The two-dimensional flow of viscous incompressible liquid in a square cavity with a free boundary and differentially heated vertical sides is considered in the present work. The influence of gravitational and thermocapillary convection on temperature and velocity fields is studied in large range of dimensionless parameters and similarity criteria using equations in a Boussinesq approximation. Limiting cases of dimensionless parameters are analyzed numerically.
Self-rewetting fluids (SRFs), such as aqueous solutions of long-chain alcohols, exhibit anomalous quadratic dependence of surface tension on temperature having a minimum and with a positive gradient. When compared to the normal fluids (NFs), the SRFs can be associated with significantly modified interfacial dynamics, which have recently been exploited to enhance flow and thermal transport in various applications (e.g., microgravity and microscale transport systems). In this work, first, we develop a new analytical solution of thermocapillary convection in superimposed two SRF layers confined w…
Effect of interfacial disturbances on instabilities of buoyant/thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The computations are carried out for several two-liquid two-layer systems taking into account properties of liquids used in previously published experiments. Relation between the interface deformations and the Boussinesq approximation is discussed. It is shown that in some systems, including the interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either destabilizing…
When the liquid has a free interface and is heated nonuniformly then besides the gravitational convection a different motion appears. This kind of a motion is originated because of a gradient of the surface tension over the liquid interface. It is suggested to call it a thermocapillary motion in analogy with an electrocapillary motion. The present paper develops a theory of thermocapillary motion for two distinct geometries: a liquid layer and a liquid drop suspended in another viscous medium. For both geometries, assuming the non-deformable interfaces, the velocity profiles are found and feas…
The long-duration fluid physics experiments on a thermocapillary-driven flow have been carried out on the Japanese experiment module 'Kibo' aboard the International Space Station (ISS) since 2008. In these experiments, various aspects of thermocapillary convection in a half-zone (HZ) liquid bridge of high Prandtl number fluid have been examined under the advantages of the long-duration high-quality microgravity environment. This fluid dynamics video introduce a pinch off of liquid bridge of 30 mm in diameter as a part of the on-orbit experiments. The effect of thermocapillary-driven flow on th…
In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier-Stokes equations with additional stress term, Cahn-Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carri…
Motived by recent ground-based and microgravity experiments investigating the interfacial dynamics of a volatile liquid (FC-72, $Pr=12.34$) contained in a heated cylindrical cell, we numerically study the thermocapillary-driven flow in such an evaporating liquid layer. Particular attention is given to the prediction of the transition of the axisymmetric flow to fully three-dimensional patterns when the applied temperature increases. The numerical simulations rely on an improved one-sided model of evaporation by including heat and mass transfer through the gas phase via the heat transfer Biot n…
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface fore (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter visa Ca…
Theresults of numerical modelinghas based on the solution of Navier-Stokes equations for convection oftwo-layer system air-water are presented.The influence of thermocapillary and gravitational convection on the deformation and time averaged position of the interface of air-water system under sudden lateral heating of a square-section cavity are shown.
This paper presents a numerical study of three-dimensional laminar mixed convection within a liquid flowing on a horizontal channel heated uniformly from below. The upper surface is free and assumed to be flat. The coupled Navier-Stokes and energy equations are solved numerically by the finite volume method taking into account the thermocapillary effects (Marangoni effect). When the strength of the buoyancy, thermocapillary effects and forced convective currents are comparable $(Ri\backsimeq O(1)$ and $Bd=Ra/Ma \backsimeq O(1))$, the results show that the development of instabilities in the fo…
Droplets are natural candidates for use as microfluidic reactors, if active control of their formation and transport can be achieved. We show here that localized heating from a laser can block the motion of a water-oil interface, acting as a microfluidic valve for two-phase flows. A theoretical model is developed to explain the forces acting on a drop due to thermocapillary flow, predicting a scaling law which favors miniaturization. Finally, we show how the laser forcing can be applied to sorting drops, thus demonstrating how it may be integrated in complex droplet microfluidic systems.
