Thermocapillary Forces Research Articles

Study of the Stability of a Free Nonisothermal Liquid Film in a Gravity Field

Problem of a free liquid film vertically bounded by solid walls and being under the influence of gravity and thermocapillary forces in a thin-layer approximation is considered. A solution in which the film thickness is constant and temperature is a linear function of the longitudinal coordinate is investigated for stability analytically using the method of matched asymptotic expansions and numerically using the orthogonalization method for various values of acceleration of gravity. The results obtained analytically and numerically are in good agreement. It is shown that the solution is unstable, but the increment of perturbations is small even under terrestrial gravity.

Single recalcitrant bubble simulation using a hybrid lattice boltzmann finite difference model

In this paper, 2D simulations of a single recalcitrant bubble using a hybrid finite difference lattice Boltzmann method are presented. To solve the flow field, the conservative phase field lattice Boltzmann model of Geier et al. (2015) is employed with a multi-relaxation-time (MRT) scheme which makes it capable of handling multiphase flows with high density and viscosity contrasts. A finite difference approach is applied to obtain the temperature field with a second-order spatial discretization (central) which marches in time with the 2nd order Runge-Kutta marching technique. The well-known continuum surface tension force (CSF) is implemented to define the thermocapillary force which depends on the temperature field. Before delving into the main aim of this work, we first assess the accuracy of the present model by verifying the Laplace law for a static bubble with four different values of surface tension. To further validate the model, thermocapillary migration of a deformable drop, and thermocapillary flow with two superimposed planar fluids are studied as our second and third benchmarks. Comparing the analytical solutions for both velocity and temperature fields with the simulation ones, good agreements are found. We then propose a simple theory with some simplification for the study of the migration of a single recalcitrant bubble, and after that weperform a series of 2D simulations to analyze the effects of density ratios, viscosity ratios, entrance average velocities of the flow, and the values of second derivative of surface tension with respect to the temperature.

3D Magneto-Buoyancy-Thermocapillary Convection of CNT-Water Nanofluid in the Presence of a Magnetic Field

A numerical study is performed to investigate the effects of adding Carbon Nano Tube (CNT) and applying a magnetic field in two directions (vertical and horizontal) on the 3D-thermo-capillary natural convection. The cavity is differentially heated with a free upper surface. Governing equations are solved using the finite volume method. Results are presented in term of flow structure, temperature field and rate of heat transfer. In fact, results revealed that the flow structure and heat transfer rate are considerably affected by the magnitude and the direction of the magnetic field, the presence of thermocapillary forces and by increasing nanoparticles volume fraction. In opposition, the increase of the magnetic field magnitude leads to the control the flow causing flow stabilization by merging vortexes and reducing heat transfer rate.

Three-Dimensional Reconstruction of Evaporation-Induced Instabilities Using Volumetric Scanning Particle Image Velocimetry

The three-dimensional (3D) flow below the interface of an evaporating liquid at a low pressure is visualized and quantified using scanning particle image velocimetry. The technique presented highlights the use of a single camera and a relatively fast moving laser sheet to image the flow for an application where using more than one camera is difficult. The technique allows collection of the full three-dimensional velocity vector map over the whole liquid volume. The out-of-plane component of the velocity has been determined using two different processing approaches: (i) deriving the full vector from a 3D cross-correlation of the particle volumes and (ii) applying the continuity equation to determine out-of-plane velocities from the calculated in-plane velocity vector fields. The results obtained from both methods showed good agreement with each other. The 3D velocity field reveals the existence of a torus shaped vortex below the evaporating meniscus that was induced by the exposure of the cold liquid to the warmer solid walls. The velocity data also shows that the maximum velocity occurs below the interface, not at the interface which highlights that the observed vortex is not driven by thermocapillary forces that usually govern the flow during evaporation at smaller scales.

