Thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

Wu, Zhongxing; Hu, Wenrui

doi:10.1007/s00707-011-0587-7

Cited by 24 publications

(21 citation statements)

References 36 publications

(85 reference statements)

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“…As was shown by Herrmann et al (2008), the assumption of quasi-steady-state is not valid also for large Marangoni numbers. The latter finding was very recently confirmed by Wu & Hu (2012.…”

Section: Introductionsupporting

confidence: 72%

Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature

et al. 2014

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We study the motion of a bubble driven by buoyancy and thermocapillarity in a tube with a non-uniformly-heated walls, containing a so-called "self-rewetting fluid"; the surface tension of the latter exhibits a parabolic dependence on temperature with a well-defined minimum. In the Stokes flow limit, we derive the conditions under which a spherical bubble can come to rest in a self-rewetting fluid whose temperature varies linearly in the vertical direction, and demonstrate that this is possible for both positive and negative temperature gradients. This is in contrast to the case of simple fluids whose surface tension decreases linearly with temperature for which bubble motion is arrested for negative temperature gradients only. In the case of self-rewetting fluids, we propose an analytical expression for the position of bubble arrestment as a function of other dimensionless numbers. We also perform direct numerical simulation of axisymmetric bubble motion in a fluid whose temperature increases linearly with vertical distance from the bottom of the tube; this is done for a range of Bond and Gallileo numbers, and for various parameters that govern the functional dependence of surface tension on temperature. We demonstrate that bubble motion can be reversed and then arrested in self-rewetting fluids only, and not in linear ones, for sufficiently small Bond numbers. We also demonstrate that considerable bubble elongation is possible under significant wall confinement, and for strongly self-rewetting fluids and large Bond numbers. The mechanisms underlying the phenomena observed are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow.

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“…As was shown by Herrmann et al (2008), the assumption of quasi-steady-state is not valid also for large Marangoni numbers. The latter finding was very recently confirmed by Wu & Hu (2012.…”

Section: Introductionsupporting

confidence: 72%

Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature

et al. 2014

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“…They are related to the eight independent characteristic quantities (R 0 , v 0 , GR 0 , σ 0 , ρ 1 , µ 1 , k 1 and κ 1 ). Based on the above five basic dimensions, the eight characteristic quantities can be described as In [19], the numerical studies on the thermocapillary droplet migration focused on the parameters of the system 0.66 ≤ Re ≤ 53.4, 44.7 ≤ Ma ≤ 3622.8 and 0.0044 ≤ Ca ≤ 0.040, which are regulated with the radius R 0 .…”

Section: Dimension Analysismentioning

confidence: 99%

Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

2017

International Journal of Heat and Mass Transfer

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In this paper, thermocapillary migration of a planar droplet at moderate and large Marangoni numbers is investigated analytically and numerically. By using the dimension-analysis method, the thermal diffusion time scale is determined as the controlling one of the thermocapillary droplet migration system. During this time, the whole thermocapillary migration process is fully developed. By using the front-tracking method, the steady/unsteady states as the terminal ones at moderate/large Marangoni numbers are captured in a longer time scale than the thermal diffusion time scale. In the terminal states, the instantaneous velocity fields in the unsteady migration process at large Marangoni numbers have the forms of the steady ones at moderate Marangoni numbers. However, in view of the former instantaneous temperature fields, the surface tension of the top surface of the droplet gradually becomes the main component of the driving force on the droplet after the inflection point appears. It is different from that the surface tension of the bottom surface of the droplet isthe main component of the driving force on the droplet for the latter ones. The physical mechanism of thermocapillary droplet migration can be described as the significance of the thermal convection around the droplet is higher than/just as the thermal conduction across the droplet at large/moderate Marangoni numbers.

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“…is the Capillary number], it is not included in this study due to the small We numbers [14,16]. Thus, the solutions of Eqs.…”

Section: Problem Formulationmentioning

confidence: 99%

Thermocapillary migration of a droplet with a thermal source at large Reynolds and Marangoni numbers

2014

International Journal of Heat and Mass Transfer

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a b s t r a c tThe unsteady process for thermocapillary droplet migration at large Reynolds and Marangoni numbers has been previously reported by identifying a nonconservative integral thermal flux across the surface in the steady thermocapillary droplet migration (Wu and Hu, 2013) [15]. Here we add a thermal source in the droplet to preserve the integral thermal flux across the surface as conservative, so that thermocapillary droplet migration at large Reynolds and Marangoni numbers can reach a quasi-steady process. Under assumptions of quasi-steady state and non-deformation of the droplet, we make an analytical result for the steady thermocapillary migration of droplet with the thermal source at large Reynolds and Marangoni numbers. The result shows that the thermocapillary droplet migration speed slowly increases with the increase of Marangoni number.

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Thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

Cited by 24 publications

References 36 publications

Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature

Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature

Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

Thermocapillary migration of a droplet with a thermal source at large Reynolds and Marangoni numbers

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