Misconceptions in wetting phenomena

Stages That Lead to Drop Depinning and Onset of Motion

In this paper, we consider drops that are subjected to a gradually increasing lateral force and follow the stages of the motion of the drops. We show that the first time a drop slides as a whole is when the receding edge of the drop is pulled by the advancing edge (the advancing edge drags the receding edge). The generality of this phenomenon includes sessile and pendant drops and spans over various chemically and topographically different cases. Because this observation is true for both pendant and sessile cases, we exclude hydrostatic pressure as its reason. Instead, we explain it in terms of the wetting adaptation and interfacial modulus, that is, the difference in the energies of the solid interface at the advancing and receding edges. At the receding edge, a slight motion exposes to the air a recently wetted solid surface whose molecules had reoriented to the liquid and will take time to reorient back to the air. This results in a high surface energy at the solid-air interface which pulls on the triple line, that is, inhibits the motion of the receding edge. On the other hand, at the advancing edge, a slight advancement does not change the nature of the solid interfacial molecules outside the drop, and the advancing side's sliding can continue. Moreover, the solid molecules under the drop at the advancing edge take time to reorient, and hence, their configuration is not yet adapted for the liquid and therefore not adapted for retention of the advancing edge. Therefore, in sliding-drop experiments, the advancing edge moves before the receding one, typically a few times before the receding edge moves. For the same reason, the last motion of the receding edge usually happens as a result of the advancing edge pulling on it.

How and When the Cassie-Baxter Droplet Starts to Slide on Textured Surfaces

A theoretical analysis of the sliding of a Cassie-Baxter droplet on a microstructured surface is conducted. The conventional theory based on the force balance has been frequently used to predict the sliding condition of the droplet; however, the sliding condition cannot be precisely determined because the theory requires the available ranges of the contact angles at the rear and front ends of the droplet. In this study, by calculating the droplet shape and examining the stability of a droplet at every possible pinning point, we propose a new theoretical model that can predict the sliding condition of a two-dimensional (2D) Cassie-Baxter droplet without any a priori measurement but using only the surface information. With the proposed theory, we answer two open questions in sliding research: (i) whether the sliding initiates with front end slip or rear end slip and (ii) whether the advancing and receding contact angles measured on the horizontal surface are comparable with the front and rear contact angles of the droplet at the onset of sliding. Additionally, a new droplet translation motion mechanism promoted by a cycle of condensation and evaporation is suggested, which can be further utilized for precise droplet transportation. Finally, the theoretical results are validated against the 2D line-tension-based front-tracking method (LTM), which can seamlessly capture the attachment and detachment between the droplet and the textured surface.

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

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 two-dimensional 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 and 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 are affected by gravity. In addition, the advancing and receding of the droplet with continuously increasing or decreasing volume are analyzed, and it is shown that the gravitational effect plays a key role in the movement of the droplet tip. Also, the gravitational effect on the degree of the stability of the droplet upon the external effect such as vibration is discussed. Finally, the theoretical predictions were validated against line tension-based front tracking modeling (LTM) 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 into designing devices that utilize the wettability of rough surfaces.

Reply to Comment on "Comparison of the Lateral Retention Forces on Sessile, Pendant, and Inverted Sessile Drops"

We address the issues raised in the Tadmor article (Tadmor, T., et al. Comment on "Comparison of the Lateral Retention Forces on Sessile, Pendant, and Inverted Sessile Drops". Langmuir 2019, 10.1021/acs.langmuir.9b02660). In particular, we explain why we did not use Tadmor's theory to explain our results.

