Thermocapillary Convective Flows Research Articles

Thermocapillary convection in a cuboid pool with a sidewall of different temperature sections

Thermocapillary convection in a liquid cuboid pool with a sidewall of different temperature sections is investigated using 3D numerical simulation. One half section of the sidewall is heated but the other cooled. Numerical simulation is performed for Marangoni number (Ma) from 100 to 4.0 × 106 with Prandtl number (Pr) of 28.6 and aspect ratios (Ah and Aw) of 0.43. A temperature field with a weak thermocapillary convection flow is dominated by conduction for small Ma. As Ma increases, the flow becomes stronger and reveals a complex transition route to a chaotic state with a series of bifurcations. It has been demonstrated that the symmetry of the temperature field breaks between Ma = 102 and 103. A Hopf bifurcation occurs between Ma = 8.0 × 105 and 9.0 × 105 in which the flow becomes periodic. As Ma increases further, a sequence of period-doubling bifurcations occurs between Ma = 2.78 × 106 and 2.95 × 106. Once Ma exceeds 3.0 × 106, the flow becomes chaotic. Typical thermocapillary convection flows in the pool are characterized with topological analyses, spectral analyses, attractors, Lyapunov exponents, and fractal dimensions. Furthermore, the heat and mass transfer in the cuboid pool have been investigated.

Influence of External Magnetic Field on 3D Thermocapillary Convective Flow in Various Thin Annular Pools Filled with Silicon Melt

Thermocapillary convection flows can have an impact on the homogeneity of floating zone semiconductor crystals. An external magnetic field can also help to reduce this non-homogeneity. The goal of this research is to minimize thermocapillary convection in various thin annular pools filled with silicon melt. A three-dimensional (3D) numerical technique is proposed that employs an implicit finite volume formulation. The steady-state thermocapillary flow in six thin annular pools (R=0.3, 0.4, 0.5, 0.6, 0.7, and 0.8) subjected to an externally induced magnetic field was observed. Under magnetic field influence, the effects of increasing annular gap, R on the hydrothermal wave number and azimuthal pattern are obtained. The results reveal that hydrothermal waves m=14, m=11, m=8, m=6, m=4, and m=3 are observed in steady flow for R=0.3; 0.4; 0.5; 0.6; 0.7, and R=0.8, respectively. The maximum temperature occurs in the intermediate zone between the inner and outer walls when there is no magnetic field. Under a strong enough magnetic field, isothermal lines change form and become concentric circles. As the amplitude of the magnetic field (Ha) grows, the azimuthal velocity and temperature at the free surface reduce, and the asymmetric 3D flow becomes axisymmetric steady when Ha surpasses a threshold value.

Effects of thermocapillary convection and shear flow on the distribution of inclusions in half-floating zones

The distribution of inclusions plays a critical role in the performance of crystalline silicon, which is an important raw material for solar panels and semiconductors. To describe the formation of the aggregated inclusions, a three-phase gas–liquid-solid system was designed, in which the gas and liquid phases interact directly through the free surface, and the inclusions interact with them in the liquid. It is worth noting that the inclusions and gas phase did not interact directly. In the gas and liquid phases, the finite volume method was used to solve the Naiver-Stokes equations, and the CLSVOF method was used to track the free surface deformation. The motion of the inclusions was tracked using the Lagrange method. The inclusions and fluid were coupled in two ways: energy and momentum exchange. The numerical results show that the spatial distributions of the inclusion volumetric concentration, number density, and characteristic radius have some features of the recirculation zone. The closer to the center of the liquid bridge, the lower the density of inclusions. When the direction of the shear flow is opposite to that of the thermocapillary convection, this phenomenon is more obvious. This indicates that the crystal quality in the middle region is higher when various parameters are appropriate.

