Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Method

In this paper,we study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the interface.We employ an energetic variational phase field model to describe its physical phenomena,and obtain the corresponding governing equations defined by a modi-fied Navier-Stokes equations coupled with phase field and energy transport.A mixed Taylor-Hood finite element discretization together with full Newton’s method are applied to this strongly nonlinear phase field model on a specific domain.Under different boundary conditions of temperature,the resulting numerical solutions illustrate that the thermal energy plays a fundamental role in the interfacial dynamics of two-phase flows.In particular,it gives rise to a dynamic interfacial tension that depends on the direction of temperature gradient,determining the movement of the interface along a sine/cosine-like curve.

Optical Study on Concentration-Driven Rayleigh-Bénard-Marangoni Convection

By utilizing optical Schlieren method, the Rayleigh Bénard Marangoni convection in mass transfer process was observed. A recorder and a camera separately recorded dynamic and static convective flow patterns during experiments . Different organic solvents were selected to investigate the RBM effects induced by different driving mechanisms including density gradient, surface tension gradient and their combination. Thermal effects produced by solvents evaporation and solute absorption/desorption are thought as an important factor in the creation of RBM convection during the mass transfer process. Qualitative analysis of experimental results is presented on the basis of photos and videotapes that were taken as direct visual evidences. Experimental results show that the thermal effect accompanying the mass transfer can be a cause at the onset of RBM convection and can′t be neglected simply in study of RBM effect driven by mass transfer.

Impact of solutal Marangoni convection on oil recovery during chemical flooding

In this study,the impacts of solutal Marangoni phenomenon on multiphase flow in static and micromodel geometries have experimentally been studied and the interactions between oil droplet and two different alkaline solutions(i.e.MgS04 and Na_2 CO_3) were investigated.The static tests revealed that the Marangoni convection exists in the presence of the alkaline and oil which should carefully be considered in porous media.In the micromodel experiments,observations showed that in the MgS04 flooding,the fluids stayed almost stationary,while in the Na2 C03 flooding,a spontaneous movement was detected.The changes in the distribution of fluids showed that the circular movement of fluids due to the Marangoni effects can be effective in draining of the unswept regions.The dimensional analysis for possible mechanisms showed that the viscous,gravity and diffusion forces were negligible and the other mechanisms such as capillary and Marangoni effects should be considered in the investigated experiments.The value of the new defined Marangoni/capillary dimensionless number for the Na2 C03 solution was orders of magnitude larger than the MgS04 flooding scenario which explains the differences between the two cases and also between different micromodel regions.In conclusion,the Marangoni convection is activated by creating an ultra-low IFT condition in multiphase flow problems that can be profoundly effective in increasing the phase mixing and microscopic efficiency.

Numerical Simulation of the Marangoni Effect with Interphase Mass Transfer Between Two Planar Liquid Layers

The Marangoni effect induced by mass transfer at the interface between two immiscible liquids displays important influence on laboratory and industrial operation of solvent extraction. A systematic numerical study of the two-dimensional Marangoni effect in a two liquid layer system was conducted. The linear relationship of the inter- facial tension versus the solute concentration was incorporated into a mathematical model accounting for liquid flow and mass transfer in both phases. The typical cases analyzed by Sternling ＆ Scriven （AIChE J., 1959） using the linear instability theory were simulated bv the finite difference method and good agreement between the theory and the numerical simulation was observed. The simulation suggests that the Marangoni convection needs certain time to develop sufficiently in strength and scale to enhance the interphase mass transfer, the Marangoni effect is dynamic and transient, and remains at some stabilized level as long as the mass transfer driving force is kept con- stant. When certain level of shear is imposed at the interface as in most cases of practical significance, the Maran- goni effect is suppressed slightly but progressively as the shear is increased gradually. The present two-dimensional simulation of the Marangoni effect provides some insight into the underlying mechanism and also the basis for further theoretical study of the three-dimensional Marangoni effect in the real world and in chemical engineering applications.