The deformation of a fluid-fluid interface due to the thermocapillary stress induced by a continuous Gaussian laser wave is investigated analytically. We show that the direction of deformation of the liquid interface strongly depends on the viscosities and the thicknesses of the involved liquid layers. We first investigate the case of an interface separating two different liquid layers while a second part is dedicated to a thin film squeezed by two external layers of same liquid. These results are predictive for applications fields where localized thermocapillary stresses are used to produce f…
We study the thermocapillary creeping flow induced by a thermal gradient at the liquid-air interface in the presence of insoluble surfactants (impurities). Convective sweeping of the surfactants causes density inhomogeneities that confers in-plane elastic features to the interface. This mechanism is discussed for radially symmetric temperature fields, in both the deep and shallow water regimes. When mass transport is controlled by convection, it is found that surfactants are depleted from a region whose size is inversely proportional to the interfacial elasticity. Both the concentration and th…
In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam in…
The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The present study is focused on two limiting situations of surfactant transport: (i) small surface Peclet number, and (ii) high surface Peclet number. Thermocapillary-induced Marangoni stress, strength of which…
Flows in low Prandtl number liquid pools are relevant for various technical applications, and have so far only been investigated for the case of pure fluids, i.e. with a constant, negative surface tension temperature coefficient $\partialγ/\partial T$. Real-world fluids containing surfactants have a temperature dependent $\partialγ/\partial T > 0$, which may change sign to $\partialγ/\partial T < 0$ at a critical temperature $T_c$. Where thermocapillary forces are the main driving force, this can have a tremendous effect on the resulting flow patterns and the associated heat transfer. Here we …
We investigate the radial thermocapillary flow driven by a laser-heated microbead in partial wetting at the water-air interface. Particular attention is paid to the evolution of the convective flow patterns surrounding the hot sphere as the latter is increasingly heated. The flow morphology is nearly axisymmetric at low laser power P. Increasing P leads to symmetry breaking with the onset of counter-rotating vortex pairs. The boundary condition at the interface, close to no-slip in the low-P regime, turns about stress-free between the vortex pairs in the high-P regime. These observations stron…
We present a method that leverages projected light patterns as a mechanism for freeform deformations of a thin liquid film via the thermocapillary effect. We developed a closed-form solution for the inverse problem of the thin-film evolution equation, allowing to obtain the projection pattern required in order to achieve a desired topography. We experimentally implement the method using a computer controlled light projector, which illuminates any desired pattern onto the bottom of a fluidic chamber patterned with heat absorbing metal pads. The resulting heat map induces surface tension gradien…
Heat and fluid flow in low Prandtl number melting pools during laser processing of materials are sensitive to the prescribed boundary conditions, and the responses are highly nonlinear. Previous studies have shown that fluid flow in melt pools with surfactants can be unstable at high Marangoni numbers. In numerical simulations of molten metal flow in melt pools, surface deformations and its influence on the energy absorbed by the material are often neglected. However, this simplifying assumption may reduce the level of accuracy of numerical predictions with surface deformations. In the present…
We report on the thinning of supported liquid films driven by thermocapillarity. The liquids are oil films, of initial thicknesses of a few tens of microns. A local and moderate heating of the glass substrate on which they are spread on induces a thermocapillary flow, which allows the formation of ultra-thin films. We show that, within a given time range, the thinning dynamics of submicron thick films is governed by the thermocapillary stress. It results in a simple dependency of the thickness profiles with time, which is evidenced by the collapse of the data onto a master curve. The master cu…
Thermocapillary migration of a planar non-deformable droplet in flow fields with two uniform temperature gradients at moderate and large Marangoni numbers is studied numerically by using the front-tracking method. It is observed that the thermocapillary motion of planar droplets in the uniform temperature gradients is steady at moderate Marangoni numbers, but unsteady at large Marangoni numbers. The instantaneous migration velocity at a fixed migration distance decreases with increasing Marangoni numbers. The simulation results of the thermocapillary droplet migration at large Marangoni number…
Buoyancy-thermocapillary convection in a layer of volatile liquid driven by a horizontal temperature gradient arises in a variety of situations. Recent studies have shown that the composition of the gas phase, which is typically a mixture of vapour and air, has a noticeable effect on the critical Marangoni number describing the onset of convection as well as on the observed convection pattern. Specifically, as the total pressure or, equivalently, the average concentration of air is decreased, the threshold of the instability leading to the emergence of convective rolls is found to increase rat…
Exploring and controlling the physical factors that determine the topography of thin liquid dielectric films are of interest in manifold fields of research in physics, applied mathematics, and engineering and have been a key aspect of many technological advancements. Visualization of thin liquid dielectric film topography and local thickness measurements are essential tools for characterizing and interpreting the underlying processes. However, achieving high sensitivity with respect to subnanometric changes in thickness via standard optical methods is challenging. We propose a combined imaging…
