Effects Of Thermocapillarity Research Articles

SIMULACIONES NUMÉRICAS 3D DEL FLUJO DE UNA GOTA BAJO LOS EFECTOS DEUN GRADIENTE RADIAL DE TEMPERATURA

It has been shown experimentally that when a drop is deposited at the center of a substrate with an axial temperature gradient (hotter in the center), thermocapillarity effects makes an outward flow to appear so that the drop evolves towards a ring whose radius increases with time. Upon reaching a critical radius, the contact line becomes unstable, showing gentle undulations whose amplitudes grow with time. Using the lubrication approximation and adopting appropriate dimensionless variables, a parameter-free differential equation is obtained that governs this type of thermocapillary flow. Numerical solutions of this equation are presented to study the unstable stage. Experimental results are compared with those obtained from the numerical solutions.

Thermocapillary thin film flows on a slippery substrate with odd viscosity effects

This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.

Suppression of Wave Instability in a Liquid Film Flow Down a Non-Uniformly Heated Slippery Inclined Plane Using Odd Viscosity

Abstract We study the effects of odd viscosity on the stability of a thin Newtonian liquid film flowing down a nonuniformly heated plane under a slip boundary condition. The effect of odd viscosity arises in classical fluids when the time-reversal symmetry breaks down. Due to the odd viscosity, the odd part of the Cauchy stress tensor consists of symmetric and antisymmetric parts and shows several striking effects. We apply the Navier slip boundary condition for the slippery inclined plane at the solid–liquid interface. For our problem, we first derive an evolution equation whose solution describes the film thickness. The equation contains parameters considering the effect of inertia, thermocapillarity, slip length, and odd viscosity. We then perform the linear stability analysis and find that odd viscosity can significantly suppress the combined destabilizing effects of the thermocapillarity and slip length. Next, we analyze the dynamics using the weakly nonlinear approach, which provides details of different subregions of the instability zone. We observe that as the influence of the odd viscosity increases, the supercritical stable and explosive zones shrink while the unconditional stable and subcritical unstable zones expand. We also perform numerical investigation and observe that linear analysis, weakly nonlinear theory, and numerical results are consistent.

Thermocapillarity in Cross Hybrid Nanofilm Flow Past an Unsteady Stretching Sheet

The present work is highly interested in examining the transport phenomena of the thin Cross hybrid nanofluid film flow over a continuously stretching surface. The proposed thin film flow study elucidates the film extrusion process, which is prominent in the packaging industry. With the intention of improvising the quality of the coating process, the thermocapillarity and injection effects have been probed in the present model. A suitable similarity transformation and the MATLAB software aid in producing accurate numerical solutions. The accumulated numerical results indicate that an increment in the hybrid nanofluid viscosity and surface tension intensity reduces the wall shear stress past the permeable stretching sheet and improves the heat transfer rate. Remarkably, negative film thickness has been identified when the unsteadiness parameter is greater than or equal to 0.9 while the thermocapillarity parameter falls within the range of 0 and 0.6.

Numerical investigation of surface evaporation and thermocapillarity effects on natural convection within a contained fluid in cryogenic tank

Quantification of liquefied gas surface evaporation in partially filled cryogenic tank is important in both design process and operations control later. This paper focuses on effects of external heat leaks on the surface evaporation and the natural convection of a liquefied gas contained in cryogenic cylindrical tank with consideration of thermocapillarity. The evaporation mass flow rate is assumed negligible; however, the absorbed heat during the process is considered and defined according the Hashemi-Wesson model. The physical problem was formulated in dimensionless form, and then solved numerically using finite volume procedure. The external heat leaks and the surface evaporation heat flux were quantified by means of Nusselt number. Several simulations have been conducted based on the Rayleigh number (10+4 ≤ Ra ≤ 10+5), Marangoni number (0 ≤ Ma ≤ 2000) and the cavity aspect ratio (0.5 ≤ AR ≤ 2). Results showed that as Ra increases, the heat transfer rate from wall to fluid increases as well as the evaporation rate. Large value of Ma can reduce the surface evaporation heat flux up to 5% due to thermocapillary flow. High filling level reduces surface evaporation up to 42% for AR = 0.5, whereas low filling level promotes it to 46% for AR = 1.5, with respect to AR = 1. Free surface and side wall Nusselt numbers are strongly dependent on Ra, Ma and AR, and both have been correlated in simple formulas within engineering tolerance ±5%.