Numerical and theoretical analysis of fast evaporating sessile droplets with coupled fields

Sessile evaporating droplets are widely encountered in various scientific and industrial fields, therefore, it is of vital importance for accurate prediction of actual droplet evaporation rates. For slow droplet evaporation, the heat and vapor transport of the droplet are diffusion-controlled, the classic isothermal model can predict the droplet evaporation well. However, for fast droplet evaporation, the convection flow, heat and vapor transfer are strongly coupled together, which brings great difficulty for accurate prediction. In this study, both theoretical analysis and numerical simulation are carried out to study the droplet evaporation with coupled flow, heat and vapor transfer fields. The droplet evaporation is investigated under different evaporative cooling numbers, droplet contact angles and substrate superheats. It is found that droplet evaporation can always be deteriorated by the evaporative cooling effect, while it can be enhanced by thermocapillary convection flow inside the droplet and natural convection outside the droplet. It is surprisingly found that the actual evaporation rates can be higher than those in the isothermal model, especially at low contact angle, high substrate superheat and weak evaporative cooling effect. Besides, a correction factor is proposed to quantify the deviation of actual evaporating rates in our fully coupled model from those in the isothermal model, and provides the dependence of the correction factor on evaporative cooling numbers, contact angles and substrate superheats, which can help predict the actual droplet evaporation rates. These findings may be helpful to get insight into the droplet evaporation and guide for its application.

Thermocapillary Convection Flow and Heat Transfer Characteristics of Graphene Nanoplatelet Based Nanofluid Under Microgravity

Thermocapillary Convection Flow and Heat Transfer Characteristics of Graphene Nanoplatelet Based Nanofluid Under Microgravity

Transient thermocapillary convection flows in a rectangular cavity with an evenly heated lateral wall

Transient thermocapillary convection flows driven by the evenly heated lateral wall of a rectangular cavity for zero-gravity condition are investigated by scaling analysis and numerical simulation. Scaling analysis suggests a set of flow regimes in different dynamical evolutions of the surface flow, dependent on Marangoni and Prandtl numbers and aspect ratios. In the typical case, the surface flow may travel, for example, under flow regimes of unsteady inertial-thermocapillary balance, unsteady viscous-thermocapillary balance, and steady viscous-thermocapillary balance in different dynamical evolutions. Additionally, scaling laws of the thickness and velocity of transient thermocapillary convection flows under different flow regimes have been obtained. Furthermore, two-dimensional numerical simulation has been performed. The numerical results show good agreement with the corresponding scaling predictions.

Ethyl cyanoacrylate ordered porous films prepared via in‐situ polymerization and static breath figures process

Ordered microporous films were fabricated via static breath figure process and in situ polymerization of ethyl cyanoacrylate (ECA) monomers. The influences of various parameters including solvent type (dichloromethane and chloroform), ECA concentration (0.2 and 1 wt%), temperature (17°C and 26°C), and substrate (glass, mica, PE, PP, and PET) were investigated on the structure of breath Figure (BF) films. Highly ordered porous films were generally formed at lower concentration of ECA and at 17°C for dichloromethane (DCM) and at 26°C for chloroform (CLF). The pores average diameter (D̅) of the films were in the range of 1 to 5 μm. The formation of regular porous structures were elucidated using the Marangoni (thermocapillary) convection flow and the rate of the polymer precipitation around the water droplets. There were an optimum ΔT (the temperature difference between the air and the solution surface) to create ordered BF film, regardless of solvent type. The prepared films have potential for templating applications.

Observation of water droplets oscillation due to laser induced Marangoni convection

In this paper, using experimental characterizations, we explore the motion of water droplets suspended in mineral oil under exposure of a focused continuous wave (CW) fiber laser beam. The laser beam exposure heats the surrounding oil medium as well. The temperature gradient generates thermocapillary (or Marangoni) convection flows. This approach uses infrared laser-induced thermocapillary-driven flow for manipulation of droplets in the range of 10 to 30μm in diameter. The droplets are trapped in the convection flow and travel with thermocapillary convection flow (depending on the droplet sizes) along the streamline with high speed. This motion is observed at a certain critical power of the laser. The behavior of a droplet in response to thermally induced convection can be consider. we also examined the oscillatory behavior of the droplet on the x-y plane. As expected, oscillation frequency/amplitude are linearly correlated to the droplet size.

