Thermal singularity and droplet motion in one-component fluids on solid substrates with thermal gradients

Xu, Xinpeng; Qian, Tiezheng

doi:10.1103/physreve.85.061603

Cited by 18 publications

(26 citation statements)

References 59 publications

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“…We assume phase change (i.e., evaporation and condensation) and the dependence of the contact angle on wall temperature are both negligible. Effects of those factors on contact-line motions have been recently studied by Qian and co-workers, 28,29 as well as Karapetsas et al 22 We adopt a slip-length based level-set method, along the lines of that developed and tested by Spelt 30 and Sui and Spelt. [31][32][33] The model accounts for heat transfer, thermocapillarity and effects of fluids inside and outside the droplets.…”

Section: Introductionmentioning

confidence: 99%

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Sui

2014

Physics of Fluids

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We study computationally thermocapillary migration of a two-dimensional droplet attached on a horizontal substrate with a constant temperature gradient. A level-set approach is employed to track the droplet interface and a Navier slip boundary condition is imposed to alleviate a stress singularity at the moving contact lines. The present numerical model allows us to consider droplets with large contact angles and to take into account effects of the fluid outside the droplet, both have not been well studied so far. In the limits of a zero contact angle hysteresis and a small viscosity ratio of the fluids outside and inside the droplet (μout/μin ⩽ 0.1), we find the droplet finally migrates towards the cold region, and both the steady migration speed and the velocity field inside the droplet obtained from numerical simulation agree very well with the lubrication theory of Ford and Nadim [“Thermocapillary migration of an attached drop on a solid surface,” Phys. Fluids 6, 3183–3185 (1994)] when the contact angles are small (⩽45°). Beyond this regime, increasing the contact angles leads to increased deviations between numerical simulation and the lubrication theory, and the steady migration speed of the droplet towards the cold side decreases with the contact angles. The simulation results show that the droplet could fall in a motionless regime when its contact angles are around 100° even without any contact angle hysteresis. It is very interesting to find that a droplet with even larger contact angles migrates towards the hot region in a steady speed. We also find the transition of the migration direction of a droplet could strongly depend on the viscosity ratio. With increasing the viscosity of the external fluid, the transition could happen at much smaller values of contact angles. We summarize the results in a phase diagram and discuss the effects of other system parameters, including the contact angle hysteresis, the effective Marangoni number, the Prandtl number, and the slip length, on thermocapillary migration of the droplet.

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Section: Introductionmentioning

confidence: 99%

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Sui

2014

Physics of Fluids

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“…Physically, V mig / T can be regarded as the mobility coefficient associated with the droplet motion driven by asymmetric thermal singularities. In our previous continuum simulations for droplets on solid substrates with thermal gradients, the dimensionless damping coefficient α was numerically found to be of order unity [22]. To explain this numerical finding, the liquid flow within the droplet was assumed to be a Poiseuille flow driven…”

Section: Motion Of Evaporative Droplets Driven By Thermal Gradientsmentioning

confidence: 97%

“…Right panel: snapshots taken from two-dimensional continuum simulations [22] at t/τ 0 = 0, 2000, 4000, and 6000 (from top to bottom), with τ 0 ≡ 2 /ν being the time unit. The fluid space measures L x = 200 by H z = 30 .…”

Section: Motion Of Evaporative Droplets Driven By Thermal Gradientsmentioning

confidence: 99%

“…(The contact line is the intersection of the liquid-vapor interface with the solid surface.) Supplemented with appropriate boundary conditions at the fluid-solid interface [22,[25][26][27], the DVDWT is able to fully take into account the various physical processes involved in the contact line dynamics, including phase transition (evaporation/condensation), capillary flow [23,24], and boundary slip of fluid [25,28,29], etc. It is worth pointing out that although major physical mechanisms and processes are described by this continuum hydrodynamic model, its numerical predictions can only be semi-quantitative because microscopic length scales are involved in the droplet motion and thermodynamic fluctuations are neglected.…”

