Showing papers on "Marangoni effect published in 2010"
TL;DR: In this article, the final stage of a whole blood drop evaporation reveals regular patterns with a good reproducibility for a healthy person, and the same axisymetric pattern formation is observed, and can be forecast for different blood drop diameters.
Abstract: The drying of a drop of human blood exhibits coupled physical mechanisms, such as Marangoni flow, evaporation and wettability. The final stage of a whole blood drop evaporation reveals regular patterns with a good reproducibility for a healthy person. Other experiments on anaemic and hyperlipidemic people were performed, and different patterns were revealed. The flow motion inside the blood drop is observed and analyzed with the use of a digital camera: the influence of the red blood cells (RBCs) motion is revealed at the drop periphery as well as its consequences on the final stage of drying. The mechanisms which lead to the final pattern of the dried blood drops are presented and explained on the basis of fluid mechanics in conjunction with the principles of haematology. The blood drop evaporation process is evidenced to be driven only by Marangoni flow. The same axisymetric pattern formation is observed, and can be forecast for different blood drop diameters. The evaporation mass flux can be predicted with a good agreement, assuming only the knowledge of the colloids mass concentration.
249 citations
TL;DR: It is argued that the dramatic reduction in hydrodynamic resistance is a transition from viscosity-controlled drainage to inertia- controlled drainage associated with a change from immobile to mobile air/water interfaces on increasing the speed of approach of two bubbles.
Abstract: Film thinning experiments have been conducted with aqueous films between two air phases in a thin film pressure balance. The films are free of added surfactant but simple NaCl electrolyte is added in some experiments. Initially the experiments begin with a comparatively large volume of water in a cylindrical capillary tube a few millimeters in diameter, and by withdrawing water from the center of the tube the two bounding menisci are drawn together at a prescribed rate. This models two air bubbles approaching at a controlled speed. In pure water, the results show three regimes of behavior depending on the approach speed; at slow speed (<1 microm/s) it is possible to form a flat film of pure water, approximately 100 nm thick, that is stabilized indefinitely by disjoining pressure due to repulsive double-layer interactions between naturally charged air/water interfaces. The data are consistent with a surface potential of -57 mV on the bubble surfaces. At intermediate approach speed (approximately 1-150 microm/s), the films are transiently stable due to hydrodynamic drainage effects, and bubble coalescence is delayed by approximately 10-100 s. At approach speeds greater than approximately 150 microm/s, the hydrodynamic resistance appears to become negligible, and the bubbles coalesce without any measurable delay. Explanations for these observations are presented that take into account Derjaguin-Landau-Verwey-Overbeek and Marangoni effects entering through disjoining pressure, surface mobility, and hydrodynamic flow regimes in thin film drainage. In particular, it is argued that the dramatic reduction in hydrodynamic resistance is a transition from viscosity-controlled drainage to inertia-controlled drainage associated with a change from immobile to mobile air/water interfaces on increasing the speed of approach of two bubbles. A simple model is developed that accounts for the boundaries between different film stability or coalescence regimes. Predictions of the model are consistent with the data, and the effects of adding electrolyte can be explained. In particular, addition of electrolyte at high concentration inhibits the near-instantaneous coalescence phenomenon, thereby contributing to increased foam film stability at high approach speeds, as reported in previous literature. This work highlights the significance of bubble approach speed as well as electrolyte concentration in affecting bubble coalescence.
148 citations
TL;DR: The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence, and it is demonstrated that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process.
121 citations
20 Apr 2010
TL;DR: In this paper, Eustathopoulos et al. presented a theoretical analysis of the shape stability in the Czochralski process with respect to the surface energy and surface tension.
