Why Drops Bounce on Smooth Surfaces

Tadmor, Rafael; Yadav, Sakshi; Gulec, Semih; Leh, Aisha; Dang, Lan; N’guessan, Hartmann E.; Das, Ratul; Turmine, Mireille; Tadmor, Maria

doi:10.1021/acs.langmuir.8b00157

Cited by 11 publications

(7 citation statements)

References 35 publications

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“…We compute the free energy change upon small perturbations on the pining point to determine the stability of a droplet, while assuming the flat bottom surface of the CB state. The free energy of a droplet with the gravitational effect can be expressed as where A LV and A LS refer to the surface area between the liquid and vapor, and liquid and substrate, respectively. We fix one end of a droplet at the pining point and compute the free energy change upon horizontal and vertical perturbations of the other end (inset of Figure c,d) in the presence and absence of gravity.…”

Section: Methodssupporting

confidence: 90%

Gravitational Effect on the Advancing and Receding Angles of a Two-Dimensional Cassie–Baxter Droplet on a Textured Surface

et al. 2020

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Advancing and receding angles are physical quantities frequently measured to characterize the wetting properties of a rough surface. Thermodynamically, the advancing and receding angles are often interpreted as the maximum and minimum contact angles that can be formed by a droplet without losing its stability. Despite intensive research on wetting of rough surfaces, the gravitational effect on these angles has been overlooked because most studies have considered droplets smaller than the capillary length. In this study, however, by combining theoretical and numerical modeling, we show that the shape of a droplet smaller than the capillary length can be substantially modified by gravity under advancing and receding conditions. First, based on the Laplace pressure equation, we predict the shape of a twodimensional Cassie-Baxter droplet on a textured surface with gravity at each pinning point.Then the stability of the droplet is tested by examining the interference between the liquid surface and neighboring pillars as well as analyzing the free energy change upon depinning.Interestingly, it turns out that the apparent contact angles under advancing and receding conditions are not affected by gravity, while the overall shape of a droplet and the position of the pinning point is affected by gravity. In addition, the advancing and receding of the droplet with continuously increasing or decreasing volume is analyzed, and it is showed that the gravitational effect plays a key role on the movement of the droplet tip. Finally, the theoretical predictions were validated against line-tension based front tracking modeling that seamlessly captures the attachment and detachment between the liquid surface and the solid substrate. Our findings provide a deeper understanding on the advancing and receding phenomena of a droplet, and essential insight on designing devices that utilize the wettability of rough surfaces.

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Section: Methodssupporting

confidence: 90%

Gravitational Effect on the Advancing and Receding Angles of a Two-Dimensional Cassie–Baxter Droplet on a Textured Surface

et al. 2020

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“…To describe the effect of gravity on wetting properties, − often, Bond number (or capillary length) is used. The Bond number ( Bo ) describes the ratio of the gravitational to surface tension forces and is defined as where L is a characteristic length scale, ρ is the difference between the density of the drop’s liquid and that of the surrounding, g is the gravitational acceleration, and γ LV is the liquid’s surface tension.…”

Section: Introductionmentioning

confidence: 99%

The Influence of Gravity on Contact Angle and Circumference of Sessile and Pendant Drops has a Crucial Historic Aspect

et al. 2019

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Normally, pendant drops adapt contact angles that are closer to 90°than their sessile analogues. This is due to the drop's weight that pulls the pendant drop and straightens its contact angles. In this paper, we show a case in which the opposite happens: sessile drops that adapt contact angles that are closer to 90°than their pendant analogues. To achieve these peculiar states, one needs to increase the effective gravity on the drops and then relax it again to 1 g. Apparently, this and other phenomena depend not only on the direction of the gravitational force but also on the drop's history. We show that the drop's contact angle (and resultant area) is affected by two types of histories: short-term history and long-term history. For example, if we gradually increase the effective gravity on the drop, decrease it back to 1 g, and then repeat this cycle again and again, we see that the first cycle is drastically different, whereas other cycles approach a plateau in their behavior. In addition to drop's history, we explain these observations in terms of volume conservation, drop contact area, and pinning effect. This study may be generalized for other body forces such as electrical and magnetic or accelerating systems.

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“…Then, the Helmholtz free energy is minimized to seek for the equilibrium contact angle θ for fixed volume. Very recently, Tadmor et al [47] have discussed the gravitational line tension by using the variation of the Gibbs free energy, which allows for the fluctuation of droplet volume. They derived two formulas for the cosine of the contact angle θ.…”

Section: Gravitational Line Tensionmentioning

confidence: 99%

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

Iwamatsu

2018

Preprint

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A generalized Young's equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid-vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman's formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of µN so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretical calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible.

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Why Drops Bounce on Smooth Surfaces

Cited by 11 publications

References 35 publications

Gravitational Effect on the Advancing and Receding Angles of a Two-Dimensional Cassie–Baxter Droplet on a Textured Surface

Gravitational Effect on the Advancing and Receding Angles of a Two-Dimensional Cassie–Baxter Droplet on a Textured Surface

The Influence of Gravity on Contact Angle and Circumference of Sessile and Pendant Drops has a Crucial Historic Aspect

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

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