Influences of Marangoni effect on solidification of curved interfaces with constant curvature

The asymptotic method and phase field simulation are applied to study the influences of variation of the surface tension with temperature on the movements of solid-liquid interfaces in the solidification process of spherical and cylindrical nuclei, respectively. Results indicate that Marangoni effect will increase the critical nucleation radius, slow up the movement of interface. The tip speed of dendrite decreases linearly with Marangoni number for melt without convection. The results of phase field simulation are qualitatively in accord with that of asymptotic method.

Water-Excluding Underwater Glue Induced by Marangoni Effect

Marangoni effect at the two-phase interface with different surface tension as a unique mass transfer phenomenon has been widely used in daily life and industrialmanufacture.However,their marvelous liquid-driving capability between miscible liquids has long been ignored,especially in water environments.Here,we first reveal a distinct underwater Marangoni effect between the solvent of glues and the water layer on solid surfaces.Driven by the Marangoni effect,organic solvents with water solubility,high dielectric constant,and low diffusivity could effectively exclude the interfacial water layer,enabling direct and effective contact between glues and solid surfaces.Our experimental results and theoretical simulation proved that a relatively large ratio of the Marangoni number in the horizontal direction and to the vertical direction ensured an effective underwater adhesion of the water-excluding glue.This surface engineering approach provides an alternative to the traditional methods of molecular engineering for realizing underwater adhesion.

Performance evaluation of ultra-long lithium heat pipe using an improved lumped parameter model

Lithium heat pipes have broad applications in heat pipe cooling reactors and hypersonic vehicles owing to their ultra-high working temperature.In particular,when the length of the lithium heat pipe is ultra-long,the flow and heat transfer characteristics are more complex.In this study,an improved lumped parameter model that considers the Marangoni effect,bending effect,and different vapor flow patterns and Mach numbers was developed.Thereafter,the proposed model was verified using the University of New Mexico’s Heat Pipe and HTPIPE models.Finally,the verified model was applied to simulate the steady-state operation of an ultra-long lithium heat pipe in a Heat PipeSegmented Thermoelectric Module Converters space reactor.Based on the results:(1)Vapor thermal resistance was dominant at low heating power and decreased with increasing heating power.The vapor flow inside the heat pipe developed from the laminar to the turbulent phase,whereas the liquid phase in the heat pipe was always laminar.(2)The vapor pressure drop caused by bending was approximately 22–23%of the total,and the bending effect on the liquid pressure drop could be ignored.(3)The Marangoni effect reduced the capillary limit by hindering the liquid reflux,especially at low vapor temperatures.Without considering the Marangoni effect,the capillary limit of the lithium heat pipe was overestimated by 9%when the vapor temperature was 1400 K.(4)The total thermal resistance of the heat pipe significantly increased with increasing adiabatic length when the vapor temperature was low.Further,the wick dryness increased with increasing adiabatic length at any vapor temperature.Such findings improve on current knowledge for the optimal design and safety analysis of a heat pipe reactor,which adopts ultra-long lithium heat pipes.

Effect of Helium-Argon Mixtures on the Heat Transfer and Fluid Flow in Gas Tungsten Arc Welding

A transient finite element model has been developed to study the heat transfer and fluid flow during spot Gas Tungsten Arc Welding （GTAW） on stainless steel. Temperature field, fluid velocity and electromagnetic fields are computed inside the cathode, arc-plasma and anode using a unified MHD formulation. The developed model is then used to study the influence of different helium-argon gas mixtures on both the energy transferred to the workpiece and the time evolution of the weld pool dimensions. It is found that the addition of helium to argon increases the heat flux density on the weld axis by a factor that can reach 6.5. This induces an increase in the weld pool depth by a factor of 3. It is also found that the addition of only 10% of argon to helium decreases considerably the weld pool depth, which is due to the electrical conductivity of the mixture that increases significantly when argon is added to helium.