Mathematical model of gas-free combustion of a binary powder mixture with allowance Marangoni convection

A macroscopic mathematical model has been developed for the gas-free combustion of a binary reaction mixture with allowance for thermocapillary convection of a low-melting reagent. The model includes equations as follows: mass balance of reaction substances, chemical transformation, melt motion, thermal conductivity. Melt formed during the melting of one of the components is believed to move in the porous carcass of the mixture due to thermocapillary forces. The dynamics of changes in temperature, chemical conversion depth, melt fraction and porosity are numerically calculated in a gasless combustion wave. Depending on the main parameters characterizing the process, conductive, convective, and mixed modes of synthesis front propagation are revealed. Analytical relationships are derived to estimate the combustion rate for these modes. An approximate criterion that reveals the synthesis mode from the structural and physicochemical parameters of the binary mixture is found.

Biomimetic liquid lenses actuated by a laser beam: effects of evaporation and orientation to gravity

Liquid lenses actuated by thermocapillary and solutocapillary forces via heating with a laser beam demonstrate a high level of adaptability.

Numerical simulation of small pool fires incorporating liquid fuel motion

For small-scale pool fires, Vali et al. [1] showed a pair of vortices in the liquid pool. The first vortex appeared just close to the sidewall of the container, and the second one emerged slightly away from the first vortex. Large-eddy simulations of small methanol pool fires coupled with liquid fuel convective flow were conducted using an in-house version of FireFOAM to investigate the above phenomenon. In this study, a three-dimensional liquid phase model is newly developed. The model incorporates the effects of thermocapillary Marangoni convection, buoyancy, shear stress, and evaporation. For the gas phase, the combustion model is the extended eddy dissipation concept model coupled with the laminar combustion model. This combustion model uses the viscous diffusion rate to consider laminar-turbulent transition. The predictions were in reasonably good agreement with the measured local mass burning rate, flame height and distributions of liquid temperature. The error of the mass burning rate was within 4%. The present predictions captured a pair of vortices in line with Vali et al.'s experiment [1]. Their sizes increased with increasing the liquid temperature. The Reynolds analogy could explain the sensible reason behind this trend. Shear stress and thermocapillary force caused convection in the liquid pool, and this convection formed a pair of vortices. Thermocapillary force was due to the different distributions of convective and radiative heat transfer. Sensitivity test for sub-models for the liquid phase demonstrated that their effects on the mass burning rate were all less than 5.1%. Conversely, the simulation assuming zero gravity only in the liquid phase resulted in almost 64% reduction in the mass burning rate.

Localization of Melt Components in a Crucible as a Result of Inserting Anisothermic Rod with Non-wettable Boundaries

Concentration-induced convection of a binary metal melt in a rectangular crucible has been studied numerically in the case of a mixture with a eutectic phase diagram. The calculations are performed for realistic parameters which correspond to the pair of metals Sn-Pb. A solid rod with non-wettable boundaries and a non-uniform longitudinal temperature distribution on the surface is immersed into the melt vertically at the center of the crucible. The condition of complete non-wetting allows us to consider the interface between the melt and the rod to be free. The temperature non-uniformity leads to inhomogeneity of the surface tension. As a result, the thermocapillary force generates a steady convective flow first on the surface of the rod and then in the volume. Due to this motion, the heavy component of the alloy is transferred along the rod’s surface to the butt-end. At the boundary patches with the excess of concentration it has been extracted into the volume by means of the desorption mechanism. In the presence of weak convection in the volume, this component is partially accumulated near the bottom of the crucible under the butt-end. Thus, there takes place a process of separation of heavy admixture for the two-component metal melts.

Thermocapillary Convection Instability in Annular Two-Layer System under Various Gravity Levels

In order to reveal the impact mechanism of gravity acceleration on thermocapillary convection instability in two-layer system, the flow characteristics of two-layered thermocapillary convection in annular pool under various gravity levels is investigated by 3D numerical simulation, in which the outer and inner walls are differentially heated. The interface of fluids is assumed to be a flat non-deformable interface, where thermocapillary forces act on. The computational results show that, with the increase of gravitational acceleration the convective structure of the upper layer changes from multi-cell structure to singe cell structure, then to multi-cell structure; while in the lower layer the flow changes from multi-cell to single cell structure. The convection instability mode also is modified, and the wave number at the interface decreases from seven to six. The average oscillatory amplitude of azimuthal velocity decreases with the increase of gravitational acceleration.

