Effect of wall proximity on the lateral thermocapillary migration of droplet rising in a quiescent liquid
TL;DR: In this paper, the effect of lateral wall proximity on the thermocapillary migration of a droplet near a wall has been studied in a two-dimensional and three-dimensional domain.
Abstract: A numerical study is performed to observe the effect of lateral wall proximity on the thermocapillary migration of a droplet. Three-dimensional simulations of the droplet with lateral wall proximity show that the droplet is pulled toward the wall for larger temperature gradients in the ambient and pushed away from the wall at smaller temperature gradients. Parametric studies carried out for migration of a droplet in the vicinity of a wall in a two-dimensional domain show that the droplet behavior is similar to the three-dimensional domain. At different temperature gradients, the final lateral distance of the droplet from the wall does not vary monotonically. The interaction of the temperature field at the leading and trailing ends of the migrating droplet with the wall explains the observed behavior. An extensive parametric study is performed to understand the effect of the Marangoni number, Reynolds number, and property ratios on droplet migration near the wall. Variation in each parameter influences the evolution of temperature both within the droplet and in the ambient fluid. The asymmetric interfacial temperature variation due to the asymmetric evolution of internal circulation within the droplet is correlated with the lateral migration of the droplet. The observations made in the present work reveal physical mechanisms that influence the thermocapillary migration behavior of a droplet near a wall.
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TL;DR: In this paper , a non-dimensionlized thermal radiation number is proposed to quantitatively depict the intensity ratio of the thermal radiation flux to the uniform temperature gradient, and the steady migration velocity decreases with the increasing of Reynolds and Marangoni numbers and increases with the increase of thermal radiation numbers.
Abstract: Thermocapillary migration of a droplet in a vertical temperature gradient controlled by uniform and non-uniform thermal radiations is theoretically analyzed and numerically investigated. A non-dimensionlized thermal radiation number is proposed to quantitatively depict the intensity ratio of the thermal radiation flux to the uniform temperature gradient. From the momentum and energy equations at zero limits of Reynolds and Marangoni numbers, analytical results for the uniform and non-uniform thermal radiations are determined. The steady migration velocity raises with the increasing of the thermal radiation number. By using the front-tracking method, it is observed that thermocapillary droplet migration under the uniform thermal radiation at moderate Marangoni and moderate thermal radiation numbers reaches a steady process. The steady migration velocity decreases with the increasing of Marangoni number and increases with the increasing of thermal radiation number. Moreover, the intensity of thermal energy transferred from the interface to both fluids depends on the volume heat capacity ratio. For the larger/smaller volume heat capacity ratio, more heat is transferred into the continuous phase fluid/the droplet. Furthermore, when the uniform thermal radiation is replaced by the non-uniform ones, the time evolutions, the structures of temperature fields, and parameter dependencies of thermocapillary droplet migration at moderate Marangoni and moderate thermal radiation numbers remain qualitatively unchanged. This study provides a profound understanding of thermocapillary droplet migration in a vertical temperature gradient controlled by thermal radiations, which is of great significance for practical applications in microgravity and microfluidic fields.
5 citations
TL;DR: In this paper , the authors analyzed the role of interfacial rheology on thermocapillary migration of a deformed droplet in the combined vertical temperature gradient and thermal radiations with uniform and non-uniform fluxes.
Abstract: Thermocapillary migration of a deformed droplet in the combined vertical temperature gradient and thermal radiations with uniform and non-uniform fluxes is first analyzed. The creeping flow solutions show that the deformed droplet has a slender or a cardioid shape, which depends on the form of the radiation flux. The deviation from a sphere depends not only on the viscosity and the conductivity ratios of two-phase fluids but also on capillary and thermal radiation numbers. Moreover, in the roles of interfacial rheology on thermocapillary migration of a deformed droplet, only the surface dilatational viscosity and the surface internal energy can reduce the steady migration velocity, but the surface shear viscosity has not any effects on the steady migration velocity. The surface shear and dilatational viscosities affect the deformation of the droplet by increasing the viscosity ratio of two-phase fluids. The surface internal energy directly reduces the deformation of the droplet. However, the deformed droplet still keeps its original shape without the influence of interfacial rheology. Furthermore, it is found that, based on the net force balance condition of the droplet, the normal stress balance at the interface can be used to determine the steady migration velocity, which is not affected by the surface deformation in the creeping flow. From the expressions of the normal/the tangential stress balance, it can be proved that the surface shear viscosity does not affect the steady migration velocity. The results could not only provide a valuable understanding of thermocapillary migration of a deformed droplet with/without the interfacial rheology in a vertical temperature gradient controlled by thermal radiation but also inspire its potential practical applications in microgravity and microfluidic fields.