Thermocapillary Convective Flows Generated by Laser Points or Patterns: Comparison for the Noncontact Micromanipulation of Particles at the Interface

This letter compares the controlled manipulation of micrometer size particles using thermocapillary convective flows generated by laser points or patterns. Such flows are generated when a surface tension stress is generated at the fluid/gas interface due to a thermal gradient. Laser heating allows to generate fast, localized flows that are used to displace a particle towards a desired position. However, these flows are repulsive and so the system is unstable. Although using the simple laser spot with a closed-loop control enables to control the particle displacement, the control of the particle movement direction is somehow difficult and the particle position stabilization remains challenging. In this letter, it is proposed to use laser patterns to overcome these limitations. Experimental tests are performed using a 500-μm-diameter steel spherical particle that is displaced towards a target position. The preliminary experimental results show that it is possible to overcome the above mentioned limitations while still obtaining maximal particle velocities ranging from 4 to 9 mm/s during the displacement phase.

Closed-Loop Particle Motion Control Using Laser-Induced Thermocapillary Convective Flows at the Fluid/Gas Interface at Micrometric Scale

Noncontact actuation has gained a large interest over the last few years, and many works have been performed on magnetic actuation, dielectrophoresis, or optical tweezers. Thermocapillary convective flows are an attractive alternative to manipulate micrometric scale particles at the water/air interface. These flows are generated when a surface tension stress is generated at the fluid/gas interface due to a thermal gradient. Laser heating allows to generate fast, localized flows that improve the actuation performance. In this paper, a closed-loop controller is used to control the particle motion. To design this controller, a model for the system is proposed and experimentally identified. Proof of concept experiments are performed using a 500-μm-diameter steel spherical particle that show that the particle can be successfully displaced towards a target position. Experimental results show that maximal particle velocities between 4-9 mm/s can be attained during the control phase, which can be compared against some of the fastest actuation principles that use Marangoni effect.

Optimizing the speed of single infrared-laser-induced thermocapillary flows micromanipulation by using design of experiments

Laser-induced thermocapillary convection flows is a promising technique to manipulate micrometer size particles. Several parameters, such as the laser exposure time, the laser-particle distance, the particles’ diameter and the water layer thickness can be used to control the particles’ speed. This article deals with the study of the influence of the control parameters in the manipulation process using a systematic method: Design of Experiments (DoE). Additionally, a mathematical speed model of the manipulated particle as function of the mentioned parameters is proposed in order to enhance the manipulation accuracy and speed paving the way toward future works related to control strategies. Acid-washed glass beads ranging from 50 up to 150 microns were used for this purpose.

Laser-Induced Thermocapillary Convective Flows: A New Approach for Noncontact Actuation at Microscale at the Fluid/Gas Interface

This paper proposes a new actuation principle for noncontact actuation. Thermocapillary convection is a promising principle to manipulate particles at the fluid/gas interface. Compared with approaches based on natural and Marangoni convections, our approach uses thermocapillary convection generated by a laser heating the fluid from the top and not from the bottom. This has several advantages, the most relevant being that it does not depend on an hydrodynamic instability to onset the flow motion. Laser heating creates large localized thermal gradients that make the flow velocity fast and localized. Simulations show that flow velocities up to 8.5 mm/s can be obtained using as little power as 38 mW with a temperature increase as little as 4 °C. As a proof of concept, steel spherical particles of 500 $\mu$ m diameter are successfully displaced using this principle, which attain a mean maximal speed up to 4 mm/s. Also, 1000- $\mu$ m-diameter steel spherical particles are displaced along a given trajectory using a manual control. These results first demonstrate the high potential of this new approach based on thermocapillary convection for controlled noncontact actuation at high speeds at microscale.