Abstract: Preface. Introduction. Acknowledgements. Nomenclature. Contributors. 1. Basic Principles of Capillarity in Relation to Crystal Growth (Nicolas Eustathopoulos, Beatrice Drevet, Simon Brandon and Alexander Virozub). 1.1 Definitions. 1.1.1 Characteristic Energies of Surfaces and Interfaces. 1.1.2 Capillary Pressure. 1.1.3 Surface Energy versus Surface Tension. 1.2 Contact Angles. 1.2.1 Thermodynamics. 1.2.2 Dynamics of Wetting. 1.2.3 Measurements of Contact Angle and Surface Tension by the Sessile Drop Technique. 1.2.4 Selected Data for the Contact Angle for Systems of Interest for Crystal Growth. 1.3 Growth Angles. 1.3.1 Theory. 1.3.2 Measurements of Growth Angles: Methods and Values. 1.3.3 Application of the Growth Angle Condition in Simulations of Crystal Growth. 1.3.4 Summary. Acknowledgements. References. 2. The Possibility of Shape Stability in Capillary Crystal Growth and Practical Realization of Shaped Crystals (Vitali A. Tatartchenko). 2.1 Crucible-Free Crystal Growth Capillary Shaping Techniques. 2.2 Dynamic Stability of Crystallization the Basis of Shaped Crystal Growth by CST. 2.2.1 Lyapunov Equations. 2.2.2 Capillary Problem Common Approach. 2.2.3 Equation of Crystal Dimension Change Rate. 2.2.4 Equation of Crystallization Front Displacement Rate. 2.2.5 Stability Analysis in a System with Two Degrees of Freedom. 2.3 Stability Analysis and Growth of Shaped Crystals by the Cz Technique. 2.3.1 Capillary Problem. 2.3.2 Temperature Distribution in the Crystal Melt System. 2.3.3 Stability Analysis and Shaped Crystal Growth. 2.3.4 Dynamic Stability Problem for the Kyropoulos Technique. 2.4 Stability Analysis and Growth of Shaped Crystals by the Verneuil Technique. 2.4.1 Principal Schemes of Growth. 2.4.2 Theoretical Investigation. 2.4.3 Practical Results of the Theoretical Analysis. 2.4.4 Stability Analysis-Based Automation. 2.5 Stability Analysis and Growth of Shaped Crystals by the FZ Technique. 2.6 TPS Techniques: Capillary Shaping and Impurity Distribution. 2.6.1 Capillary Boundary Problem for TPS. 2.6.2 Stability Analysis. 2.6.3 Experimental Tests of the Capillary Shaping Theory Statements. 2.6.4 Impurity Distribution. 2.6.5 Definition of TPS. 2.6.6 Brief History of TPS. 2.7 Shaped Growth of Ge, Sapphire, Si, and Metals: a Brief Presentation. 2.7.1 Ge. 2.7.2 Sapphire. 2.7.3 Si. 2.7.4 Metals and Alloys. 2.8 TPS Peculiarities. References. 3 Czochralski Process Dynamics and Control Design (Jan Winkler, Michael Neubert, Joachim Rudolph, Ning Duanmu and Michael Gevelber). 3.1 Introduction and Motivation. 3.1.1 Overview of Cz Control Issues. 3.1.2 Diameter Control. 3.1.3 Growth Rate Control. 3.1.4 Reconstruction of Quantities not Directly Measured. 3.1.5 Specifi c Problems for Control in Cz Crystal Growth. 3.1.6 PID Control vs. Model-Based Control. 3.1.7 Components of a Control System. 3.1.8 Modelling in Crystal Growth Analysis and Control. 3.2 Cz Control Approaches. 3.2.1 Proper Choice of Manipulated Variables. 3.2.2 Feedforward Control. 3.2.3 Model-Based Analysis of the Process. 3.2.4 Stability. 3.2.5 Model-Based Control. 3.2.6 Identification. 3.2.7 Measurement Issues and State Estimation. 3.3 Mathematical Model. 3.3.1 Hydromechanical Geometrical Model. 3.3.2 Model of Thermal Behaviour. 3.3.3 Linear System Model Analysis. 3.4 Process Dynamics Analysis for Control. 3.4.1 Operating Regime and Batch Implications. 3.4.2 Actuator Performance Analysis. 3.4.3 Curved Interface. 3.4.4 Nonlinear Dynamics. 3.5 Conventional Control Design. 3.5.1 Control Based on Optical Diameter Estimation. 3.5.2 Weight-Based Control. 3.6 Geometry-Based Nonlinear Control Design. 3.6.1 Basic Idea. 3.6.2 Parametrization of the Hydromechanical Geometrical Model in Crystal Length. 3.6.3 Flatness and Model-Based Feedback Control of the Length-Parametrized Model. 3.6.4 Control of Radius and Growth Rate. 3.7 Advanced Techniques. 3.7.1 Linear Observer Design. 3.7.2 Nonlinear Observer Design. 3.7.3 Control Structure Design for Batch Disturbance Rejection. References. 