The spreading of volatile liquid droplets on heated surfaces

Anderson, Daniel M.; Davis, Stephen H.

doi:10.1063/1.868623

Cited by 255 publications

(246 citation statements)

References 23 publications

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“…The consideration of these seemingly large values of K is further supported by several authors ͑e.g., Anderson and Davis 38 ͒ who associated the value of K with the inverse of the Biot number and argued that larger values of K ͑than calculated from the kinetic theory͒ are relevant for these evaporating films. Consideration of the larger range of K in the results below further allows a smooth transition from the regime of a highly volatile liquid, which corresponds to a large heat transfer rate from the free surface to the case of a nonvolatile liquid, which corresponds to a very small rate of heat transfer ͑small Biot number for these thin films͒.…”

Section: B Interfacial Heat Transfermentioning

confidence: 99%

Linear stability of a volatile liquid film flowing over a locally heated surface

Tiwari

Davis

2009

Physics of Fluids

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The dynamics and linear stability of a volatile liquid film flowing over a locally heated surface are investigated. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that leads to the formation of a pronounced capillary ridge. Lubrication theory is used to develop a model for the film evolution that contains three key dimensionless groups: a Marangoni parameter ͑M͒, an evaporation number ͑E͒, and a measure of the vapor pressure driving force for evaporation ͑K͒, which behaves as an inverse Biot number. The two-dimensional, steady solutions for the local film thickness are computed as functions of these parameters. A linear stability analysis of these steady profiles with respect to perturbations in the spanwise direction reveals that the operator of the linearized system can have both a discrete and a continuous spectrum. The continuous spectrum exists for all values of the spanwise wave number and is always stable. The discrete spectrum, which corresponds to eigenfunctions localized around the ridge, appears for values of M larger than a critical value for a finite band of wave numbers separated from zero. Above a second, larger critical value of M, a portion of the discrete spectrum becomes unstable, corresponding to rivulet formation at the forward portion of the capillary ridge. For sufficiently large heat transfer at the free surface, due either to phase change or to convection, a second band of unstable discrete modes appears, which is associated with an oscillatory, thermocapillary instability above the heater. The critical Marangoni parameter above which instability develops, M crit ͑K , E͒, has a nonmonotonic dependence on the steepness of the temperature increase at the heater, in contrast to the monotonic decrease for a nonvolatile film at vanishing Biot number. An energy analysis reveals that the dominant instability mechanism resulting from perturbations to the film thickness is either streamwise capillary flow or gravity for weakly volatile fluids and thermocapillary flow due to spanwise temperature gradients for more volatile fluids. The stability results are rather sensitive to the steepness of the temperature increase and heater width due to the nonlinear coupling of gravity, capillary pressure gradients, thermocapillary flow, and evaporation through the base states.

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Section: B Interfacial Heat Transfermentioning

confidence: 99%

Linear stability of a volatile liquid film flowing over a locally heated surface

Tiwari

Davis

2009

Physics of Fluids

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“…Due to the use of diffuse-interface method, the stress and thermal singularities are resolved automatically. Furthermore, in the DVDWT the evaporation or condensation rate at the liquid-gas interface becomes an outcome of calculation rather than a pre-requisite as in most of the existing models proposed for evaporative droplets [18,[47][48][49][50]. Recently, the DVDWT has been used to study the thermohydrodynamics of boiling in one-component fluids [51].…”

Section: Introductionmentioning

confidence: 99%

“…Though there has been extensive work on the subject, many aspects of this seemingly simple phenomenon remain issues of interest to fundamental research. In the present work, we focus on the hydrodynamics of liquid droplets in one-component liquid-gas systems on heated or cooled substrates [16][17][18][19][20][21][22] and substrates with temperature gradients [5,23]. Here the major challenges lie in the complicated dynamics at the intersection of the free (liquid-gas) interface with the solid substrate, i.e., the threephase contact line.…”

Section: Introductionmentioning

confidence: 99%

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

Qian

2012

Phys. Rev. E

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Using a continuum model capable of describing the one-component liquid-gas hydrodynamics down to the contact line scale, we carry out numerical simulation and physical analysis for the droplet motion driven by thermal singularity. For liquid droplets in one-component fluids on heated or cooled substrates, the liquid-gas interface is nearly isothermal. Consequently, a thermal singularity occurs at the contact line and the Marangoni effect due to temperature gradient is suppressed. Through evaporation or condensation in the vicinity of the contact line, the thermal singularity makes the contact angle increase with the increasing substrate temperature. This effect on the contact angle can be used to move the droplets on substrates with thermal gradients. Our numerical results for this kind of droplet motion are explained by a simple fluid dynamical model at the droplet length scale. Since the mechanism for droplet motion is based on the change of contact angle, a separation of length scales is exhibited through a comparison between the droplet motion induced by a wettability gradient and that by a thermal gradient. It is shown that the flow field at the droplet length scale is independent of the statics or dynamics at the contact line scale.

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“…Ford and Nadim 10 generalized the work of Brochard 9 to allow for arbitrary shapes of the drop and also allowed the contact angles to be different at the two ends. Ehrhard and Davis 11 used lubrication theory to describe the spreading of a droplet on a uniformely heated plate, and Anderson and Davis 12 took into account the effect of evaporation. The latter effect was also studied recently by Karapetsas et al 13 Chen and co-workers took into account the effect of buoyancy convection 14 and studied the phenomenon of thermocapillary nonwetting.…”

Section: ■ Introductionmentioning

confidence: 99%

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

2013

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ABSTRACT:We study the two-dimensional dynamics of a droplet on an inclined, nonisothermal solid substrate. We use lubrication theory to obtain a single evolution equation for the interface, which accounts for gravity, capillarity, and thermocapillarity, brought about by the dependence of the surface tension on temperature. The contact line motion is modeled using a relation that couples the contact line speed to the difference between the dynamic and equilibrium contact angles. The latter are allowed to vary dynamically during the droplet motion through the dependence of the liquid−gas, liquid−solid, and solid−gas surface tensions on the local contact line temperature, thereby altering the local substrate wettability at the two edges of the drop. This is an important feature of our model, which distinguishes it from previous work wherein the contact angle was kept constant. We use finite-elements for the discretization of all spatial derivatives and the implicit Euler method to advance the solution in time. A full parametric study is carried out in order to investigate the interplay between Marangoni stresses, induced by thermo-capillarity, gravity, and contact line dynamics in the presence of local wettability variations. Our results, which are generated for constant substrate temperature gradients, demonstrate that temperature-induced variations of the equilibrium contact angle give rise to complex dynamics. This includes enhanced spreading rates, nonmonotonic dependence of the contact line speed on the applied substrate temperature gradient, as well as "stick−slip" behavior. The mechanisms underlying this dynamics are elucidated herein.

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The spreading of volatile liquid droplets on heated surfaces

Cited by 255 publications

References 23 publications

Linear stability of a volatile liquid film flowing over a locally heated surface

Linear stability of a volatile liquid film flowing over a locally heated surface

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

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

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