Thermocapillary migration of a deformable droplet

Samareh, B.; Mostaghimi, J.; Moreau, Christian

doi:10.1016/j.ijheatmasstransfer.2014.02.022

Cited by 19 publications

(12 citation statements)

References 18 publications

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“…In multiphase flows, numerical study of droplets has been of interest to many researchers due to applications in fields like spray coating and inkjet printing. Many studies like the works of Samareh et al [8], Raessi et al [9], and Bussmann et al [10] have been dedicated to numerical study of droplets in various conditions. Various investigations have been conducted on numerical modeling of liquid drops and bubbles like the work of Tripathi et al [11].…”

Section: Introductionmentioning

confidence: 99%

Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model

Farrokhpanah

Samareh

Mostaghimi

2015

Journal of Fluids Engineering

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Section: Introductionmentioning

confidence: 99%

Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model

Farrokhpanah

Samareh

Mostaghimi

2015

Journal of Fluids Engineering

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“…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%

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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“…On the other hand, Wu & Hu(2007) pointed out an ill-posedness thermal flux boundary condition for the steady thermocapillary droplet migration at large Re numbers and large Ma numbers [17]. Herrmann et al(2008) [18], Wu & Hu(2012) [19] and Samereh et al(2014) [20] investigated the thermocapillary motion of deformable and non-deformable droplets by the numerical methods and indicated that the assumption of the quasi-steady state was not valid in cases of large Re numbers and large Ma numbers. In particular, it was shown [19,20] that the rise velocities of the droplet against the time/the vertical position in the numerical simulations are in qualitative agreement with those in the experimental investigations [13,16].…”

Section: Introductionmentioning

confidence: 99%

“…Herrmann et al(2008) [18], Wu & Hu(2012) [19] and Samereh et al(2014) [20] investigated the thermocapillary motion of deformable and non-deformable droplets by the numerical methods and indicated that the assumption of the quasi-steady state was not valid in cases of large Re numbers and large Ma numbers. In particular, it was shown [19,20] that the rise velocities of the droplet against the time/the vertical position in the numerical simulations are in qualitative agreement with those in the experimental investigations [13,16]. Yin et al(2012) [21] reported a dramatic increase of the computed stable droplet velocities when Ma > 200 in numerical simulations, which also supports the above investigations.…”

Section: Introductionmentioning

confidence: 99%

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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Thermocapillary migration of a deformable droplet

Cited by 19 publications

References 18 publications

Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model

Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model

A lattice Boltzmann method for axisymmetric thermocapillary flows

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

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