4 Floating Zone Crystal Growth (Anke Ludge, Helge Riemann, Michael Wunscher, Gunter Behr, Wolfgang Loser, Andris Muiznieks and Arne Croll). 4.1 FZ Processes with RF Heating. 4.1.1 FZ Method for Si by RF Heating. 4.1.2 FZ Growth for Metallic Melts. 4.2 FZ Growth with Optical Heating. 4.2.1 Introduction. 4.2.2 Image Furnaces. 4.2.3 Laser Heating. 4.2.4 FZ Growth for Oxide Melts. 4.3 Numerical Analysis of the Needle-Eye FZ Process. 4.3.1 Literature Overview. 4.3.2 Quasi-Stationary Axisymmetric Mathematical Model of the Shape of the Molten Zone. 4.3.3 Numerical Investigation of the Influence of Growth Parameters on the Shape of the Molten Zone. 4.3.4 Nonstationary Axisymmetric Mathematical Model for Transient Crystal Growth Processes. Appendix: Code for Calculating the Free Surface During a FZ Process in Python. References. 5 Shaped Crystal Growth (Vladimir N. Kurlov, Sergei N. Rossolenko, Nikolai V. Abrosimov and Kheirreddine Lebbou). 5.1 Introduction. 5.2 Shaped Si. 5.2.1 EFG Method. 5.2.2 Dendritic Web Growth. 5.2.3 String Ribbon. 5.2.4 Ribbon Growth on Substrate (RGS). 5.3 Sapphire Shaped Crystal Growth. 5.3.1 EFG. 5.3.2 Variable Shaping Technique (VST). 5.3.3 Noncapillary Shaping (NCS). 5.3.4 Growth from an Element of Shape (GES). 5.3.5 Modulation-Doped Shaped Crystal Growth Techniques. 5.3.6 Automated Control of Shaped Crystal Growth. 5.4 Shaped Crystals Grown by the Micro-Pulling Down Technique ( -PD). 5.4.1 Crucible Melt Relation During Crystal Growth by the -PD Technique. 5.4.2 Examples of Crystals Grown by the -PD Technique. 5.5 Conclusions. References. 6 Vertical Bridgman Technique and Dewetting (Thierry Duffar and Lamine Sylla). 6.1 Peculiarities and Drawbacks of the Bridgman Processes. 6.1.1 Thermal Interface Curvature. 6.1.2 Melt Crystal Crucible Contact Angle. 6.1.3 Crystal Crucible Adhesion and Thermomechanical Detachment. 6.1.4 Spurious Nucleation on Crucible Walls. 6.2 Full Encapsulation. 6.2.1 Introduction. 6.2.2 LiCl KCl Encapsulant for Antimonides. 6.2.3 B2O3 Encapsulant. 6.2.4 Conclusion. 6.3 The Dewetting Process: a Modified VB Technique. 6.3.1 Introduction. 6.3.2 Dewetting in Microgravity. 6.3.3 Dewetting in Normal Gravity. 6.3.4 Theoretical Models of Dewetting. 6.3.5 Stability Analysis. 6.4 Conclusion and Outlook. References. 7 Marangoni Convection in Crystal Growth (Arne Croll, Taketoshi Hibiya, Suguru Shiratori, Koichi Kakimoto and Lijun Liu). 7.1 Thermocapillary Convection in Float Zones. 7.1.1 Model Materials. 7.1.2 Semiconductors and Metals. 7.1.3 Effect of Oxygen Partial Pressure on Thermocapillary Flow in Si. 7.1.4 Fluid Dynamics of Thermocapillary Flow in Half-Zones. 7.1.5 Full Float Zones. 7.1.6 The Critical Marangoni Number Mac2. 7.1.7 Controlling Thermocapillary Convection in Float Zones. 7.2 Thermocapillary Convection in Cz Crystal Growth of Si. 7.2.1 Introduction. 7.2.2 Surface Tension-Driven Flow in Cz Growth. 7.2.3 Numerical Model. 7.2.4 Calculation Results. 7.2.5 Summary of Cz Results. 7.3 Thermocapillary Convection in EFG Set-Ups. 7.4 Thermocapillary Convection in Bridgman and Related Set-Ups. 7.5 Solutocapillary Convection. References. 8 Mathematical and Numerical Analysis of Capillarity Problems and Processes (Liliana Braescu, Simona Epure and Thierry Duffar). 8.1 Mathematical Formulation of the Capillary Problem. 8.1.1 Boundary Value Problems for the Young Laplace Equation. 8.1.2 Initial and Boundary Conditions of the Meniscus Problem. 8.1.3 Approximate Solutions of the Axisymmetric Meniscus Problem. 8.2 Analytical and Numerical Solutions for the Meniscus Equation in the Cz Method. 8.3 Analytical and Numerical Solutions for the Meniscus Equation in the EFG Method. 8.3.1 Sheets. 8.3.2 Cylindrical Crystals. 8.4 Analytical and Numerical Solutions for the Meniscus Equation in the Dewetted Bridgman Method. 8.4.1 Zero Gravity. 8.4.2 Normal Gravity. 8.5 Conclusions. Appendix: Runge Kutta Methods. A.1 Fourth-Order Runge Kutta Method (RK4). A.2 Rkfixed and Rkadapt Routines for Solving IVP. References. Index.