Destruction of waves and formation of rivulets on the surface of a heated liquid film at Re = 10

The mechanism of transformation of developed naturally formed waves into thermocapillary-wave structures in the vertical flow of a heated water film was studied experimentally. The motion of large waves whose width significantly exceeds the distance between the thermocapillary rivulets (transverse inhomogeneities of thickness and temperature), which have already formed in the residual film layer in front of the incoming large wave was studied in detail. It is shown that combination of thermocapillary and inertial effects in a wavy liquid film leads to deformation of large waves and their decay into the waves of a smaller width. Various scenarios of large wave destruction are considered. It is found out that when medium and small waves move, the thermocapillary forces change the distance between their crests, adjusting them to the distance between the forming structures in the residual layer.The regime maps, where the flow is divided into two zones: the region of deformation of three-dimensional waves and the region of developed rivulet flow, have been plotted for different heat fluxes.Various scenarios of changes in three-dimensional waves occur in the region of their deformation. In the region of developed rivulet flow, the motion of waves obeys the general laws. Waves propagate only along the rivulets with the average inter-rivulet distance equal to five capillary constants. Between the rivulets, the film is smooth. The amplitude of waves (the maximal film thickness) in the rivulets and their velocity increase as they move along the heater.

Dynamics of laser-induced microbubbles in an absorbing liquid

The generation and subsequent dynamics of a microbubble in a liquid are investigated, both experimentally and theoretically. When a laser beam is focused into an absorbing liquid comprising colloidal red dye particles in isopropanol alcohol inside a thick quartz cuvette, microbubbles can be generated at around the focus due to nucleation and thermal cavitation. It is experimentally shown that in some cases, the generated microbubble that initially moves away from the focus due to the longitudinal optical gradient force is later attracted to the focus due to the longitudinal thermocapillary force. In our previous work, the thermocapillary force acting on a microbubble is studied two dimensionally. The thermocapillary force acting on the microbubble is determined by directly solving the three-dimensional (3-D) heat equation by 3-D Fourier transform methods. When developing the complete force model in microbubble dynamics, the thermo-capillary force, optical force, buoyancy force, gravity, and the viscous force have been considered.

Thermocapillary rivulets in a locally heated falling liquid film

The formation of a three-dimensional rivulet structure in a heated falling liquid film is investigated theoretically. For a description of the dynamics of a non-isothermal film, the theoretical model is developed taking into account the thermocapillary force. Within the framework of the spatial approach, a linear analysis of the stability of the heated film relative to perturbations in the spanwise direction to the flow is performed for the first time. A spatial growth rate of these perturbations down-stream is obtained. Analysis of experimental data for different liquids and different Reynolds numbers has shown that the distance between the rivulets corresponds well to the wavelength of most amplified perturbation. The stationary rivulet structure in the film is simulated by numerical method for two types of heating conditions implemented in our previous experiments: with constant wall temperature and heat flux on the wall. Calculations show, that on a heater with constant temperature of a wall the developed rivulet structure has a quasistationary character and very slightly changes downstream. The development of rivulets on a heater with a constant heat flux on the wall has been calculated for the first time. The good agreement between calculations and our experimental data is found for both types of heating conditions implemented in the experiments.

The influence of the surface microtexture on wettability properties and drop evaporation

The influence of different microstructure of the surface of aluminum alloy on the free convection in the liquid and the evaporation of the water drop were studied experimentally. Various textures were created using laser surface treatment. The character of water drop evaporation on heated structured surfaces was compared with that on untreated rough surface. Velocity fields were measured using the Micro Particle Image Velocimetry (Micro PIV) method. A chemical analysis of sample surfaces in the cavity and in its vicinity was carried out. The effect of different textures on the wettability properties is shown. The evaporation rate of a drop depends on several competing factors: the diameter of the wetted drop spot, the drop height, the convection due to the surface thermocapillary forces, and the convection caused by the surface microstructures. The article also assesses the individual impact of these factors. The greatest intensification of convection and evaporation is associated with textures in the form of craters with a diameter of about 50–100 μm. The competing influence of several parameters leads to the need of their optimization. This paper demonstrates a general approach to such an optimization.