Section: Introductionmentioning

confidence: 99%

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Molecular dynamics simulations for the motion of evaporative droplets driven by thermal gradients along nanochannels

Qian

2013

J. Phys.: Condens. Matter

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For a one-component fluid on a solid substrate, a thermal singularity may occur at the contact line where the liquid-vapor interface intersects the solid surface. Physically, the liquid-vapor interface is almost isothermal at the liquid-vapor coexistence temperature in one-component fluids while the solid surface is almost isothermal for solids of high thermal conductivity. Therefore, a temperature discontinuity is formed if the two isothermal interfaces are of different temperatures and intersect at the contact line. This leads to the so-called thermal singularity. The localized hydrodynamics involving evaporation/condensation near the contact line leads to a contact angle depending on the underlying substrate temperature. This dependence has been shown to lead to the motion of liquid droplets on solid substrates with thermal gradients (Xu and Qian 2012 Phys. Rev. E 85 061603). In the present work, we carry out molecular dynamics (MD) simulations as numerical experiments to further confirm the predictions made from our previous continuum hydrodynamic modeling and simulations, which are actually semi-quantitatively accurate down to the small length scales in the problem. Using MD simulations, we investigate the motion of evaporative droplets in one-component Lennard-Jones fluids confined in nanochannels with thermal gradients. The droplet is found to migrate in the direction of decreasing temperature of solid walls, with a migration velocity linearly proportional to the temperature gradient. This agrees with the prediction of our continuum model. We then measure the effect of droplet size on the droplet motion. It is found that the droplet mobility is inversely proportional to a dimensionless coefficient associated with the total rate of dissipation due to droplet movement. Our results show that this coefficient is of order unity and increases with the droplet size for the small droplets (~10 nm) simulated in the present work. These findings are in semi-quantitative agreement with the predictions of our continuum model. Finally, we measure the effect of liquid-vapor coexistence temperature on the droplet motion. Through a theoretical analysis on the size of the thermal singularity, it can be shown that the droplet mobility decreases with decreasing coexistence temperature. This is observed in our MD simulations.

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“…14 Other techniques for droplet mobilization include substrate vibrations 15,16 or A.C. electrowetting. 17 Many authors have studied droplet actuation by means of thermocapillary stresses as a consequence of localized heating [18][19][20][21][22][23][24][25][26][27][28] and specifically the effect of thermocapillary stresses on the dynamics of the moving contact lines. [29][30][31][32][33][34][35][36] If either the driving force or the imposed speed exceeds a critical limit, commonly residual liquid is left behind on the substrate.…”

Section: Numerical Simulations I Introductionmentioning

confidence: 99%

Enhancement of contact line mobility by means of infrared laser illumination. II. Numerical simulations

Wedershoven

Tempel

Zeegers

et al. 2016

Journal of Applied Physics

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A droplet that moves on a solid substrate with a velocity higher than a certain critical velocity disintegrates, i.e., leaves behind residual droplets. Infrared laser illumination can be used to increase the droplet mobility and suppress the shedding of droplets. By means of two-dimensional numerical simulations, we studied the effect of a non-uniform temperature distribution on the dynamics of straight receding contact lines. A streamfunction-vorticity model is used to describe the liquid flow in the vicinity of the receding contact line. The model takes into account the thermocapillary shear stress and the temperature-dependent liquid viscosity and density. A second, coupled model describes the laser-induced displacement of the contact line. Our results show that the reduction of the liquid viscosity with increasing temperature is the dominant mechanism for the increase of the critical velocity. Thermocapillary shear stresses are important primarily for low substrate speeds. V C 2016 AIP Publishing LLC. [http://dx

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Thermal singularity and droplet motion in one-component fluids on solid substrates with thermal gradients

Cited by 18 publications

References 59 publications

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Molecular dynamics simulations for the motion of evaporative droplets driven by thermal gradients along nanochannels

Enhancement of contact line mobility by means of infrared laser illumination. II. Numerical simulations

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