118 citations
TL;DR: The asymptotic analysis indicates that these two directions will reverse at a critical contact angle, which depends not only on the relative thermal conductivities of the substrate and liquid, but also on the ratio of the substrates thickness to the contact-line radius of the droplet.
Abstract: The thermal Marangoni flow induced by nonuniform surface temperature has been widely invoked to interpret the deposition pattern from drying drops. The surface temperature distribution of a drying droplet, although being crucial to the Marangoni flow, is still controversial. In this paper, the surface temperature in the drop central region is analyzed theoretically based on an asymptotic analysis on the heat transfer in such region, and a quantitative criterion is established for the direction of the surface temperature gradient and the direction of the induced Marangoni flow of drying drops. The asymptotic analysis indicates that these two directions will reverse at a critical contact angle, which depends not only on the relative thermal conductivities of the substrate and liquid, but also on the ratio of the substrate thickness to the contact-line radius of the droplet. The theory is corroborated experimentally and numerically, and may provide a potential means to control deposition patterns from drying droplets.
101 citations
TL;DR: In this paper, the evolution of dissolved oxygen in the weld pool as a function of temperature can have a profound influence on the fluid flow and hence on energy transport, and time-dependent changes in oxygen concentration at the surface are observed to flip the surface tension temperature gradient from negative to positive under appropriate shielding conditions.
96 citations
TL;DR: In this article, a non-normal approach was used to predict the onset of instability, critical wavenumber and time in a plane liquid layer with time-dependent temperature profile by means of a general method suitable for linear stability analysis of an unsteady basic flow.
Abstract: The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wavenumber and time. The method is applied to transient Rayleigh–Benard–Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.
85 citations
TL;DR: In this paper, the role of surface viscosity in the classical film-coating problem is investigated, and a theoretical model that predicts film thickening based on a purely surface-viscous theory is proposed.
Abstract: The role of surface rheology in fundamental fluid dynamical systems, such as liquid coating flows and soap film formation, is poorly understood. We investigate the role of surface viscosity in the classical film-coating problem. We propose a theoretical model that predicts film thickening based on a purely surface-viscous theory. The theory is supported by a set of new experimental data that demonstrates slight thickening even at very high surfactant concentrations for which Marangoni effects are irrelevant. The model and experiments represent a new regime that has not been identified before.
72 citations
TL;DR: In this article, a finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well as Laplace and Marangoni stresses on the liquid-gas boundary.
71 citations
TL;DR: A novel method for bubble or droplet displacement, capture and switching within a bifurcation channel for applications in digital microfluidics based on the Marangoni effect, i.e. the appearance of thermocapillary tangential interface stresses stemming from local surface tension variations.
