hydrothermal waves with different number of waves, which are characterized by spoke patterns traveling in the clockwise and counter-clockwise directions. Details of the flow and temperature disturbances are discussed and number of waves and traveling velocity of the hydro- thermal wave are determined.

Two-dimensional numerical simulation of thermocapillary convection in detached solidification

Numerical simulations of flow in the melt(CdZnTe) with different conditions are conducted using the finite-difference method.When the top surface of the melt is solid wall under microgravity condition,the thermocapillary convection is caused in the melt by the surface tension gradient on the free surface.As the Marangoni number is small,the flow is steady thermocapillary convection.As the Marangoni number exceeds the critical value,the steady flow transits into unstable thermocapillary convection.When the top surface of the melt is free surface under microgravity,two roll cells are observed in the melt,which are driven by both the surface tension gradients on the upper and lower free surfaces.When the top surface of the melt is free surface under gravity condition,the effect of the buoyancy on the flow is little as the Marangoni number is small.With the Marangoni number increasing,the effect of the buoyancy increases,which makes the upper roll cell weaken and the lower roll cell strengthen.

Simulation of Thermocapillary Convection in a TwoLayer Immiscible Fluid System Using a Boundary Element Method

A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity gradients are eliminated and the complete formulation is written in terms of velocity.This avoids the difficulty of convective discretizations and provides considerable reductions in storage and computational requirements while improving accuracy.In this paper,we give the influence of different parameters(Marangoni number, Reynolds number)on thermocapillary convection in cavity with two-layer immiscible fluids.As shown by the numerical results,when the physical parameters between liquid encapsulant and melt are chosen appropriately, the detrimental flow in the bottom melt layer can be greatly suppressed.The influence of the free interface on thermocapillary convection is also shown.

Effect of Marangoni Number on Thermocapillary Convection and Free-Surface Deformation in Liquid Bridges

Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.

Influence of the heating rate on the critical Marangoni number of oscillatory thermocapillary convection in the floating half zone

In the present study, numerical simulations were conducted on thermocapillary convection in floating half zones of 5 cSt silicone oil of different scales in comparison with the experimental studies in the microgravity conditions. The effect of heating rate on the marginal instability boundaries is indicated as a possible explanation for the significant quantitative discrepancies between the experimental results in the terrestrial conditions and in the microgravity conditions.

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several millimeters in diameter.In the present work,terrestrial experimental studies were conducted on the floating half zones of 5 Centistokes(cSt) silicon oil and 10 cSt silicon oil.The experimental results show that the critical Marangoni number generally increases with the increasing aspect ratio of the floating half zone and then decreases.Moreover,a further increase of the critical Marangoni number with the increasing aspect ratio occurs for the slender floating half zones.

TWO BIFURCATION TRANSITION PROCESSES IN FLOATING HALF ZONE CONVECTION OF LARGER PRANDTL NUMBER FLUID

Processes of the onset oscillation in the thermocapillary convection under the Earth's gravity are investigated by the numerical simulation and exper- iments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=l for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge.It implies that,there are two critical Marangoni numbers related,respectively,to these two bifurcation transitions for the fat liquid bridge.The computational results agree with the results of ground-based experiments.

Instability of thermocapillary flow in liquid layers under microgravity

The instability of the thermocapillary flow in liquid layers is studied in the present paper using the linear stability analysis.Based on the two-dimensional steady flow state,the three-dimensional disturbance with a wave number in the spanwise direction is considered.The effects of the aspect ratio and free surface shape of the liquid layer on the flow instability are studied,and the results are compared with the case with the two-dimensional disturbance.

Influence of Heating Rate on the Onset of Oscillation in Liquid Bridge of Half Floating Zone

Many research works were completed to observe the critical applied temperature difference (△T)c in a small liquid bridge of floating zone. Different heating rates have been designed for detailed experiment,and relatively high heating rate is especially demanded for space experiment due to the limited time of experiment. In the present paper, the influence of heating rate on (△T)c was studied experimentally for cases of upper or lower rod heating for different geometry of liquid bridge. The results show that there is large variation of (△T)c for different heating rate, changing from around 0.1℃/s to 1.6℃/s.This result is helpful for the design of Marangoni convection experiment and the explanation of the dispersion of experimental results.

Bifurcation Diversity in an Annular Pool Heated from Below:Prandtl and Biot Numbers Effects

In this article the instabilities appearing in a liquid layer are studied numerically by means of the linear stability method.The fluid is confined in an annular pool and is heated from below with a linear decreasing temperature profile from the inner to the outer wall.The top surface is open to the atmosphere and both lateral walls are adiabatic.Using the Rayleigh number as the only control parameter,many kind of bifurcations appear at moderately low Prandtl numbers and depending on the Biot number.Several regions on the Prandtl-Biot plane are identified,their boundaries being formed from competing solutions at codimension-two bifurcation points.