We demonstrate that the active thermocapillary stresses induced by multiple microbubbles offer simple routes to directed self-assembly and complex but controllable micromanipulation of mesoscopic colloidal particles embedded in a liquid. The microbubbles are nucleated on a liquid-glass interface using optical tweezers. The flow around a single bubble causes self-assembly of the particles in rings at the bubble-base, while an asymmetric temperature profile generated across the bubble interface breaks the azimuthal symmetry of the flow, and induces simultaneous accumulation and repulsion of part…
Flow structure stability of a steady radial thermocapillary flow from the local heat source in cylindrical geometry has been studied numerically. The up boundary of the liquid was partially covered by the stationary film of an insoluble surfactant, pushed to the wall of the cavity. The calculations are fulfilled on the base of interfacial hydrodynamics equations by using mathematical package Comsol Multiphysics. It is shown that the effect of a radial flow symmetry breakdown is appeared as a result of convective instability, so that the initial poloidal rotation of the liquid transforms into t…
This report summarises the results for the numerical simulation of thermocapillary convection in a two-fluid system with a deformable interface. An explicit technique with 3rd order Runge-Kutta method in time, 2nd order ENO for the advection terms, and 2nd order central-differencing for the diffusion terms are employed in the momentum equations for simulating the flow on a staggered grid using a Marker and Cell method. An energy equation is solved numerically and a level-set method is used to implicitly capture the interface. A constant contact angle condition is assumed between the end walls …
In Rayleigh-Bénard convection, it has been found that the amount of heat passing through the fluid has a power law dependence on the imposed temperature difference. Modifying this dependence, either enhancing or reducing the heat transfer capability of fluids, is important in many scientific and practical applications. Here, we present a simple means to control the vertical heat transfer in Rayleigh-Bénard convection by injecting heat through one lateral side of the fluid domain and extracting the same amount of heat from the opposite side. This horizontal heat flux regulates the large-scale c…
Comment on Conjugate heat transfer of mixed convection for viscoelastic fluid past a stretching sheet, by Kai-Long Hsiao and Guan-Bang Chen, Mathematical Problems in Engineering, Volume 2007, article 17058, 21 pages
Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that penetrates into the stably stratified lower region. The fraction of produced heat escaping across the bottom plate, which is one half without convection, initially decreases as convection strengthens. Entering the turbulent regime, this decrease reverses in two dimensions but continues monotonically in three dimensions. The mean fluid temperature, which grows prop…
This letter confirms the existence of heat transfer enhancement (HTE) and reduction (HTR) in turbulent natural convection with polymer additives. HTE and HTR were numerically predicted by Benzi et al.(PRL, 104, 024502, 2010) in homogenous turbulent convection, but experiments by Ahlers & Nikolaenko(PRL, 104, 034503, 2010) in turbulent natural convection observed HTR only. Using direct numerical simulation of natural convection, the present study reconciles earlier numerical and experimental work on the basis of the dominant role of polymer length in the polymer dynamics in extensional flows.
Rayleigh--Bénard convection, which is the buoyancy-induced motion of a fluid enclosed between two horizontal plates, is an idealised setup to study thermal convection. We analyse the modes that transport the most heat between the plates by computing the proper orthogonal decomposition (POD) of numerical data. Instead of the usual POD ansatz of finding modes that describe the energy best, we propose a method that is optimal in describing the heat transport. Thereby, we can determine the modes with the major influence on the heat transport and the coherent structures in the convection cell. We a…
We report experimental measurements of heat transport in rotating Rayleigh-B{é}nard convection in a cylindrical convection cell with aspect ratio $Γ= 1/2$. The fluid was helium gas with Prandtl number Pr = 0.7. The range of control parameters was Rayleigh number $4 \times 10^9 < {\rm Ra} < 4 \times 10^{11}$ and Ekman number $2 \times 10^{-7} < {\rm Ek} < 3 \times 10^{-5}$(corresponding to Taylor number $4 \times 10^9 < {\rm Ta} < 1 \times 10^{14}$ and convective Rossby number $0.07 < {\rm Ro} < 5$). We determine the crossover from weakly rotating turbulent convection to rotation dominated geos…
Upper bounds on the heat transport and other quantities of interest in Rayleigh-Bénard convection are derived in previous work from constraints resulting from the equations of time evolution for kinetic energy, the root mean square of temperature, and the temperature averaged over horizontal planes. Here, we investigate the effect of a new constraint derived from the time evolution equation for the advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.
Measurements of heat transport, as expressed by the Nusselt number $Nu$, are reported for turbulent Rayleigh-Bénard convection of water containing up to 120 ppm by weight of poly-[ethylene oxide] with a molecular weight of $4\times10^6$ g/mole. Over the Rayleigh number range $ 5\times 10^9 \alt Ra \alt 7 \times 10^{10}$ $Nu$ is smaller than it is for pure water by up to 10%.
We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-Bénard convection, at $Ra \sim 10^{10}$. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume t…
Experimental and numerical data for the heat transfer as a function of the Rayleigh-, Prandtl-, and Rossby numbers in turbulent rotating Rayleigh-Benard convection are presented. For relatively small $Ra ~ 10^8$ and large Pr modest rotation can enhance the heat transfer by up to 30%. At larger Ra there is less heat-transfer enhancement, and at small Pr = 0.7. there is no heat-transfer enhancement at all. We suggest that the small-Pr behavior is due to the breakdown of the heat-transfer-enhancing Ekman pumping because of larger thermal diffusion.