Abstract: We report a novel method for bubble or droplet displacement, capture and switching within a bifurcation channel for applications in digital microfluidics based on the Marangoni effect, i.e. the appearance of thermocapillary tangential interface stresses stemming from local surface tension variations. The specificity of the reported actuation is that heating is provided by an optimized resistor pattern (B. Selva, J. Marchalot and M.-C. Jullien, An optimized resistor pattern for temperature gradient control in microfluidics, J. Micromech. Microeng., 2009, 19, 065002) leading to a constant temperature gradient along a microfluidic cavity. In this context, bubbles or droplets to be actuated entail a surface force originating from the thermal Marangoni effect. This actuator has been characterized (B. Selva, I. Cantat, and M.-C. Jullien, Migration of a bubble towards a higher surface tension under the effect of thermocapillary stress, preprint, 2009) and it was found that the bubble/droplet (called further element) is driven toward a high surface tension region, i.e. toward cold region, and the element velocity increases while decreasing the cavity thickness. Taking advantage of these properties three applications are presented: (1) element displacement, (2) element switching, detailed in a given range of working, in which elements are redirected towards a specific evacuation, (3) a system able to trap, and consequently stop on demand, the elements on an alveolus structure while the continuous phase is still flowing. The strength of this method lies in its simplicity: single layer system, in situ heating leading to a high level of integration, low power consumption (P < 0.4 W), low applied voltage (about 10 V), and finally this system is able to manipulate elements within a flow velocity up to 1 cm s−1.
65 citations
TL;DR: In this paper, the authors considered the instantaneous distribution of mass and thermal fluxes inside and outside of an evaporating sessile droplet using computer simulations and calculated the latter distribution in a self consistent way by considering an interconnected problem of vapour transfer in the vapour phase outside the droplet, heat transfer in vapour, liquid and solid substrate, and Marangoni convection inside the liquid droplet.
01 Sep 2010
TL;DR: It appears that the solutal Marangoni effect is by far the most important instability mechanism, and its global action can be described within a Pearson-like model, with an appropriately defined Biot number depending on the wavenumber.
Abstract: A linear stability analysis is performed for a horizontal layer of a binary liquid of which solely the solute evaporates into an inert gas, the latter being assumed to be insoluble in the liquid. In particular, a water-ethanol system in contact with air is considered, with the evaporation of water being neglected (which can be justified for a certain humidity of the air). External constraints on the system are introduced by imposing fixed "ambient" mass fraction and temperature values at a certain effective distance above the free liquid-gas interface. The temperature is the same as at the bottom of the liquid layer, where, besides, a fixed mass fraction of the solute is presumed to be maintained. Proceeding from a (quasi-)stationary reference solution, neutral (monotonic) stability curves are calculated in terms of solutal/thermal Marangoni/Rayleigh numbers as functions of the wavenumber for different values of the ratio of the gas and liquid layer thicknesses. The results are also presented in terms of the critical values of the liquid layer thickness as a function of the thickness of the gas layer. The solutal and thermal Rayleigh and Marangoni effects are compared to one another. For a water-ethanol mixture of 10wt.% ethanol, it appears that the solutal Marangoni effect is by far the most important instability mechanism. Furthermore, its global action can be described within a Pearson-like model, with an appropriately defined Biot number depending on the wavenumber. On the other hand, it is also shown that, if taken into account, water evaporation has only minor quantitative consequences upon the results for this predominant, solutal Marangoni mechanism.
TL;DR: In this paper, the authors performed the first quantitative, spatiotemporally resolved measurements of the spreading of an insoluble surfactant on a thin fluid layer and observed both the radial height profile of spreading droplet and the spatial distribution of fluorescently tagged surfactants.
Abstract: The spreading of surfactants on thin films is an industrially and medically important phenomenon, but the dynamics are highly nonlinear and visualization of the surfactant dynamics has been a long-standing experimental challenge. We perform the first quantitative, spatiotemporally resolved measurements of the spreading of an insoluble surfactant on a thin fluid layer. During the spreading process, we directly observe both the radial height profile of the spreading droplet and the spatial distribution of the fluorescently tagged surfactant. We find that the leading edge of a spreading circular layer of surfactant forms a Marangoni ridge in the underlying fluid, with a trough trailing the ridge as expected. However, several novel features are observed using the fluorescence technique, including a peak in the surfactant concentration that trails the leading edge, and a flat, monolayer-scale spreading film that differs from concentration profiles predicted by current models. Both the Marangoni ridge and the surfactant leading edge can be described to spread as R∝tδ. We find spreading exponents δH≈0.30 and δΓ≈0.22 for the ridge peak and surfactant leading edge, respectively, which are in good agreement with theoretical predictions of δ=1/4. In addition, we observe that the surfactant leading edge initially leads the peak of the Marangoni ridge, with the peak later catching up to the leading edge.