Exploiting the transient behavior of thermocapillary convection flows to enhance non-contact mesoscale manipulation

In this work it is demonstrated that the manipulation of the mesoscale-sized particles through Marangoni flows occurs during the transient regime of the convection cell evolution. By exploiting this fact, it was possible to selectively separate a single glass bead out of a group of other beads ranging from 150 to 212 μm. This task was accomplished by controlling the Marangoni convection cell growth. The growth was controlled by varying the pulse width of an infrared laser beam that acts as a thermal source. Thus, extending the use of the Marangoni flows for single particles sorting or manipulation.

Laser-Induced Thermocapillary Convection for Mesoscale Manipulation

Modulation of surface stresses is a recent and promising method to perform mesoscale manipulation of components in liquid medium. We present a promising approach using infra red laser-induced thermocapillary-driven flow for handling multiple or single large and heavy objects. The objects are immersed in thin liquid layers and in contact with the substrate surface. These objects can be handled with high speed thermocapillary convection flow reaching significant forces depending on the object sizes. Velocity measurements showed that 92 µm-sized spherical beads can be dragged with velocities of about 5.5 mm/s. Parallel non-contact micromanipulation can be achieved.

Virtual Rheoscopic Fluids for Flow Visualization

Physics-based flow visualization techniques seek to mimic laboratory flow visualization methods with virtual analogues. In this work we describe the rendering of a virtual rheoscopic fluid to produce images with results strikingly similar to laboratory experiments with real-world rheoscopic fluids using products such as Kalliroscope. These fluid additives consist of microscopic, anisotropic particles which, when suspended in the flow, align with both the flow velocity and the local shear to produce high-quality depictions of complex flow structures. Our virtual rheoscopic fluid is produced by defining a closed-form formula for the orientation of shear layers in the flow and using this orientation to volume render the flow as a material with anisotropic reflectance and transparency. Examples are presented for natural convection, thermocapillary convection, and Taylor-Couette flow simulations. The latter agree well with photographs of experimental results of Taylor-Couette flows from the literature.

Stability of thermocapillary convection and regimes of a fluid flow acted upon by a standing surface wave

It has been established that, in the case where a standing surface wave acts on a thermocapillary-convection flow in a cylindrical volume, there arises an oscillating-convection zone between the laminar and turbulent regimes of flow. It is shown that the boundary between these regimes is determined by the amplitude δ and the number of periods n of the standing wave and is practically independent of the Marangoni number and the oscillation frequency of this wave. At n = 2, in the range 0.004 < δ < 0.006, the parameters of the fluid cease to oscillate. The mechanisms by which the thermocapillary convection in closed volumes loses its stability are discussed.

Steady and oscillatory thermocapillary convection generated by a bubble

In this article, we study steady and oscillatory thermocapillary and natural convective flows generated by a bubble on a heated solid surface. The dynamic characteristics of the time-dependent convection are captured using a combined numerical-experimental approach. The index of refraction fringe distribution patterns constructed numerically by taking an inverse Abel transform of the computed temperature fields are compared directly to the experimental Wollaston prism (WP) interferograms for both steady-state and oscillatory convection. The agreement between numerical predictions and experimental measurements is excellent in all cases. It is shown that below the critical Marangoni number, steady-state conditions are attainable. With increasing Ma, there is a complete transition from steady state up to a final nonperiodic fluctuating flow regime through several complicated symmetric and asymmetric oscillatory states. The most prevalent oscillatory mode corresponds to a symmetric up and down fluctuation of the temperature and flow fields associated with an axially traveling wave. Careful examination of the numerical results reveals that the origin of this class of convective instability is closely related to an intricate temporal coupling between large-scale thermal structures which develop in the fluid in the form of the cold return flow and the temperature sensitive surface of the bubble. Gravity and natural convection play an important role in the formation of these thermal structures and the initiation of the oscillatory convection. Consequently, at low-g, the time evolution of the temperature and flow fields around the bubble are very different from their 1-g counterparts for all Marangoni numbers.