A fundamental investigation of thermo-capillarity in laser powder bed fusion of metals and alloys

Several different interfacial forces affect the free surface of liquid metals during metal additive manufacturing processes. One of these is thermo-capillarity or the so-called Marangoni effect. In this work, a novel framework is introduced for unraveling the effects of thermo-capillarity on the melt pool morphology/size and its thermo-fluid conditions during the Laser Powder Bed Fusion (L-PBF) process. In this respect, a multi-physics numerical model is developed based on the commercial software package Flow-3D. The model is verified and validated via mesh-independency analysis and by comparison of the predicted melt pool profile with those from lab-scale single-track experiments. Two sets of parametric studies are carried out to find the role of both positive and inverse thermo-capillarity on the melt pool shape and its thermal and fluid dynamics conditions. The thermo-fluid conditions of the melt pool are further investigated using appropriate dimensionless numbers. The results show that for the higher Marangoni number cases, the melt pool temperature drops, and at the same time, the temperature field becomes more uniform. Also, it is shown that at higher Marangoni numbers, temperature gradients decrease, thus reducing the role of conduction in the heat transfer from the melt pool. Furthermore, for the first time, a novel methodology is introduced for the calculation of the melt pool's average Nusselt number. The average Nusselt numbers calculated for the positive and inverse thermo-capillarity are then used for finding the effective liquid conductivity required for a computationally cheaper pure heat conduction simulation. The results show that the deviation between the average melt pool temperature, using the pure conduction model with effective conductivity, and the one obtained from the advanced fluid dynamics model is less than 2%.

Stability of slowly evaporating thin liquid films of binary mixtures

We consider the evaporation of a thin liquid layer which consists of a binary mixture of volatile liquids. The mixture is on top of a heated substrate and in contact with the gas phase that consists of the same vapour as the binary mixture. The effect of thermocapillarity, solutocapillarity and the van der Waals interactions are considered. We derive the long-wave evolution equations for the free interface and the volume fraction that govern the two-dimensional stability of the layer subject to the above coupled mechanisms and perform a linear stability analysis. Our results demonstrate two modes of instabilities, a monotonic instability mode and an oscillatory instability mode. We supplement our results from stability analysis with transient simulations to examine the dynamics in the nonlinear regime and analyse how these instabilities evolve with time. More precisely we discuss how the effect of relative volatility along with the competition between thermal and solutal Marangoni effect defines the mode of instability that develops during the evaporation of the liquid layer due to preferential evaporation of one of the components.

Thermally Mediated Double Emulsion Breakup in Bifurcating Bi-Layer Microchannel

Abstract In this paper, we report the breakup dynamics of double emulsion droplets, as they flow through the bifurcating junction in bi-layer microchannel. Two cases have been investigated: the first involves double emulsion with core of water and shell of silicone oil with constant interfacial tension, this case shows that breakup dynamics of double emulsion can be demarcated into three regimes when the thermal effect is not dominant; whilst the second involves double emulsion with core of water and shell of dodecanoic acid where the thermocapillarity effect arises from change of interfacial tension subject to temperature variations. As demonstrated in the case, the Marangoni stress induced by the thermocapillary effect plays an important role in controlling the stability and release kinetics of double emulsion when flowing through complex microstructures. Our work will inspire novel applications, including droplet fission and actuation controlled by Marangoni flow via thermal mediation.

