Effect of Contact Line Dynamics on the Thermocapillary Motion of a Droplet on an Inclined Plate

Karapetsas, George; Sahu, Kirti Chandra; Matar, Omar

doi:10.1021/la4014027

Cited by 79 publications

(74 citation statements)

References 24 publications

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“…Other forms of a similar power law dependence have been suggested in the literature based on local analysis near the contact line, i.e., dx ci /dt ≈ θ i 3 − θ a,i 3 , 45 which, however, give qualitatively similar predictions. As noted by Karapetsas et al, 20 imposing the Navier slip condition away from the contact line, and the Cox-Voinov relation at the contact line, is similar to using a generalized Navier boundary, 46 which relates the contact line speed to a viscous stress contribution, and an extra contribution due to an uncompensated Young stress; the latter is present in out-of-equilibrium situations such as the one considered in the present work and exceeds greatly the viscous stress contribution at the contact line.…”

Section: T T T T T T I Lg Ls Sgmentioning

confidence: 70%

“…Thus, only in this unlikely case does the advancing contact angle remain equal to the equilibrium contact angle at the reference temperature and independent of the position of the contact line. 20 We map the transient physical domain, (x,t), onto a computational domain fixed in time, (x′,t′), using …”

Section: T T T T T T I Lg Ls Sgmentioning

confidence: 99%

“…cl cr cl cr cl (20) so that the interior of the drop is mapped to 0 ≤ x′ ≤ 1, and the time-derivatives are expressed as follows:…”

Section: T T T T T T I Lg Ls Sgmentioning

confidence: 99%

“…35 The rest of the paper is organized as follows. In Section II, we outline the main steps of the derivation of the evolution equation for the interface dynamics, and the numerical method used for its numerical solution; full details of this derivation are provided by Karapetsas et al 20 The results are presented and discussed in Section III. Finally, the concluding remarks are given in Section IV.…”

Section: ■ Introductionmentioning

confidence: 99%

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Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

et al. 2014

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ABSTRACT:We study the thermocapillary-driven spreading of a droplet on a nonuniformly heated substrate for fluids associated with a non-monotonic dependence of the surface tension on temperature. We use lubrication theory to derive an evolution equation for the interface that accounts for capillarity and thermocapillarity. The contact line singularity is relieved by using a slip model and a Cox-Voinov relation; the latter features equilibrium contact angles that vary depending on the substrate wettability, which, in turn, is linked to the local temperature. We simulate the spreading of droplets of fluids whose surface tension−temperature curves exhibit a turning point. For cases wherein these turning points correspond to minima, and when these minima are located within the droplet, then thermocapillary stresses drive rapid spreading away from the minima. This gives rise to a significant acceleration of the spreading whose characteristics resemble those associated with the "superspreading" of droplets on hydrophobic substrates. No such behavior is observed for cases in which the turning point corresponds to a surface tension maximum. ■ INTRODUCTIONThe motion of sessile droplets over liquids and solids is of central importance to a number of industrial applications such as coating flow technology, inkjet printing, microfluidics and microelectronics, and medical diagnostics. Despite the apparent simplicity of the physical setup involved, this motion is rather complex and some of its aspects remain poorly understood; in particular, the mechanisms underlying the dynamics of the threephase contact line are still the subject of debate. In view of its complexity 1 and its practical importance, droplet motion has received considerable attention in the literature and has been the subject of two major reviews. 2,3 In this work, we consider the motion of sessile droplets on non-isothermal solid walls, driven by thermocapillarity. The walls underlying the droplets are subjected to a temperature gradient which induces surface tension gradient-driven droplet deformation and migration from low to high surface tension regions. Thermocapillary-driven droplet motion was studied by Bouasse 4 who demonstrated the possibility of inducing droplet-climbing on a heated wire, against the action of gravity, by heating its lower end. Studies involving horizontal substrates have shown that, unless the magnitude of the imposed temperature gradient is sufficiently large, no droplet motion is possible due to contact angle hysteresis, while under certain conditions, steady migration of droplets has been shown. 5,6 A number of studies have examined the thermocapillary motion of droplets theoretically. Brochard 7 determined the spreading characteristics of a wedge-shaped drop in the presence of chemical or thermal gradients via local force and energy balances. This work was generalized by Ford and Nadim 8 to arbitrary, two-dimensional droplet shapes and different contact angles at the two contact lines. Lubrication theory was used to describe the...

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Section: T T T T T T I Lg Ls Sgmentioning

confidence: 70%

Section: T T T T T T I Lg Ls Sgmentioning

confidence: 99%

“…cl cr cl cr cl (20) so that the interior of the drop is mapped to 0 ≤ x′ ≤ 1, and the time-derivatives are expressed as follows:…”

Section: T T T T T T I Lg Ls Sgmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

et al. 2014

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“…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. [37][38][39][40][41][42][43][44] Our study is motivated by immersion lithography, where the occurrence of such residual liquid is undesirable.…”

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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Numerical scrutinization of dropwise condensation heat transfer on an inclined surface

2022

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Recently, achieving an ameliorated heat transfer rate in dropwise condensation (DWC) has attracted the attention of many researchers. Several parameters, including chemical and physical properties of the substrate, inclination, and interfacial characteristics influence DWC heat transfer rate. The variation of inclination angle is followed by the change in droplet shape and consequently, the heat transfer rate are changed. In this study, the effect of droplet shape variation on diverse inclined substrates is simulated. Moreover, three‐dimensional mass, momentum, and energy equations considering the desired boundary conditions on the unstructured grid are utilized for the scrutinization of flow behavior and heat transfer for static and sliding droplets. For the sake of validation, the outcomes obtained from the simulation were compared with existent data in the literature and a proper agreement was attained. Regarding the outcomes, it was of concern that the influence of inclination angle on the droplet shape is more distinct at higher droplet volume; while no considerable change was seen on heat flux of small droplets by increasing the inclination angle. Furthermore, a higher heat transfer rate was noted by exceeding the inclination angle beyond a definite angle. Additionally, the increased heat transfer rate was affirmed by increasing the Marangoni number ( italicMa ) $({Ma})$.

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Effect of Contact Line Dynamics on the Thermocapillary Motion of a Droplet on an Inclined Plate

Cited by 79 publications

References 24 publications

Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

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

Numerical scrutinization of dropwise condensation heat transfer on an inclined surface

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