Why Drops Bounce on Smooth Surfaces

It is shown that introducing gravity in the energy minimization of drops on surfaces results in different expressions when minimized with respect to volume or with respect to contact angle. This phenomenon correlates with the probability of drops to bounce on smooth surfaces on which they otherwise form a very small contact angle or wet them completely. Theoretically, none of the two minima is stable: the drop should oscillate from one minimum to the other as long as no other force or friction will dissipate the energy. Experimentally, smooth surfaces indeed show drops that bounce on them. In some cases, they bounce after touching the solid surface, and in some cases they bounce from a nanometric air, or vacuum film. The bouncing energy can be stored in the interfaces: liquid-air, liquid-solid, and solid-air. The lack of a single energy minimum prevents a simple convergence of the drop's shape on the solid surface, and supports its bouncing back to the air. Therefore, the lack of a simple minimum described here supports drop bouncing on hydrophilic surfaces such as that reported by Kolinski et al. Our calculation shows that the smaller the surface tension, the bigger the difference between the contact angles calculated based on the two minima. This agrees with experimental finding where reducing the surface tension, for example, by adding surfactants, increases the probability for bouncing of the drops on smooth surfaces.

The load-bearing ability of a particle raft under the transverse compression of a slender rod

Liquid marbles and particle rafts are liquid interfaces covered with tiny particles, which are accompanied with many exotic behaviors. This study seeks to extend our understanding on the load-bearing ability of a particle raft under the transverse compression of a slender rod. At first, the interface morphologies of the particle raft and water are captured and compared with each other. Then the load-distance curves of the particle raft and water surface are measured using a self-developed device. For the particle raft, the hydrophobicity of the rod almost does not affect the interface morphology and the supporting load. To address the mechanism of this phenomenon, we perform the experiment and find that the surface tension of the particle raft is almost the same as that of water, but the equivalent contact angle of the rod attached to the particles is greatly enhanced. Finally, the model of an axisymmetrical rod pressing liquid is built, and the numerical result is in excellent agreement with the experimental data. These analyses may be beneficial to the measurement of mechanical behaviors for soft interfaces, separation of oil and water, flotation in minerals, and design of miniature boats.

Lateral actuation of an organic droplet on conjugated polymer electrodes via imbalanced interfacial tensions

This paper presents a new mechanism for the controlled lateral actuation of organic droplets on dodecylbenzenesulfonate-doped polypyrrole (PPy(DBS)) electrodes at low voltages (∼0.9 V) in an aqueous environment. The droplet actuation is based on the tunable surface wetting properties of the polymer electrodes induced by electrochemical redox reactions. The contact angle of a dichloromethane (DCM) droplet on the PPy(DBS) surface switches between ∼119° upon oxidation (0.6 V) and ∼150° upon reduction (-0.9 V) in 0.1 M NaNO3 solution. The droplet placed across the reduced and oxidized PPy(DBS) electrodes experiences imbalanced interfacial tensions, which prompt the actuation of the droplet from the reduced electrode to the oxidized electrode. The lateral actuation of DCM droplets on two PPy(DBS) electrodes is demonstrated, and the actuation process is studied. The driving force due to the imbalanced interfacial tensions is estimated to be approximately 10(-7) N for a 6 μL droplet.

On the uniqueness of the receding contact angle: effects of substrate roughness and humidity on evaporation of water drops

Could a unique receding contact angle be indicated for describing the wetting properties of a real gas-liquid-solid system? Could a receding contact angle be defined if the triple line of a sessile drop is not moving at all during the whole measurement process? To what extent is the receding contact angle influenced by the intrinsic properties of the system or the measurement procedures? In order to answer these questions, a systematic investigation was conducted in this study on the effects of substrate roughness and relative humidity on the behavior of pure water drops spreading and evaporating on polycarbonate (PC) surfaces characterized by different morphologies. Dynamic, advancing, and receding contact angles were found to be strongly affected by substrate roughness. Specifically, a receding contact angle could not be measured at all for drops evaporating on the more rugged PC surfaces, since the drops were observed strongly pinning to the substrate almost until their complete disappearance. Substrate roughness and system relative humidity were also found responsible for drastic changes in the depinning time (from ∼10 to ∼60 min). Thus, for measurement observations not sufficiently long, no movement of the triple line could be noted, with, again, the failure to find a receding contact angle. Therefore, to keep using concepts such as the receding contact angle as meaningful specifications of a given gas-liquid-solid system, the imperative to carefully investigate and report the inner characteristics of the system (substrate roughness, topography, impurities, defects, chemical properties, etc.) is pointed out in this study. The necessity of establishing methodological standards (drop size, measurement method, system history, observation interval, relative humidity, etc.) is also suggested.