Topography-Dependent Effective Contact Line in Droplet Depinning

Adhesion Reduction at Solid/Liquid Interfaces Based on Topologically Optimized Microtextures

Artificial microtextures adopted to achieve adhesion reduction help avoid the vulnerability associated with chemical coatings. Most current microtextures strongly rely on biological inspiration or designers' physical intuition. There are also manufacturing challenges due to the complex geometrical configurations. Topology optimization can determine the structural configurations encompassing geometric information on topology, shape, and size and ensure the manufacturability of the optimized microtextures by controlling the feature size corresponding to a specified fabrication process. Herein, we present an approach to reduce the liquid adhesion on solid surfaces by employing artificial microtextures with hexagonal periodicity, where the microtextures are inversely designed through topology optimization. The microtextures are fabricated of polydimethylsiloxane by using a soft lithography process. The liquid adhesion on the microtextures is measured via the tilting plate method. Experimental results demonstrate that the topologically optimized microtextures can significantly reduce the liquid adhesion by 45.0%, which is achieved by the robust Cassie-Baxter state of the wetting behavior. The topologically optimized microtextures can also support the robust Cassie-Baxter state underwater and accelerate the speed when the droplets slide off the surface with them. The findings can be utilized in the context of the reduction of underwater drag and bioadhesion.

Soft wetting: Substrate softness- and time-dependent droplet/bubble adhesion

HYPOTHESIS

The droplet/bubble adhesion characteristics depend on the length of the droplet/bubble three-phase contact line. Since the deformation caused by the liquid-gas interfacial tension on the soft substrate, referred as to the wetting ridge, retards contact line spreading and retraction, we conjecture that the droplet/bubble adhesion characteristics depend also on the substrate softness.

EXPERIMENTS

Soft substrates with various shear moduli are prepared and characterized by the spreading and receding dynamics of water droplets and underwater bubbles. Snap-in and normal adhesion forces of droplets/bubbles on such soft substrates are directly measured along with the visualized droplet/bubble shape profiles.

FINDINGS

The droplet/bubble snap-in force, which corresponds to the short-time spreading dynamics, decreases with a decrease in the substrate shear modulus because of the retarded contact line spreading. The droplet maximal adhesion force on a soft substrate can be counterintuitively either smaller or larger than its counterpart on the rigid substrate depending on different dwelling times, i.e., the droplet/bubble-substrate contact time before droplet/bubble-substrate separation. The former is attributed to the retarded contact line spreading, whereas the latter is attributed to the retarded contact line retraction. The substrate softness- and dwelling time-dependent droplet/bubble adhesion reported in this study will benefit various applications related to soft substrates.

Soft wetting: an analytical model for pillar topography- and softness-dependent droplet depinning force

The extent to which a droplet pins on a textured substrate is determined by the dynamics of the contact line and the liquid-vapor interface. However, the synergistic contribution of contact line sliding and interface distortion to the droplet depinning force remains unknown. More strikingly, current models fail to predict the depinning force per unit length of droplets on soft pillar arrays. Therefore, we fabricate soft pillar arrays with varying geometrical dimensions and mechanical properties and measure the depinning forces per unit length by allowing droplets to evaporate on such substrates. We then analyze the decrease in excess Gibbs free energy of the apparent droplet caused by the detachment of the droplet boundary from the previously pinned pillars. In contrast to prior notions, based on the measured decreases in excess Gibbs free energy, we find that the coefficient, that governs the ratio of interface distortion's contribution to the depinning force to that of the sliding contact line, increases with a decrease in pillar packing density. By considering the combined contribution from contact line sliding, liquid-vapor interface distortion, and pillar deflection, we introduce an analytical model to predict the droplet depinning force per unit length and corroborate the model using experimental data reported in this and prior studies.