15 Feb 2010
TL;DR: In this paper, the apparent contact angle is modeled as the transition region between the macroscopic film and ultra-thin adsorbed film dominated by disjoining pressure effects, and the static contact angle increases with the temperature of the heater.
Abstract: We studied both static and dynamic values of the apparent contact angle for gravity-driven flow of a volatile liquid down a heated inclined plane. The apparent contact line is modeled as the transition region between the macroscopic film and ultra-thin adsorbed film dominated by disjoining pressure effects. Four commonly used disjoining pressure models are investigated. The static contact angle is shown to increase with heater temperature, in qualitative agreement with experimental observations. The angle is less sensitive to the details of the disjoining pressure curves than in the isothermal regime. A generalization of the classical Frumkin-Derjaguin theory is proposed to explain this observation. The dynamic contact angle follows the Tanner's law remarkably well over a range of evaporation conditions. However, deviations from the predictions based on the Tanner's law are found when interface shape changes rapidly in response to rapid changes of the heater temperature. The Marangoni stresses are shown to result in increase of the values of apparent contact angles.
TL;DR: In this paper, a simple analytical model was formulated for analysing the influence on wetting of the interfacial atomic processes and of Si transport in the liquid, under their experimental conditions, solute transport by Marangoni convection controlled the spreading kinetics.
TL;DR: Using the VOF multiphase flow model, numerical simulations are conducted to investigate the nucleate boiling of water in micro-channels in this article, and the Marangoni heat transfer through the bubble surface is analyzed.
TL;DR: In this paper, the authors address the coupled heat transfer and fluid dynamic modeling of the SiC solution growth process, with special attention being paid to the different convective flows in the liquid.
TL;DR: In this paper, the gravity-driven laminar flow of a thin layer of fluid down a heated wavy inclined surface is discussed, and the coupled effect of bottom topography, variable surface tension and heating has been investigated both analytically and numerically.
Abstract: The two-dimensional problem of gravity-driven laminar flow of a thin layer of fluid down a heated wavy inclined surface is discussed. The coupled effect of bottom topography, variable surface tension and heating has been investigated both analytically and numerically. A stability analysis is conducted while nonlinear simulations are used to validate the stability predictions and also to study thermocapillary effects. The governing equations are based on the Navier–Stokes equations for a thin fluid layer with the cross-stream dependence eliminated by means of a weighted residual technique. Comparisons with experimental data and direct numerical simulations have been carried out and the agreement is good. New interesting results regarding the combined role of surface tension and sinusoidal topography on the stability of the flow are presented. The influence of heating and the Marangoni effect are also deduced.
TL;DR: In this paper, double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered and linear stability analysis and direct numerical simulation show that this critical value corresponds to a supercritical Hopf bifurcation point, which leads the quiescent fluid directly into the oscillatory flow regime.
Abstract: Double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the case where the opposing thermal and solutal Marangoni effects are of equal magnitude solutal to thermal Marangoni number ratio R =�1 . In this case a no-flow equilibrium solution exists and can remain stable up to a critical thermal Marangoni number. Linear stability analysis and direct numerical simulation show that this critical value corresponds to a supercritical Hopf bifurcation point, which leads the quiescent fluid directly into the oscillatory flow regime. Influences of the Lewis number Le, Prandtl number Pr, and the cavity aspect ratio A height/length on the onset of instability are systematically investigated and different modes of oscillation are obtained. The first mode is first destabilized and then stabilized. Sometimes it never gets onset. A physical illustration is provided to demonstrate the instability mechanism and to explain why the oscillatory flow after the onset of instability corresponds to countersense rotating vortices traveling from right to left in the present configuration, as obtained by direct numerical simulation. Finally the simultaneous existence of both steady and oscillatory flow regimes is shown. While the oscillatory flow arises from small disturbances, the steady flow, which has been described in the literature, is induced by finite amplitude disturbances. © 2010 American Institute of Physics. doi:10.1063/1.3333436
TL;DR: In this paper, the effect of magnetic field dependent viscosity on the onset of Benard-Marangoni ferroconvection in a horizontal layer of ferrofluid is investigated theoretically.
