7
Conclusions
In this dissertation, we examined the behavior of sessile drops of perfectly wetting liquids of different volatilities as they evaporated to open air under normal ambient conditions. After a general intro-duction (Chapter 1), which highlighted one’s daily interaction (either deliberate or accidental) with wetting and capillarity, and a brief discussion on related theoretical concepts (Chapter 2), we gave a detailed description of the experimental apparatus developed in order to investigate these phenomena (Chapter 3). In particular, three different interferometric techniques were explored, experimentally and theoretically, before deciding upon the optimum solution. The final choice was basically made in terms of the maximum contact angle that we could possibly measure with each of the three setups for a given level of magnification. Under the given constraints, the Mach-Zehnder interferometer proved to be the most efficient one. The algorithm used to process the acquired images was also considered in that chapter.
As soon as we presented the principles of our experimental procedure, we continued by showing tests performed on a plate of polycarbonate (poor thermal conductor) with freely receding evaporating droplets (∼ 2mm radius) of three different wetting liquids, i.e., HFE-7100, 7200 and 7500 (Chap-ter 4). The difference between them consists mainly in the vapor pressure and consequently in the evaporation rate of each of them, with the former being the most volatile one. Our main goal here was to measure the evaporation-induced contact angles that act in a micro-region close to the contact line. To this purpose, we first measured the apparent contact angles. The obtained results indicated that for the largest part of the receding motion the contact angle was constant with the radius. Yet, before directly relating the measured angles to the evaporation-induced ones, we tried to estimate and eventually exclude any velocity-induced contributions, using a modified version of the Cox-Voinov law. Velocity effects were negligible for HFE-7100 and 7200, except for small radii (< 0.5mm), but not for HFE-7500. Even more interestingly, the calculated evaporation-induced contact angles for HFE-7500 varied with the radius in a way similar to what has already been predicted theoretically. Nevertheless, our analysis assumed that in the conducted experiments the only mechanism that could influence the apparent contact angle (with respect to the evaporation-induced one) was the contact line speed. Moreover, the value of the logarithm used in the modified Cox-Voinov equation was based on rational but not necessarily accurate arguments. Thus, as an extension of the present study, a deeper theoretical analysis to clarify these points could be useful.
CHAPTER 7. CONCLUSIONS
In parallel with the above developments, we studied the evaporation rates as well, since these were also measured in our experiments. Clearly, the evaporation rates deviated from the classical the-ory for diffusion-limited evaporation, which predicts a linear behavior of the global evaporation rate with the radius. The non-linear trend observed here, attributed to the buoyancy-induced convection, would become more apparent with increasing radius and volatility. We also attempted to correlate the evaporation-induced angles with the evaporation rate, incorporating however the effect of convection in a semi-heuristic way. The power law predicted by theory was matching nicely with our results. As a recommendation for future work, one could perform similar experiments, yet on a highly conductive substrate, while its surface temperature is both measured and controlled.
Nevertheless, our study was not restricted only to the above observations. The droplets examined in Chapter 4 demonstrated a noteworthy feature concerning their shape. This issue was extensively reviewed in Chapter 5. Surprisingly, the experimentally obtained profiles turned out to deviate from the classical macroscopic static shape of a sessile droplet (as determined by gravity and capillar-ity), often used when modeling evaporating droplets. These deviations could be seen in two ways. Namely, either the droplet appeared to be inflated as compared to the classical static shape assum-ing the same contact angle and contact radius, or the apparent contact angle appeared lower than the classical static one assuming the same volume and contact radius. More specifically, the experimen-tal profiles exhibited a local decrease of the slope near the contact line, which we attributed to the Marangoni effect in an evaporating sessile droplet. In this case, the radially inward (along the liquid-air interface) direction of the flow delivered more liquid to the center of the droplet making it appear inflated. When the Marangoni effect was weak, as in the case of the poorly volatile HFE-7500, no significant influence was noticed on the drop shape. The experimental results were compared and eventually agreed fairly well with the predictions of a lubrication-type theoretical model that incor-porated the evaporation-induced Marangoni flow. The described model was in fact a generalization of the classical static shape theory. Additional experiments with pinned droplets of various radii were also performed. Although the results were not as reliable as in the freely receding case, mainly due to a strong cooling-down of the substrate, we could still observe an inflation of the droplet for most of the cases. Yet, the direction of the Marangoni flow in this configuration was debatable. The repe-tition, particularly of the latter experiments, on a highly conductive substrate would possibly lead to far more enlightening conclusions.
Furthermore, the vapor measurement technique developed by Dehaeck et al. [2014] could be used simultaneously in order to measure the real liquid-air interfacial temperature profile, which could serve as a more accurate input for the model. Similarly, we could also perform the experiments on substrates where a negative Marangoni effect is expected, which was only hypothesized in the case of pinned droplets, and hopefully extract the corresponding Marangoni shapes.
Finally, in Chapter 6, we mainly demonstrated, both experimentally and theoretically, that evapora-tion enhanced the pinning of contact lines at sharp edges in the case of the perfectly wetting liquids considered here. The critical angle to be reached for depinning was augmented above the value ex-pected from equilibrium thermodynamics by a value increasing with the evaporation rate. To account for this effect, we suggested to replace the Young’s angle in the classical Gibbs’ criterion by an angle dynamically induced by evaporation, and established within some microscale vicinity of the contact line. The qualitative agreement between the experiments and the theory showed that this suggestion is indeed reasonable. Further experimental work should consider partially wetting situations, and extend current theories to account for diffusion-limited evaporation into air.
In addition, we also showed experimentally that the speed at which the contact line advances towards a defect could also increase the depinning angle. Nevertheless, this was apparent only for the least volatile liquid. A simple approach was attempted in order to link the Gibbs’ criterion for depinning
with the advancing contact angle and more specifically with the (modified) Cox-Voinov law. The re-sult could indeed make someone believe that depinning will take place as soon as the drop has reached the advancing angle with respect to the inclined surface. Yet, a more thorough study is necessary here before one definitely arrives at such a conclusion. In the same chapter, we also discussed the effect of a non-axisymmetric boundary constraint on the variation of the contact angle of pinned drops along the perimeter. The remarks presented there were in line with the existing literature.
As a final comment, it is believed that the presented work can significantly help advancing concurrent research related to the evaporation of sessile droplets in open air conditions and more specifically to evaporation-induced contact angles, Marangoni effects and contact line hysteresis. Furthermore, it can pave the way for understanding the impact of various non-equilibrium processes on these phe-nomena, what is rather important for both fundamental and applied research.