Convection heat transfer in porous media is a universal phenomenon in nature, and it is also frequently encountered in scientific and engineering fields. An in-depth understanding of the fundamental mechanism of convection heat transfer in porous media requires efficient and powerful numerical tools. In this paper, a cascaded lattice Boltzmann (CLB) method for convection heat transfer in porous media at the representative elementary volume (REV) scale is presented. In the CLB method, the flow field is solved by an isothermal CLB model with the D2Q9 lattice based on the generalized non-Darcy mo…
Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting versus plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ultimately ejecting dominated at a Rayleigh number of $Ra\approx 3 \times 10^{11}$. This is consistent with the trends observed in 3-…
The paper presents a theoretical study using the Karman-Pohlhausen method for describing the transient heat exchange between the boundary-layer free convection and a vertical flat plate embedded in a porous medium. The unsteady behavior is developed after the generation of an impulsive heat flux step at the right-hand side of the plate. Two cases are considered according to whether the plate has a finite thickness or no thickness. The time and space evolution of the interface temperature is evidenced.
Heat transport in turbulent thermal convection increases with the thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport became independent of the molecular diffusivities -- the heat transport scaling is slower than the mixing-length (or `ultimate') scaling. In configurations driven by either thermal boundary conditions or internal heating, thermal boundary layers instead lead to a boundary-limited (or `classical') scaling. With net-zero internal heating and cooling in different regions, mixing-length scaling can occur because heat need not…
We perform a numerical study of the heat transfer and flow structure of Rayleigh-Bénard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $ϕ$ in the flow properties during the transition process from the traditional RB convection with $ϕ=1$ (so no obstacles included) to Darcy-type porous-media convection with $ϕ$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities…
In the above paper the author treats the boundary layer flow along a vertical flat plate, immersed in a Darcy Brinkman Forchheimer porous medium. The porosity and the permeability of the porous medium are variable across the boundary layer. In addition a magnetic field with constant strength is applied normal to the plate. The fluid temperature at the plate is constant and different from that of the ambient fluid. This temperature difference creates a buoyancy force and the flow is characterized as mixed convection. The partial differential equations of the boundary layer flow are transformed …
Thermal convection driven by internal heat sources and sinks was recently shown experimentally to exhibit the mixing-length, or "ultimate", scaling-regime: the Nusselt number $Nu$ (dimensionless heat flux) increases as the square-root of the Rayleigh-number $Ra$ (dimensionless internal temperature difference). While for standard Rayleigh-Bénard convection this scaling regime was proven to be a rigorous upper bound on the Nusselt number, we show that this is not so for convection driven by internal sources and sinks. To wit, we introduce an asymptotic expansion to derive steady nonlinear soluti…
We report a numerical study of Rayleigh--Bénard convection through random porous media using pore-scale modelling, focusing on the Lagrangian dynamics of fluid particles and heat transfer for varied porosities $ϕ$. Due to the interaction between the porous medium and the coherent flow structures, the flow is found to be highly heterogeneous, consisting of convection channels with strong flow strength and stagnant regions with low velocities. The modifications of flow field due to porous structure have a significant influence on the dynamics of fluid particles. Evaluation of the particle displa…
The non-hydrostatic, quasigeostrophic approximation for rapidly rotating Rayleigh-Bénard convection admits a class of exact `single mode' solutions. These solutions correspond to steady laminar convection with a separable structure consisting of a horizontal planform characterized by a single wavenumber multiplied by a vertical amplitude profile, with the latter given as the solution of a nonlinear boundary value problem. The heat transport associated with these solutions is studied in the regime of strong thermal forcing (large reduced Rayleigh number $\widetilde{Ra}$). It is shown that the N…
A numerical method is presented which conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with earlier results. These bounds imply upper bounds for the poloidal energy which follow directly from the definitions of dissipation and energy. The same constraints used for computing upper bounds on the heat transport lead to improved bounds for the poloidal energy.
A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the transversal direction and countercurrent boundary layers are formed on the both sides of the wall. The governing equations of this problem and their corresponding boundary conditions are all cast into a dimensionless form by using a non-similarity transformation. These resultant equations with multiple singular points are solved numerically using a very efficie…
Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold places. Here, we experimentally study the Rayleigh-Bénard convection of aqueous glycerol solution in a cubic cell with suspensions of rod-like particles made of polydimethylsiloxane (PDMS). The particles are inertial due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the particles is three times larger than that of the background fluid. This contrast makes the suspended particles lighter than the local fluid in hot regions and heavier in…