Stability of thin film flowing down the outer surface of a rotating non-uniformly heated vertical cylinder

We investigated an incompressible viscous liquid film flow over a rotating vertical cylinder of radius R and of infinite length rotating with a uniform angular velocity $$\varvec{\Omega }$$ about its axis. The surface of the vertical cylinder is non-uniformly heated where the temperature varies linearly in the downstream direction. The flow is assumed to be axisymmetric, and the component of the velocity along the azimuthal direction is assumed to be constant. The surface tension of the liquid is assumed to vary linearly with temperature such that as the temperature increases, the surface tension decreases. This gives rise to Marangoni stress over the free surface of the thin film. Using the long-wave approximation method, we derived a free surface evolution equation. For linear stability analysis, we used a normal mode approach and found that the Marangoni number plays a double role. There exists a critical Marangoni number $$\left( \mathrm{Mn}^{*}\right) $$ such that for $$\mathrm{Mn} \mathrm{Mn}^{*}$$ it plays a destabilizing role. We also found that as the rotation number $$\mathrm{Ro}$$ increases, the destabilizing zone increases but it decreases with the increment of the radius R of the cylinder. We further performed a weakly nonlinear analysis of the flow using the method of multiple scales. The study reveals that the Marangoni number Mn, the radius R and the rotation number $$\mathrm{Ro}$$ have substantial effects on different stability zones. The study also reveals that in the supercritical stable (subcritical unstable) zone, the threshold amplitude of the nonlinear disturbance increases (decreases) with the increment of Mn and $$\mathrm{Ro}$$ but decreases (increases) with the increment of R. The nonlinear wave speed in the supercritical stable zone decreases with the increment of Mn and $$\mathrm{Ro}$$, whereas it increases with the increment of R. We also examined the effect of thermocapillarity and rotation on the profile of the steady travelling wave solutions of the leading order part of the evolution equation.

Effect of Thermocapillary on Absolute and Convective Instability of Film Flow of Self-Rewetting Fluid

The dynamics of a self-rewetting film falling along a vertical fiber under the influence of gravity are considered. The evolution equation of the interface of the self-rewetting film is established in the framework of a long-wave approximation theory. The effect of thermocapillarity (Marangoni effect) on the absolute/convective instability (AI/CI) is investigated for self-rewetting fluids of which the surface tension is a quadratic function of the temperature at the surface. The effect of thermocapillarity on the Rayleigh-Plateau instability is investigated by examining the dispersion relation. The characteristics of self-rewetting fluids are considered for different Marangoni numbers (Ma) in different regions of absolute/convective instability using a spatio-temporal stability analysis. Numerical simulations of the nonlinear evolution in various regions of absolute/convective instability are also performed. The results of numerical simulations are in excellent agreement with the spatio-temporal stability analysis. The effect of thermocapillarity on absolute and convective instability depends on the difference between the temperature at the interface $\bar {\varTheta }_{i}$ , and the temperature corresponding the minimum surface tension Θ0. The results indicate that the thermocapillarity suppresses the absolute instability and enhances the convective instability as Ma increases when $\bar {\varTheta }_{i}-{\varTheta }_{0}> 0$ , and enhances the absolute instability as Ma increases when $\bar {\varTheta }_{i}-{\varTheta }_{0}< 0$ .

The Effects of Thermocapillarity on the Thin Film Flow of MHD UCM Fluid over an Unsteady Elastic Surface with Convective Boundary Conditions

The study of two-dimensional flow and heat transfer in a liquid film of MHD Upper Convective Maxwell (UCM) fluid over an unsteady elastic stretching sheet subject to velocity slip and convective boundary condition is presented. Thermocapillarity effects are considered. Using suitable similarity transformations, the momentum and thermal energy equations are converted to a set of coupled nonlinear ordinary differential equations. These equations are solved numerically using the Keller-Box method. The velocity and the temperature distributions are presented graphically for different values of the pertinent parameters. The effects of the unsteady parameter on the skin friction, the wall temperature gradient, and the film thickness are tabulated and analyzed. The thermocapillarity parameter has a decreasing effect on the temperature field and the local skin-friction coefficient.