Numerical simulation of Marangoni effect induced by species transfer across iron droplet–molten slag interface

A mathematical model accounting for unsteady mass transfer across interface of a stationary iron droplet immersed into molten slag was established through the volume of fluid coupled with level set method.The Marangoni effect induced by mass transfer was reproduced successfully,and the hydrodynamic instability phenomena at the interface,such as the Marangoni convection flow,the evolution of the interfacial tension during the mass transfer,and the influence of Marangoni effect on the mass transfer rate,were revealed.The results show that the Marangoni convection flow develops quickly and behaves as an ordered structure in the forms of four pairs of the convection cell at the edge of the droplet once the oxygen transfer across the interface starts.The average convection flow velocity along the interface is high,even more than 0.025 m/s,depending on the droplet diameter,which facilitates the mass transfer.The Marangoni convection flow of the large droplet develops more easily than that of the small droplet,and the larger the droplet diameter is,the higher the convection flow velocity and the mass transfer rate are.Moreover,it is shown that the droplet diameter influences the impacting region of the Marangoni convection flow and its duration period.

Controllable formation of periodic wrinkles in Marangoni-driven self-assembled graphene film for sensitive strain detection

Controllable formation of microstructures in the assembled graphene film could tune the physical properties and broaden its applications in flexible electronics.Many efforts have been made to control the formation of wrinkles and ripples in graphene films.However,the formation of orderly wrinkles in graphene film remains a challenge.Here,we reported a simple strategy for the fabrication of graphene film with periodic and parallel wrinkles with a pre-stretched polydimethylsiloxane substrate.The width of the wrinkles in graphene can be controlled by changing the pre-stretched strain of the substrate.The average width of wrinkles in graphene film on the substrate with pre-stretched strain of 10%,20%,and 50%was about 3.68,2.99 and 2.01µm,respectively.The morphological evolution of wrinkled double-layered graphene under mechanical deformation was observed and studied.Furthermore,a strain sensor was constructed based on the wrinkled graphene,showing high sensitivity,large working range and excellent cyclic stability.These strain sensors show great potential in real-time motion detection,health surveillance and electronic skins.

Interface Shape and Marangoni Effect Around aBubble Within the Thermal Boundary Layer

The characteristics of a vapor bubble within the thermal boundary layer were theoretically analyzed.The physical models accounting for the variation of ioterfacial tension and nuid density with tempera-ture were proposed to investigate bubble interfaCe aspects and the fluid flow around the bubble. The analyses demonstrated that the variation in interfacial tension results in variations in the liquid-vapor interface shape and bubble dynamics, which may play a significant role in the departure process of a vapor bubble from a heated wall surface. Increasing temperature gradients in the boundary layer and the gravitational field induce a contact line contraction and correspondingly promotes bubble depar-ture. The simulation of liquid now around the bubble shows that natural convection dominates the flow for earth conditions; however, the thermocapillary forces provide the principal catalyst for bubble departure in a microgravity environment. The results indicate that both the vapor bubble contraction and the Marangoni flow may increase the heat transfer around the vapor bubble and may cause the bubble to mov away from the heating surface, further increasing heat transfer.

Tackling the Short-Lived Marangoni Motion Using a Supramolecular Strategy

Inspired by the intriguing capability of beetles to quickly slide on water,scientists have long imagined the use of this surface-tension-gradient-dominated Marangoni motion in various applications,for exam-ple,self-propulsion.