TL;DR: In this paper, the influence of differently shaped colloidal or simply pure immiscible droplets to the main liquid,flow on the thermal transport in microchannels was numerically investigated and results of parametric studies on the infience of all major factors connected to microchannel heat transfer were presented.
Abstract: We show that heat transfer in microchannels can be considerably augmented by introducing droplets or slugs of an immiscible liquid into the main fluid flow. We numerically investigate the influence of differently shaped colloidal or simply pure immiscible droplets to the main liquid,flow on the thermal transport in microchannels. Results of parametric studies on the infiuence of all major factors connected to microchannel heat transfer are presented. The effect of induced Marangoni fiow at the liquid interfaces is also taken into account and quantified. The calculation of the multiphase, multispecies flow problem is performed, applying a front tracking method, extended to account for nanoparticle transport in the suspended phase when relevant. This study reveals that the use of a second suspended liquid (with or without nanoparticles) is an efficient way to significantly increase the thermal performance without unacceptably large pressure losses. In the case of slug-train coflow, the Nusselt number can be increased by as much as 400% compared with single liquid flow.
TL;DR: In this paper, the authors analyzed the dynamics of the triple gas-liquid-solid contact line for the case where the gas is the saturated vapor corresponding to the liquid and showed that Navier slip alone alone alone is not sufficient to relax the hydrodynamic contact line singularity: the Marangoni term is equally important when the heat transfer is involved.
Abstract: The dynamics of the triple gas-liquid-solid contact line is analyzed for the case where the gas is the saturated vapor corresponding to the liquid. For partial wetting conditions, a nonstationary contact line problem where the contact line motion is caused by evaporation or condensation is treated. It is shown that the Navier slip condition alone is not sufficient to relax the hydrodynamic contact line singularity: the Marangoni term is equally important when the heat transfer is involved. The transient heat conduction inside the heater is accounted for. A multiscale problem of drop evaporation with freely moving contact line is solved in the lubrication approximation as an illustration of the proposed approach.
TL;DR: Three-dimensional double-diffusive Marangoni convection in a cubic cavity with horizontal temperature and concentration gradients is studied, and as the thermal forcing of the system increases, the flow can undergo a reverse transition from a temporal chaotic to a steady state.
Abstract: Three-dimensional double-diffusive Marangoni convection in a cubic cavity is studied in the present paper. Both the temperature and solute concentration gradients are applied horizontally. Direct numerical simulations are carried out for surface-tension Reynolds number $10\ensuremath{\le}\text{Re}\ensuremath{\le}500$, surface-tension ratio $\ensuremath{-}2\ensuremath{\le}{R}_{\ensuremath{\sigma}}\ensuremath{\le}1$, and Lewis number $1l\text{Le}\ensuremath{\le}200$. Symmetry-breaking pitchfork bifurcation is observed, which does not exist in the pure thermocapillary case, and the flow field is essentially three dimensional. The evolution of the flow structure, as well as the dependence of the heat and mass transfer rates on the different parameters, is investigated systematically. The simulations are performed until the temporal chaotic flow regime is reached and an atypical bifurcation sequence is identified. Namely, as the thermal forcing of the system increases, the flow can undergo a reverse transition from a temporal chaotic to a steady state. Multiple solution branches exist in some parameter ranges, and these are depicted in terms of the heat and mass transfer rates. Corresponding two-dimensional simulations are also performed to clearly illustrate the deviations from the three-dimensional model. The onset of oscillatory flow from the quiescent equilibrium state is also considered. The present work intends to initiate the study of double-diffusive Marangoni convection in three-dimensional confined cavities with horizontal temperature and concentration gradients.
TL;DR: In this article, the main activities in preparation of microgravity experiments dedicated to performances characterization of innovative heat pipes systems based on self-rewetting fluids are summarized, including measurements of surface tension, contact angles and thermal conductivities for a number of multicomponent solutions, including self-reordering alcohol solutions, brines and nanofluids.
TL;DR: In this article, the authors studied the thermocapillary migration of two-dimensional droplets of partially wetting liquids on a non-uniform heated substrate and derived an equation for the thickness profile of the droplet by employing lubrication approximations.