Coupling effect of phase change heat transfer on free surface in pure steam environment and thermocapillary convection in annular pool

In order to reveal the coupling effect between surface phase change heat transfer in pure steam environment and thermocapillary convection in annular pool, we performed a series of three-dimensional numerical simulations by using the finite volume method based on the statistical evaporation rate theory. The inner and the outer radii of the annular pool are respectively 20 mm and 40 mm, the depth ranges from 1 mm to 20 mm. The selected working fluid is water with Prandtl number of 6.13. Results show that the radial temperature gradient on the free surface near the cylinders increases due to the latent heat absorbed and/or released as a result of phase change heat transfer, which leads to the increase of the thermocapillary force near the cylinders and the enhancement of the flow. Therefore, the isotherms converge to the cylinders. The axial velocity on the free surface caused by surface phase change is much less than the inward radial velocity. Flow pattern depends slightly on Marangoni number. But with the increase of Marangoni number, the flow is enhanced and the flow cells near the cylinders gradually expand to the middle of the annular pool. With the increase of the aspect ratio, thermocapillary convection is enhanced and the evaporation strengthens. With the increase of ambient steam temperature and pressure, the condensation mass flux near the inner cylinder increases, the radial temperature gradient rises, and thermocapillary convection strengthens. However, near the outer cylinder, it is the opposite.

Pore elimination mechanisms during 3D printing of metals

Laser powder bed fusion (LPBF) is a 3D printing technology that can print metal parts with complex geometries without the design constraints of traditional manufacturing routes. However, the parts printed by LPBF normally contain many more pores than those made by conventional methods, which severely deteriorates their properties. Here, by combining in-situ high-speed high-resolution synchrotron x-ray imaging experiments and multi-physics modeling, we unveil the dynamics and mechanisms of pore motion and elimination in the LPBF process. We find that the high thermocapillary force, induced by the high temperature gradient in the laser interaction region, can rapidly eliminate pores from the melt pool during the LPBF process. The thermocapillary force driven pore elimination mechanism revealed here may guide the development of 3D printing approaches to achieve pore-free 3D printing of metals.

Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall

Thermocapillary flow of silicon melt (Pr=0.011) in shallow annular pool heated from inner wall was simulated at the dimensionless rotation rate ω ranging from 0~7000. The effect of pool rotation on the stability of the thermocapillary flow was investigated. The steady axisymmetric basic state was solved by using the spectral element method; the critical stability parameters were determined by linear stability analysis; the mechanism of the flow instability was explored by the analysis of energy balance. A stability diagram, exhibiting the variation of the critical Marangoni number versus the dimensionless rotation rate ω was presented. The results reveal that only one Hopf bifurcation point appeared in the intervals of ω 3965, and the corresponding instability was caused by the shear energy, which was provided by the thermocapillary force and pool rotation, respectively. In addition, the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.

On the Thermocapillary Migration on Radially Microgrooved Surfaces.

Thermocapillary migration describes the phenomenon in which a droplet placed on a nonuniformly heated surface can migrate from warm to cold regions. Herein, we report an experimental investigation of the migration of silicone oil droplets on radially microgrooved surfaces subjected to a thermal gradient; the effects of the initial divergence angle and divergent direction on the migration behavior are highlighted. A theoretical model is established to predict the migration velocity considering the thermocapillary, viscous resistance, and radial structure-induced forces; furthermore, the proposed theoretical derivation is validated. This study advances the understanding of this interfacial phenomenon, which has great potential for regulating and controlling liquid motion in lubrication systems, condensation and heat-transfer devices, and open microfluidics.