Effects of thermocapillarity on the dynamics of an exterior coating flow of a self-rewetting fluid

The effects of thermocapillarity on the dynamics of an exterior coating flow of a self-rewetting fluid on a vertical fibre are investigated theoretically. Whereas surface tension decreases linearly with temperature for most fluids, the surface tension of a self-rewetting fluid exhibits a well-defined minimum. We developed an evolution equation for the interface in the framework of the long wave approximation. Linear stability analysis and numerical simulations on the nonlinear evolution have been performed to investigate the effects of thermocapillarity for axisymmetric disturbances. The results showed that thermocapillarity plays different roles in the stability and dynamics depending on the value of difference between the temperature at the interface, Θ¯i, and the temperature corresponding the minimum of the surface tension, Θ0. The results of linear stability analysis showed that the thermocapillarity is destabilizing or stabilizing as Θ¯i-Θ0 is negative or positive. At the nonlinear stage, for Θ¯i-Θ0<0 more pronounced beads-like structures are observed due to the reinforcement between the thermocapillarity and the Rayleigh-Plateau instability. However, for Θ¯i-Θ0>0 the thermocapillarity weakens the tendency of formation of beads due to the Rayleigh-Plateau mechanism.

Simulation of Single Bubble Evaporation in a Microchannel in Zero Gravity With Thermocapillary Effect

This paper presents fundamental research on the hydrodynamics and heat transfer surrounding a single elongated bubble during flow boiling in a circular microchannel. A continuum surface force (CSF) model based on the volume of fluid (VOF) method is combined with the thermocapillary force to explore the effects of thermocapillarity for flow boiling in microchannels. To validate the self-defined codes, a two-phase thermocapillary-driven flow and a Taylor bubble growing in a capillary tube are studied. Results of both test cases show good convergence and agreement with data from the earlier literature. The bubble motion and the local heat transfer coefficient (HTC) on the heated wall with respect to time are discussed. It is found that for large Marangoni number (case 3), variation of surface tension has affected the bubble shape and temperature profile. The thermocapillary effect induces convection in a thin liquid film region, which augments the HTCs at specified positions. The numerical investigation also shows that the average HTC increased by 6.7% in case 3 when compared with case 1. Thus, it is very important to study further the effects of themocapillarity and the Marangoni effect on bubble growth in microchannels.

Effects of gravity on the thermo-hydrodynamics of moving contact lines

In this paper, we demonstrate the effects of gravity on the interfacial thermo-hydrodynamics as modulated by the patterned wettability gradients placed on the surfaces of a narrow fluidic channel. We investigate the dynamics of contact line motion of two-component incompressible immiscible liquid mixtures under the framework of a thermodynamically consistent phase field model. We validate our model with the experimental results available in the literature in the purview of thermocapillary-actuated microscale transport. We show that the gravity-induced forces in the presence of the thermocapillarity effect play a unique role on the interfacial dynamics at small scales, leading to a uniform movement of the interface in the channel, and offer a greater degree of controllability in the filling/wetting rate in the capillary. We show that the change in patch width, placed on the walls of the channel, leads to a change in the filling dynamics into the capillary. Also, we investigate the rate of different dissipations during the movement of the contact line along the channel and show that the kinetic energy modulated dissipation provides maximum energy to the motion of the contact line.

The effect of thermocapillarity on the dynamics of an exterior coating film flow down a fibre subject to an axial temperature gradient

The dynamics of a viscous film flowing down a vertical fibre under the action of gravity and the thermocapillarity induced by an axial temperature gradient is investigated theoretically. The instability of this exterior coating flow is driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity. We derived an evolution equation for the interface in the framework of the long wave approximation. A linear stability analysis and a nonlinear simulation are performed to investigate the influence of the thermocapillarity on the dynamics of axisymmetric disturbances. The results of linear stability showed that the thermocapillarity does not influence the growth rate of the disturbance and only affects its frequency. For the nonlinear evolution, the thermocapillarity plays an important role in influencing the profile of the interface in different flow regimes. We also examined the effect of thermocapillarity on the wave speed and the characteristics of the structures of travelling wave solutions.

Effect of thermocapillarity and variable thermal conductivity on the heat transfer analysis of a non-Newtonian liquid thin film over a stretching surface in the presence of thermal radiation and heat source/sink

Abstract An analysis illustrating the flow of an Ostwald-de-Waele liquid film on an unsteady stretching sheet under the influence of thermocapillary force, magnetic field and viscous dissipation is carried out. In this study, thermal conductivity is assumed to be a function of fluid temperature. Numerical solutions for the partial differential equations governing the flow are obtained by employing the elegant Runge-Kutta-Fehlberg method for certain representative values of controlling parameters, such as thermocapillarity number, magnetic field parameter, etc. Film thickness is calculated for various values of flow parameters. Film thickness of shear thinning fluids is found to be smaller than that of a Newtonian fluid and a converse trend holds true for shear thickening fluids. Thicker films are noticed for increasing values of thermocapillarity number. In the presence of thermocapillary force, an initial decrease in the velocity of a shear thinning fluid occurs before fluid velocity experiences a significant increase towards the free surface. Stronger magnetic field strengths are seen to increase the free surface velocity. Themocapillary force on temperature in a shear thinning fluid is more prominent.