2 citations
TL;DR: In this article , four different modes of thermally activated migration of a droplet-pair in microchannels are investigated: pure reversing motion, sliding-over motion, follow-up motion, and direct coalescence.
Abstract: Pattern formation and dynamics of interacting droplets in confined passages are ubiquitous in a variety of natural, physical, and chemical processes and appears to be contrasting as compared to single droplet dynamics. However, while the dynamical evolution of single droplets under various forces, including their thermally driven motion, has been explored extensively, the concerned physical facets cannot be trivially extended for addressing the motion of multiple droplets. By considering temperature-gradient-driven interfacial transport, here, we unveil four different modes of thermally activated migration of a droplet-pair in microchannels. These include pure reversing motion, sliding-over motion, follow-up motion, and direct coalescence. The presence of follow-up motion, because of the imposed temperature gradient, has not been investigated before. We further put forward the possibility of conversion of one pattern to another by modulating different tuning parameters, such as the wall temperature, channel dimension, and the relative initial positioning of the droplets. These results may turn out to be of profound importance in a wide variety of applications ranging from materials processing to micro-reactor technology.
1 citations
TL;DR: In this article , the authors studied the thermocapillary migration dynamics of a droplet with a non-circular footprint on an oleophilic track numerically and found that reducing the width of the track improves the droplet migration velocity only upto a specific track width.
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TL;DR: In this paper, a force density proportional to the surface curvature of constant color is defined at each point in the transition region; this force-density is normalized in such a way that the conventional description of surface tension on an interface is recovered when the ratio of local transition-reion thickness to local curvature radius approaches zero.
7,863 citations
TL;DR: In this article, it has been demonstrated that small bubbles in pure liquids can be held stationary or driven downwards by means of a sufficiently strong negative temperature gradient in the vertical direction, due to the stresses resulting from the thermal variation of surface tension at the bubble surface.
Abstract: It has been observed experimentally that small bubbles in pure liquids can be held stationary or driven downwards by means of a sufficiently strong negative temperature gradient in the vertical direction. This effect is demonstrated to be due to the stresses resulting from the thermal variation of surface tension at the bubble surface. The flow field within and around the bubble is derived, and an expression for the magnitude of the temperature gradient required to hold the bubble stationary is obtained. This expression is verified experimentally.
894 citations
TL;DR: In this article, experiments on the thermocapillary migration of air bubbles and Fluorinert drops in a Dow-Corning silicone oil aboard a NASA Space Shuttle mission are presented and discussed.
Abstract: Results from experiments on the thermocapillary migration of air bubbles and Fluorinert drops in a Dow–Corning silicone oil aboard a NASA Space Shuttle mission are presented and discussed. The experiments cover a wider range of Marangoni and Reynolds numbers than that attained in a prior flight experiment. The data are consistent with earlier results, and are compared with theoretical predictions. Large air bubbles were found to deform slightly in shape to oblate spheroids while the deformation of even the largest drops was within the uncertainty of the size measurements.
107 citations
TL;DR: In this article, numerical simulations of the thermocapillary motion of a pair of two-and three-dimensional fully deformable bubbles and drops are presented, where the Navier-Stokes equations coupled with the energy conservation equation are solved by a Front Tracking/Finite Difference Method.
101 citations
TL;DR: In this article, the authors present the results of numerical simulations of the three-dimensional thermocapillary motion of deformable viscous drops under the influence of a constant temperature gradient within a second liquid medium and examine the effects of shape deformations and convective transport of momentum and energy on the migration velocity of the drop.
Abstract: We present the results of numerical simulations of the three-dimensional thermocapillary motion of deformable viscous drops under the influence of a constant temperature gradient within a second liquid medium. In particular, we examine the effects of shape deformations and convective transport of momentum and energy on the migration velocity of the drop. A numerical method based on a continuum model for the fluid–fluid interface is used to account for finite drop deformations. An oct-tree adaptive grid refinement scheme is integrated into the numerical method in order to track the interface without the need for interface reconstruction. Interface deformations arising from the convection of energy at small Reynolds numbers are found to be negligible. On the other hand, deformations of the drop shape due to inertial effects, though small in magnitude, are found to retard the motion of the drop. The steady drop shapes are found to resemble oblate or prolate spheroids without fore and aft symmetry, with the d...
98 citations