Abstract: We study the thermocapillary migration of two-dimensional droplets of partially wetting liquids on a non-uniform heated substrate. An equation for the thickness profile of the droplet is derived by employing lubrication approximations. The model includes the effect of a non-zero contact angle introduced through a disjoining― conjoining pressure term. Instead of assuming a fixed shape for the droplet, as in previous works, here we allow the droplet to change its profile with time. We identify and describe three different regimes of behaviour. For small contact angles, the droplet spreads into a long film profile with a capillary ridge near the leading edge, a behaviour that resembles the experiments on Marangoni films reported by Ludviksson & Lightfoot (Am. Inst. Chem. Eng. J., vol. 17, 1971, pp. 1166). For large contact angles, the droplet moves as a single entity, weakly distorted from its static shape. This regime is the usual one reported in experiments on thermocapillary migration of droplets. We also show some intriguing morphologies that appear in the transition between these two regimes. The occurrence of these three regimes and their dependence on various parameters is analysed.
TL;DR: In this paper, the transition to chaos in double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered, and the transition is restricted to the special case when the resultant thermal and solutal MARANGON effects are equal and opposing.
TL;DR: In this paper, a mechanism of Marangoni instability in evaporating thin films is presented and analyzed, which has its origin on the effects of a soluble surfactant, and a thin-film analysis is applied and evolution equations for the film thickness and the surfactants concentration are derived and analyzed by the techniques of linear stability and numerical simulation.
Abstract: In film coating and other applications involving thin liquid films, surfactants are typically employed to suppress the usually undesirable instabilities driven by surface phenomena. Yet, in the present study a mechanism of Marangoni instability in evaporating thin films is presented and analyzed, which has its origin on the effects of a soluble surfactant. As the film thins due to evaporation, thickness perturbations lead to surfactant concentration perturbations, which in turn drive film motion and tend to enhance uneven drying. A thin-film analysis is applied and evolution equations for the film thickness and the surfactant concentration are derived and analyzed by the techniques of linear stability and numerical simulation. In the linear analysis a nonautonomous system is obtained for the film thickness and surfactant concentration perturbations, which shows that the instability will manifest itself provided that an appropriate Marangoni number is relatively large and the surfactant solubility in the b...
TL;DR: In this article, a stationary coupled problem of convective convection in a horizontal layer with free boundary under conditions of a co-current gas flow is studied, and the exact solutions for different types of thermal boundary conditions have been obtained.
TL;DR: In this article, the effect of insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor-Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis.
Abstract: The effect of an insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor–Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis. The interface is assumed to be concentric with the cylinders. The gravitational effects are ignored. Influences of density and viscosity stratification, surface tension, surfactant concentration distribution and Taylor–Couette shearing are considered comprehensively. The instability characteristics due to competition and interaction between various physical instability mechanisms are of principal concern. Neutral curves with upper and lower branches in the Reynolds number (Re1)/axial wavenumber (k) plane are obtained. A window of parameters is identified in which the flow is linearly stable. The Marangoni traction force caused by the gradient of surfactant concentration stabilizes the axisymmetric perturbations but initiates an instability corresponding to non-axisymmetric modes in the presence of basic Couette shearing flow. Co-rotation of the outer cylinder has a stabilizing effect in expanding the stable region, which dwindles in the counter-rotation situation.
TL;DR: In this paper, the long-wave Marangoni convection in a horizontal liquid layer with insoluble surfactant absorbed on the free surface is studied and the linear stability analysis of this system is performed.
Abstract: The subject of this paper is the long-wave Marangoni convection in a horizontal liquid layer with insoluble surfactant absorbed on the free surface. The surfactant is convected by interfacial velocity field and diffuses over the interface but not into the bulk of the fluid. The layer is subjected to a transverse temperature gradient. The buoyancy effects are negligible as compared to the Marangoni forces. We consider both cases of flat nondeformable and deformable surface. The linear stability analysis of this system is performed. It is shown that in both cases of the upper surface monotonic and oscillatory modes exist. Convection thresholds are determined and the critical Marangoni numbers for monotonic as well as for oscillatory mode are obtained. It is shown that the monotonic long-wave instability is more dangerous than oscillatory one only for small elasticity numbers, if the Lewis number is small.