Thermocapillarity Effects on Power-Law Liquids Thin Film Over an Unsteady Stretching Sheet

This paper investigates the effects of thermocapillarity on the flow and heat transfer in power-law liquid film over an unsteady stretching sheet. The surface tension is assumed to vary linearly with temperature, and the thermal conductivity of the fluid is assumed power-law-dependent on the velocity gradient with modified Fourier's law. The local similarity solutions are obtained numerically, and some interesting new phenomena are found. Results indicate that the thermally induced surface tension provides an opposite force in the direction of the stretching sheet which may cause the fluid adjacent to the free surface to flow in the opposite directions. The effect of thermocapillarity tends to decrease the thin film thickness and results in a smaller temperature distribution. With the increasing unsteadiness parameter, the thin film thickness has a local maximum, and thermal boundary layer is confined to the lower part of the thin film for bigger Prandtl number, while the temperature in the thin film remains equal to the slit temperature with Prandtl number close to 0.

Thermocapillary effect on the absolute and convective instabilities of film flows down a fibre

We consider the motion of a gravity-driven flow down a uniformly heated vertical fibre. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity at the interface. A spatio-temporal stability analysis is performed to investigate the effect of thermocapillarity (Marangoni effect) on the convective/absolute instability (CI/AI) characteristics of the problem. We also performed a numerical simulation of Eq. (30) on the nonlinear evolution of the film to connect the breakup behaviours with the CI/AI characteristics. Our numerical results showed that for various Marangoni number (Ma), breakup of the film mainly occurs in the AI regime. With the increase of Ma, the film has a tendency to break up into droplets due to the enhancement of the absolute instability.

Heat transfer performance and melting dynamic of a phase change material subjected to thermocapillary effects

We carry out extensive numerical simulations on the melting of the Phase Change Material n-octadecane subjected to thermocapillary driving at a free surface on geometries with the form of circular sections of radius in order of centimeters. Simulations employ Stefan numbers Ste=0.22 and Ste=0.67. We compare the heat transfer performance with melting induced only by conduction and find a reduction of melting times by thermocapillarity up to a factor five for semicircular geometries. As a consequence, we propose the use of this mechanism in applications of thermoregulation in microgravity that require fast charge and discharge cycles. We show how a longer free surface enhances the effect of thermocapillarity on the heat transfer performance due to a greater contact area of solid PCM with regions of melted PCM dominated by thermocapillary flows. The length of the free surface has more impact on the heat transfer performance than the contact area between PCM and heat source in the geometries studied in this work. Besides, we observe as well how greater thermal gradients for higher Stefan number augment the importance of thermocapillary effects on the heat transfer performance.

On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient

This manuscript addresses the linear stability analysis of a thermoconvective problem in an annular domain. The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. The effects of several parameters in the flow are evaluated. Three different values for the ratio of the momentum diffusivity and thermal diffusivity are considered: relatively low Prandtl number (Pr = 1), intermediate Prandtl number (Pr = 5) and high Prandtl number (ideally Pr ? ? , namely Pr = 50). The thermal boundary condition on the top surface is changed by imposing different values of the Biot number, Bi. The influence of the aspect ratio (?) is assessed for through by studying several aspect ratios, ?. The study has been performed for two values of the Bond number (namely Bo = 5 and 50), estimating the perturbation given by thermocapillarity effects on buoyancy effects. Different kinds of competing solutions appear on localized zones of the ?-Bi plane. The boundaries of these zones are made up of co-dimension two points. Co-dimension two points are found to be function of Bond number, Marangoni number and boundary conditions but to be independent on the Prandtl number.