A Superhydrophobicity-Slipperiness Switchable Surface with Magneto- and Thermo-responsive Wires for Repelling Complex Droplets

The inefficacy of repelling water droplets laden with macromolecules (complex droplets or diluted polymer solution) is a long-standing shortcoming of superhydrophobic surfaces, which severely limits their reliability in practical applications. Here, we design a surface termed the superhydrophobicity-slipperiness switchable surface (3S surface), which demonstrates superhydrophobicity at room temperature and slipperiness when heated. The 3S surface is composed of magneto-responsive wires coated with superhydrophobic nanoparticles and impregnated with thermoresponsive paraffin, exhibiting lotus leaf-inspired passive water repellency and respiratory cilia-inspired active water repellency at room temperature. When heated, the impregnated paraffin melts and forms a lubricant layer atop the surface structures, exhibiting the pitcher-plant-inspired removal of complex droplets that remain pinned on conventional superhydrophobic surfaces. The counterintuitive integration of superhydrophobicity (a liquid-solid-gas composite system) and slipperiness (a liquid-lubricant-gas system) into a surface and the on-demand switch between them are not only important to the applicability of self-cleaning surfaces to real-world environments, where complex liquids are inevitable, but also provide insights into various interface-related applications.

Soft Wetting: Droplet Receding Contact Angles on Soft Superhydrophobic Surfaces

Despite intensive investigations on the droplet receding contact angle on superhydrophobic surfaces, i.e., a key parameter characterizing surface wettability and adhesion, the quantitative correlation between the surface structure mechanical properties (softness) and the droplet receding contact angles remains vague. By systematically varying the geometric dimensions and mechanical properties of soft pillar arrays, we find that the droplet receding contact angles decrease with the decrease in the pillar spring constant. Most surprisingly, the densely packed pillar arrays may result in larger receding contact angles than those on sparsely packed pillars, opposing the understanding of rigid pillar arrays, where the receding contact angles increase with a decrease in the packing density of pillars. This is attributed to the collective effects of capillarity and elasticity, where the energy consumed by the sliding contact line, the energy stored in the distorted liquid-vapor interface, and the energy stored in the deflected pillar contribute to the droplet depinning characteristics. We develop an analytical model to predict the droplet receding contact angles on soft superhydrophobic pillar arrays with knowledge of the material intrinsic receding contact angle, the pillar geometry, and the pillar mechanical properties. The predictions are corroborated by the experimental data measured in this and prior studies.

Bioinspired Wire-on-Pillar Magneto-Responsive Superhydrophobic Arrays

Versatile surfaces demonstrating multiple interfacial functionalities are highly demanded as a surface typically serves various duties and faces multiple challenges in real practice. However, such versatile surfaces are rarely reported mainly due to the challenges in integrating multiple structural characteristics. Here, by mimicking lotus leaves, butterfly wing, and respiratory cilia, we develop a surface termed wire-on-pillar magneto-responsive superhydrophobic arrays (WP-MRSA), which possess interfacial properties of structural superhydrophobicity, anisotropicity, stimuli responsiveness, and flexibility. By combining soft lithography and self-alignment of iron-laden aerosols under a magnetic field, iron-laden wires are planted atop prefabricated pillar arrays, resulting in well-ordered, sparse, high-aspect-ratio, flexible, and superhydrophobic wires, which largely deflect in response to a magnetic field. This unique integration of structural properties and configurations enables various functionalities, such as on-demand control of droplet impact dynamics, real-time regulation of surface lateral adhesion force, fast removal and sorting of objects, and precise manipulation of droplets for selective reactions. Those functionalities benefit various applications especially droplet-based microfluidics and active self-cleaning surfaces.

The control of dry-out patterns using bubble-containing droplets

HYPOTHESIS

For an evaporating nanofluid droplet that contains a bubble inside, we suspect the bubble boundary remains pinned during evaporation whereas the droplet perimeter recedes. Thus, the dry-out patterns are mainly determined by the presence of the bubble and their morphology can be tuned by the size and location of the added bubble.

EXPERIMENTS

Bubbles with varying base diameters and lifetimes are added into evaporating droplets that contain nanoparticles with different types, sizes, concentrations, shapes, and wettability. The geometric dimensions of the dry-out patterns are measured.

FINDINGS

For a droplet containing a long-lifetime bubble, a complete ring-like deposit forms, and its diameter and thickness increases and decreases with the bubble base diameter, respectively. The ring completeness, i.e., the ratio of actual ring length to its imaginary perimeter, decreases with the decrease in bubble lifetime. The pinning of droplet receding contact line by particles near the bubble perimeter has been found to be the key factor leading to ring-like deposits. This study introduces a strategy of producing ring-like deposit and allows a control of the ring morphology in a simple, cheap, and impurity-free fashion, which is applicable to various applications associated with evaporative self-assembly.