Tellurium recrystallization under microgravity conditions and the resulting properties of samples

Three experiments on the tellurium recrystallization by a modified Bridgman method were performed under microgravity conditions on board the Mir orbital space laboratory using a ChSK-1 Kristallizator furnace. The physical properties of samples were studied, including the final crystal structure, the distribution of impurities and defects, and the charge carrier concentration and mobility. The results were compared to the analogous parameters of crystals remelted using the same method under the normal gravity conditions. It is established that the samples recrystallized in a close volume under the on-board microgravity conditions “break off” from the container walls and touch the walls only in a few points. This circumstance gives rise to special effects, such as the growth of crystals with a free surface and deep supercooling. Study of the distribution of electrically active impurities over the length of ingots shows evidence of the presence of thermocapillary convective flows in the melt under the microgravity conditions. The flows tend to increase upon separation of the melt from the container walls. The contributions due to impurities and electrically active structural defects to the charge carrier distribution are taken into account. The single-crystal sample obtained upon the partial recrystallization of tellurium in a close container volume under the on-board microgravity conditions exhibits the electrical characteristics comparable to those of a crystal grown by the Czochralski technique under the normal gravity conditions.

Numerical simulation of oscillatory Marangoni convective flow inside a cylindrical liquid zone

The problem of the oscillatory thermocapillary convection flow inside a NaNO 3 float zone which is suspended between a pair of coaxial disks with prescribed time-dependent temperature profiles and bounded by a cylindrical free surface, has been investigated. The system of governing equations corresponding to a three-dimensional transient model was directly solved by employing a finite control volume method, fully-implicit in time, and a staggered spatial mesh in cylindrical coordinates. It has been clearly shown that for a sufficiently low temperature difference between the disks, the flow consists of a steady and perfectly axisymmetrical toroidal structure with a purely axial moyement of the fluid on the free surface and the vortex center located near that surface. Beyond the critical Marangoni number, Ma cr U ≈ 12 500, a transition from the axisymmetrical to the three-dimensional oscillatory state occurs. Under the effects of the time-dependent thermal disturbances on the free surface, the entire velocity and temperature fields rotate around the main axis following the second mode, i.e. the symmetrical mode of instability. A complete description of the flow structure and its dynamical behavior as well as a comparison with previous numerical and experimental data is given. The phenomenon of hysteresis has also been studied. It has been observed that there is a certain range of the Marangoni number where both the axisymmetrical and the oscillatory states may exist depending on whether the zone is heated up or cooled down. It has been found that the second critical Marangoni number i.e. the one corresponding to the reverse transition from the oscillatory to the axisymmetrical state, depends strongly on the temperature time-rate at which the zone is cooled.

Bubble Dynamics on a Heated Surface

In this work, we study steady and oscillatory thermocapillary and natural convective flows generated by a bubble on a heated solid surface. The interaction between gas and vapor bubbles with the surrounding fluid is of interest for both space and ground-based processing. A combined numerical-experimental approach is adopted here. The temperature field is visualized using Mach-Zehnder and/or Wollaston Prism Interferometry and the flow field is observed by a laser sheet flow visualization technique. A finite element numerical model is developed which solves the transient two-dimensional continuity, momentum, and energy equations and includes the effects of temperature-dependent surface tension and bubble surface deformation. Below the critical Marangoni number, the steady state low-g and 1-g temperature and velocity fields predicted by the finite element model are in excellent agreement with both the visualization experiments in our laboratory and recently published experimental results in the literature. Above the critical Marangoni number, the model predicts an oscillatory flow which is also closely confirmed by experiments. It is shown that the dynamics of the oscillatory flow are directly controlled by the thermal and hydrodynamic interactions brought about by combined natural and thermocapillary convection. Therefore, as numerical simulations show, there are considerable differences between the 1-g and low-g temperature and flow fields at both low and high Marangoni numbers. This has serious implications for both materials processing and fluid management in space.