Experimental Study on Hydrodynamic Behavior of Falling Film over Vertical Tube

Falling film configurations play an important role in characterizing the heat transfer due to changes in hydrodynamic behavior.The purpose of this study is to establish a novel film distributor to investigate the hydrodynamic behavior of the falling film on the vertical tube.The falling film thickness and flow patterns on the vertical tube were analyzed at a feed water temperature of 30℃ for film Re ranged from 53 to 4544 and the heat fluxes ranged from 1.33 to 49.45 kW/m^(2).The correlation between the average falling film thickness and the film Re was fitted;the maximum deviation between the experimental data and the predicted values was 7.58%.Additionally,the film thickness changed sharply when the heat flux increased to a certain value.With the further increase of the heat flux,dry patches appeared on the surface of the experimental tube.There was Marangoni effect on vertical tube and the falling film thickness and flow patterns were significantly affected by heating.The interval value of the critical heat flux with film Re was obtained.Compared with the porous film distributor reported in the literature,the critical heat flux of the new film distributor increased by 3.72%-56.95%.

Dynamics of Discrete Bubble in Nucleate Pool Boiling on Thin Wires in Microgravity

A space experiment on bubble behavior and heat transfer in subcooled pool boiling phenomenon has been performedutilizing the temperature-controlled pool boiling (TCPB) device both in normal gravity in the laboratoryand in microgravity aboard the 22^(nd) Chinese recoverable satellite. The fluid is degassed R113 at 0.1 MPa andsubcooled by 26℃ nominally. A thin platinum wire of 60 μm in diameter and 30 mm in length is simultaneouslyused as heater and thermometer. Only the dynamics of the vapor bubbles, particularly the lateral motion and thedeparture of discrete vapor bubbles in nucleate pool boiling are reported and analyzed in the present paper. It'sfound that these distinct behaviors can be explained by the Marangoni convection in the liquid surrounding vaporbubbles. The origin of the Marangoni effect is also discussed.

Thickness Uniformity Adjustment of Inkjet Printed Light-emitting Polymer Films by Solvent Mixture

In this paper, thickness uniformity of poly（9,9-di-n-octylfluorene） films patterned by inkjet printing was im- proved by the use of solvent mixtures （a solvent with higher volatility, higher surface energy and lower viscosity, with another solvent with lower volatility, lower surface energy and higher viscosity）. The average thickness of inkjet printed poly（9,9-di-n-octylfluorene） films was increased from ca. 30 nm to ca. 100 nm when solvent mixtures were used instead of pure chlorobenzene. More flat PFO films were formed instead of the original films with con- cave-lens like cross-section formed by coffee ring effect. This improvement was explained by combination of in- tense Marangoni flow at early drying process and weak complementary flow at the later drying process formed in the solvent mixture. Patterned poly（9,9-di-n-octylfluorene） films were used for fabrication of electroluminescence devices with improved electronic property. Array of pixels with about 80% effective light-emitting area was ob- tained.

An Experimental Study on the Phenomena inside the Burning Aviation Kerosene Droplet

This paper conducted an experimental study of droplet behavior characteristics occurring within a burning aviation kerosene droplet and on the droplet interface.The droplet combustion was performed in a quiescent high-temperature environment by means of the droplet suspension technique.The soot particles were used as tracers to visualize the fluid motion in the droplet.The shape variation of droplet,internal flow pattern in the burning droplet,and instabilities at gas-liquid phase interface were recorded by a high speed camera.The internal fluid flow in the droplet was revealed to be caused by the Marangoni effect,which was generated because of the surface tension gradient induced by the temperature gradient on the droplet surface.The studies showed that the Marangoni effect has a significant impact on the internal flow.The amplitude of the capillary waves on the surface of the droplet was non-uniform and presented the amplitude characteristics of large-small-some.The wavelength of the capillary waves for burning aviation kerosene droplet ranged from 110μm to 120μm.

Numerical Study of Surfactant-Laden Drop-Drop Interactions

In this paper,we numerically investigate the effects of surfactant on dropdrop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in(Xu et al.,J.Comput.Phys.,212(2006),590–616).We find that surfactant plays a critical and nontrivial role in drop-drop interactions.In particular,we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary number.This non-monotonic behavior,which does not occur for clean drops,is found to be due to the presence of Marangoni forces along the drop interfaces.This suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops,as observed in recent experiments of Leal and co-workers.Although our study is two-dimensional,we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.