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

Abstract

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...

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

“…Savino et al (2013), and Hu et al Hu et al (2014) demonstrated that the use of these fluids within micro oscillating heat pipes led to an increase in the efficiency of these devices. In a slightly different context, it was very recently shown that the presence of a minimum in surface tension can also have a significant impact on the dynamics of the flow giving rise to very interesting phenomena such as the thermally induced "superspreading" (Karapetsas et al 2014).…”

On the motion of a sessile drop on an incline: Effect of non-monotonic thermocapillary stresses

“…More recent studies involving horizontal and inclined substrates have shown that droplet motion is associated with the effect of contact-angle hysteresis and thermocapillary actuation. [43][44][45][46][47][48] These studies demonstrated the significant dependence of the contact angle on the induced surface-tension forces (Marangoni effect) and the deviation of the droplet's footprint from a circular shape. [43][44][45][46][47][48] Furthermore, wettability gradients induced by temperature gradients along a substrate have been found to influence the ensuing flows inside evaporating droplets.…”

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

“…At x ¼ x 1 , the film thickness is fixed at h 0 ¼ 50 lm [Eq. (27)]. The pressure is fixed at the reservoir pressure…”

“…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.…”