Thermocapillary migration and interaction of drops: two non-merging drops in an aligned arrangement

Yin, Zhaohua; Li, Qiaohong

doi:10.1017/jfm.2015.10

Cited by 16 publications

(9 citation statements)

References 44 publications

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“…Quantitatively speaking, the terminal velocity of the binary droplets is around 0.0709, which is quite close to the previous result obtained by the front-tracking method (0.07, extracted from Fig.15 in Ref. [3]). This suggests that the present color-gradient LBM is able to simulate accurately axisymmetric thermocapillary flows even with droplet interactions.…”

Section: The Influence Of M Asupporting

confidence: 91%

“…The study on the thermocapillary migration of droplets or bubbles dates back to the pioneering work of Young et al [1], who derived an analytical expression for the terminal migration velocity of an isolated spherical droplet in a constant temperature gradient by assuming that the convective transport of momentum and energy are negligible. Since then, extensive works on this subject have been conducted theoretically, experimentally and numerically, and most of them have been summarized in the review book by Subramanian and Balasubramaniam [2] as well as in the recent article by Yin and Li [3]. However, it is still challenging to conduct precise experimental measurements of the local temperature and flow fields during the migration process of droplets.…”

Section: Introductionmentioning

confidence: 99%

“…A variety of numerical methods have been proposed to simulate thermocapillary flows with deformed interfaces, and they can roughly be divided into two categories: one is the interface-tracking method, which uses the Lagrangian approach to explicitly represent the interface, such as the front-tracking method [5,3], boundary-integral method [6], and immersed-boundary method [7]; and the other is the interface-capturing method, which uses an indicator function to implicitly represent the interface in an Eulerian grid, such as the volume-of-fluid (VOF) method [8], and level-set (LS) method [9]. However, the interface-tracking methods are not suitable for dealing with interface breakup and coalescence, because the interface must be manually ruptured based upon some ad-hoc criteria.…”

Section: Introductionmentioning

confidence: 99%

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A lattice Boltzmann method for axisymmetric thermocapillary flows

Liu

et al. 2017

International Journal of Heat and Mass Transfer

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In this work, we develop a two-phase lattice Boltzmann method (LBM) to simulate axisymmetric thermocapillary flows. This method simulates the immiscible axisymmetric two-phase flow by an improved color-gradient model, in which the single-phase collision, perturbation and recoloring operators are all presented with the axisymmetric effect taken into account in a simple and computational consistent manner. An additional lattice Boltzmann equation is introduced to describe the evolution of the axisymmetric temperature field, which is coupled to the hydrodynamic equations through an equation of state. This method is first validated by simulations of Rayleigh-Bénard convection in a vertical cylinder and thermocapillary migration of a deformable droplet at various Marangoni numbers. It is then used to simulate the thermocapillary migration of two spherical droplets in a constant applied temperature gradient along their line of centers, and the influence of the Marangoni number (Ca), initial distance between droplets (S 0), and the radius ratio of the leading to trailing droplets (Λ) on the migration process is systematically studied. As M a increases, the thermal wake behind the leading droplet strengthens, resulting in the transition of the droplet migration from coalescence to non-coalescence; and also, the final distance between droplets increases with M a for the non-coalescence cases. The variation of S 0 does not change the final state of the droplets although it has a direct impact on the migration process. In contrast, Λ can significantly influence the migration process of both droplets and their final state: at low M a, decreasing Λ favors the coalescence of both droplets; at high M a, the two droplets do not coalesce eventually but migrate with the same velocity for the small values of Λ, and decreasing Λ leads to a shorter equilibrium time and a faster migration velocity.

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Section: The Influence Of M Asupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A lattice Boltzmann method for axisymmetric thermocapillary flows

Liu

et al. 2017

International Journal of Heat and Mass Transfer

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“…The unsteady thermocapillary migration of a droplet at large Ma numbers was verified experimentally [13,16]. These intrinsic physical mechanisms of the thermocapillary droplet migration at small numbers and large Ma numbers are conducible to the understanding of the interaction of the droplets in both numerical simulations [29,30] and experimental investigations [31].…”

Section: Conclusion and Discussionmentioning

confidence: 75%

Terminal thermocapillary migration of a droplet at small Reynolds numbers and large Marangoni numbers

Wu¹

2017

Acta Mech

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In this paper, the overall steady-state momentum and energy balances in the thermocapillary migration of a droplet at small Reynolds numbers and large Marangoni numbers are investigated to confirm the quasi-steady-state assumption of the system. The droplet is assumed to have a slight axisymmetric deformation from a sphere shape. It is shown that under the quasi-steady-state assumption, the total momentum of the thermocapillary droplet migration system at small Reynolds numbers is conservative. The general solution of the steady momentum equations can be determined with its parameters depending on the temperature fields. However, a nonconservative integral thermal flux across the interface for the steady thermocapillary migration of the droplet at small Reynolds numbers and large Marangoni numbers is identified. The nonconservative integral thermal flux indicates that no solutions of the temperature fields exist for the steady energy equations. The terminal thermocapillary migration of the droplet at small Reynolds numbers and large Marangoni numbers cannot reach a steady state and is thus in an unsteady process.

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“…Experiments on dilute PDCs should be performed with ambient air to ensure proper scaling and reliable study of air entrainment and heating as well as unsteady sedimentation (Andrews andManga 2011, 2012). The study of dense granular flows in channel configuration should be considered with caution because lateral boundaries can have serious influence on flow dynamics (see Brodu et al 2015); this is important in the context of unconfined flows such as most high volume PDCs and debris avalanches. In addition, the temporal dynamics of these flows are often difficult to reproduce in experiments under controlled conditions, making it important of complementing the experiments with numerical simulations.…”

Section: Summary and Perspectivesmentioning

confidence: 99%

The contribution of experimental volcanology to the study of the physics of eruptive processes, and related scaling issues: A review

Roche

Carazzo

2019

Journal of Volcanology and Geothermal Research

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The experimental approach has become a major tool increasingly used by volcanologists in recent decades to investigate the physics of eruptive processes in complement to field and theoretical works. Researchers have developed various methodologies to study volcanic phenomena at reduced length scale. The works involve natural or analogue materials and their types range from first-order tests, to identify fundamental processes and make qualitative comparison with field observations, to more sophisticated experiments in which precise data obtained in a controlled environment can be used to validate outputs of theoretical models. Scaling is a central issue to ensure dynamic similarity between the small-scale experiments and the large-scale volcanic phenomena when natural conditions cannot be simulated due to inherent length scale difference and/or technical limitations. In this respect, dimensionless numbers are used to map physical regimes and to define scaling laws, which allow experimental results to be extrapolated to natural scale. This review presents the variety of experimental studies conducted to investigate subterraneous and aerial volcanic phenomena involving in particular fluid-particle mixtures. We focus on the major scaling issues and the physical regimes investigated, and we also highlight in a historical perspective some of the major advances achieved through experimental studies. Finally we conclude on some perspectives for future works.

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Thermocapillary migration and interaction of drops: two non-merging drops in an aligned arrangement

Cited by 16 publications

References 44 publications

A lattice Boltzmann method for axisymmetric thermocapillary flows

A lattice Boltzmann method for axisymmetric thermocapillary flows

Terminal thermocapillary migration of a droplet at small Reynolds numbers and large Marangoni numbers

The contribution of experimental volcanology to the study of the physics of eruptive processes, and related scaling issues: A review

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