Resonance excitation of surface capillary waves to enhance material removal for laser material processing

The results of detailed experiments and high fidelity modeling of melt pool dynamics, droplet ejections and hole drilling produced by periodic modulation of laser intensity are presented. Ultra-high speed imaging revealed that melt pool oscillations can drive large removal of material when excited at the natural oscillation frequency. The physics of capillary surface wave excitation is discussed and simulation is provided to elucidate the experimental results. The removal rates and drill through times as a function of driving frequency is investigated. The resonant removal mechanism is driven by both recoil momentum and thermocapillary force but the key observation is the latter effect does not require evaporation of material, which can significantly enhance the efficiency for laser drilling process. We compared the drilling of holes through a 2 mm-thick Al plate at modulation frequencies up to 20 kHz. At the optimal frequency of 8 kHz, near the resonant response of the melt pool, the drilling efficiency is greater than 10x with aspect ratio of 12:1, and without the collateral damage that is observed in unmodulated CW drilling.

Three-Dimensional Numerical Simulation on Thermocapillary Convection of Moderate Prandtl Number Fluid in an Annular Shallow Pool with Surface Heat Dissipation

In order to understand the effect of surface heat dissipation on thermocapillary convection of moderate Prandtl number fluid in an annular shallow pool, we performed a series of three-dimensional numerical simulations by using the finite volume method. An annular shallow pool is full of 0.65cSt silicone oil with Prandtl number of 6.7. The radius ratio and the aspect ratio of the pool are respectively fixed at 0.5 and 0.1. Surface heat dissipation Biot number is varied from 0 to 50. Results indicate that the critical Marangoni number of flow destabilization mainly depends on the coupling effect of the thermocapillary force and surface heat dissipation on the free surface, which decreases first, and then increases gradually. When Biot number is small, the steady axisymmetric flow after the flow destabilization will bifurcate to the hydrothermal wave. With the increase of Marangoni number, the flow pattern evolution at a small Biot number is similar to that of an adiabatic free surface, and the fundamental oscillatory frequency increases gradually. With the increase of Biot number, the radial roll cells near the outer cylindrical wall gradually extend to the inner wall, and eventually occupy the whole liquid pool. When Biot number is large, the flow pattern after the flow destabilization is a radial rolling cell pattern with alternating azimuthal direction. Then it gradually evolves into azimuthal waves, and the fundamental oscillatory frequency has a slight decrease.

Multiphysics modelling of lack-of-fusion voids formation and evolution in IN718 made by multi-track/multi-layer L-PBF

Laser-based powder bed fusion (L-PBF) is a branch of additive manufacturing technology which is considered to be a superior process due to its capability of producing complex designs with low material waste. Despite L-PBFs various unique characteristics, manufactured parts still suffer from a wide variety of defects, among which porosity is one of the most important. In this paper, a multiphysics numerical model for the multi-track/multi-layer L-PBF is developed and used for analysing the formation and evolution of voids caused by lack of fusion and improper melting. The multiphysics model is in meso-scale and is used to track and observe the formation of porosities, and considers phenomena such as multi-phase flow, melting/solidification, radiation heat transfer, capillary and thermo-capillary (Marangoni effect) forces, recoil pressure, geometry dependant absorptivity and finally evaporation and evaporative cooling. A novel methodology has been introduced to model the two subsequent powder-laying and fusion processes, for each layer, by means of a discrete element method (DEM) in a Lagrangian framework and a computational fluid dynamics (CFD) model, both implemented in Flow-3D. The results for the investigated process parameters indicate that the porosities (voids) are mainly formed in between the tracks, largely due to improper fusion of the particles. Moreover, it is observed that the pores are mostly elongated in the direction parallel to the laser scanning paths, as expected. The probability of the presence of pores is also observed to be higher in the first layer, where the average layer temperature is lower as well. Furthermore, the lack of fusion zones are seen to become smaller in the subsequent layers, largely due to better fluid flow and higher temperatures, because of heat accumulation in those layers.