Thermocapillary Migration of Deformable Bubbles at Moderate to Large Marangoni Number in Microgravity

Zhao, Jian-Fu; Li, Zhendong; Li, Huixiong; Li, Jing

doi:10.1007/s12217-010-9193-x

Cited by 30 publications

(14 citation statements)

References 23 publications

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“…17 that, as the viscosity ratio decreases, the initial droplet velocity increases, but the droplet blocking becomes increasingly significant. This suggests that the Marangoni convection is strengthened with decreasing viscosity ratio, which is consistent with the previous theoretical analysis and numerical results [93,94].…”

supporting

confidence: 92%

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

Liu

Valocchi

Zhang

et al. 2014

Journal of Computational Physics

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To understand how thermocapillary forces manipulate the droplet motion in a confined microchannel, a lattice Boltzmann phase-field model is developed to simulate immiscible thermocapillary flows with consideration of fluid–surface interactions. Based on our recent work of Liu et al., 2013 [54], an interfacial force of potential form is proposed to model the interfacial tension force and the Marangoni stress. As only the first-order derivatives are involved, the proposed interfacial force is easily combined with the wetting boundary condition to account for fluid–surface interactions. The hydrodynamic equations are solved using a multiple-relaxation-time algorithm with the interfacial force treated as a forcing term, while an additional convection–diffusion equation is solved by a passive-scalar approach to obtain the temperature field, which is coupled to the interfacial tension by an equation of state. The model is first validated against analytical solutions for the thermocapillary-driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then demonstrated to produce the correct equilibrium contact angle for a binary fluid with different viscosities when a constant interfacial tension is taken into account. Finally, we numerically simulate the thermocapillary flows for a microfluidic droplet adhering on a solid wall and subject to a simple shear flow when a laser is applied to locally heat the fluids, and investigate the influence of contact angle and fluid viscosity ratio on the droplet dynamical behavior. The droplet motion can be completely blocked provided that the contact angle exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and approximately constant velocity. When the droplet motion is completely blocked, three steady vortices are clearly visible, and the droplet is fully filled by two counter-rotating vortices with the smaller one close to the external vortex. The thermocapillary convection is strengthened with decreasing viscosity ratio of the droplet to the carrier fluid. For low viscosity ratios, the droplet motion is completely blocked and exhibits the similar behavior, but the structure of the internal vortices is more complicated at the lowest viscosity ratio. For high viscosity ratios, the droplet motion is partially blocked and undergoes a series of complex transitions, which can be explained as a result of the dynamically varying Marangoni forces

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supporting

confidence: 92%

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

Liu

Valocchi

Zhang

et al. 2014

Journal of Computational Physics

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“…These range from boundary-fitted grids (Chen & Lee 1992;Welch 1998), to the level-set method (Haj-Hariri et al 1997;Zhao et al 2010), the VOF method (Ma & Bothe 2011), diffuse-interface methods (Borcia & Bestehorn 2007) and hybrid schemes of the Lattice-Boltzmann and the finite difference method (Liu et al 2013). It was shown by Chen & Lee (1992) that surface deformation of gas bubbles reduces considerably their terminal velocity.…”

Section: Introductionmentioning

confidence: 99%

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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“…In the following we therefore concentrate on numerical methods for surfactant induced Marangoni flows. For numerical investigations of thermal Marangoni flows with a LS method the interested reader is referred to Haj-Hariri et al (1997) and Zhao et al (2010), with a FT method to Nas and Tryggvason (2003), and with a VOF method to Ma and Bothe (2011).…”

Section: Models For Surface Tensionmentioning

confidence: 99%

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Wörner

2012

Microfluid Nanofluid

364

197

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This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volumeof-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier-Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

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Thermocapillary Migration of Deformable Bubbles at Moderate to Large Marangoni Number in Microgravity

Cited by 30 publications

References 23 publications

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

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

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

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