Through-drop imaging of moving contact lines and contact areas on opaque water-repellent surfaces

A myriad of natural surfaces such as plant leaves and insect wings can repel water and remain unwetted inspiring scientists and engineers to develop water-repellent surfaces for various applications. Those natural and artificial water-repellent surfaces are typically opaque, containing micro- and nano-roughness, and their wetting properties are determined by the details at the actual liquid-solid interface. However, a generally applicable way to directly observe moving contact lines on opaque water-repellent surfaces is missing. Here, we show that the advancing and receding contact lines and corresponding contact area on micro- and nano-rough water-repellent surfaces can be readily and reproducibly quantified using a transparent droplet probe. Combined with a conventional optical microscope, we quantify the progression of the apparent contact area and apparent contact line irregularity in different types of superhydrophobic silicon nanograss surfaces. Contact angles near 180° can be determined with an uncertainty as low as 0.2°, that a conventional contact angle goniometer cannot distinguish. We also identify the pinning/depinning sequences of a pillared model surface with excellent repeatability and quantify the progression of the apparent contact interface and contact angle of natural plant leaves with irregular surface topography.

Wetting state transitions of individual condensed droplets on pillared textured surfaces

The ability to realize the self-removal of condensed droplets from a surface is of critical importance for science and applications such as water harvesting and thermal engineering. Despite the enormous interest in micro/nanotextured superhydrophobic materials for high-efficiency condensation, a clear picture of the wetting state transition of condensed droplets is missing, particularly, on a single-droplet level of the order of micrometers. Herein, by varying a substantial parameter space of the contact angle and the geometry of the pillared textures, we have quantified the wetting transition of individual droplets during condensation. We found that a droplet is finally either spontaneously removed from the textures due to a Laplace pressure difference or wets the textures; four different wetting state transition modes have been identified numerically and they are classified in a phase diagram. Simple theories have been constructed to correlate the critical conditions of the wetting state transition to the wettability and geometry of the textures, and they were verified experimentally. We found that the self-removal of condensed droplets benefits from the contact angle and the height of the pillars. These findings not only enhance our fundamental understanding of the wetting state transition of condensed droplets but also allow the rational design of micro/nanotextured water-repellent materials for anti-fogging and anti-wetting.

Time-Dependent Pinning of Nanoblisters Confined by Two-Dimensional Sheets. Part 2: Contact Line Pinning

Pinning of droplets on solids is an omnipresent wetting phenomenon that attracts intense research interest. Unlike in classical wetting, pinning effects in a novel wetting problem where droplets are confined onto the substrates by elastic films have hardly been investigated. Here, following our study in an accompanying paper (part 1) on the static mechanics of nanoscale blisters confined between a two-dimensional elastic sheet and its substrate, we investigate in this part the pinning behaviors of such blisters by using atomic force microscopy. The blisters' lateral retention forces are shown to scale almost linearly with their contact lines and to increase until saturation upon increasing their resting times. Our analysis reveals a mechanism of microdeformation of the substrate at the contact line. The creep of the microdeformation is found to cause the time-dependent pinning, which is evidenced by residual fine ridge structures left by blisters after their spread after long resting times.

Second-Level Microgroove Convexity is Critical for Air Plastron Restoration on Immersed Hierarchical Superhydrophobic Surfaces

Air plastrons trapped on the surfaces of underwater superhydrophobic surfaces are critical for their function. Fibrillar morphologies offer a natural pathway, yet they are limited to a narrow range of liquid-surface systems and are vulnerable to pressure fluctuations that irreversibly destroy the air layer plastron. Inspired by the convexly grooved bases of water fern (Salvinia) leaves that support their fibrous outgrowths, we focus on the effect of such second-level grooved structures or microgrooves on the plastron restoration on immersed three-dimensional (3D)-printed hierarchical surfaces. Elliptical, interconnected microgrooves are fabricated with varying surface curvatures to study the effect of their morphology. Immersion experiments reveal that the convex groove curvature stabilizes a seed gas layer (SGL) that facilitates plastron restoration for all immersed hydrophobic surfaces. Theoretical calculations and atomic-scale computations reveal that the SGL storage capacity that sets the SGL robustness follows from the liquid menisci adaption to the groove geometry and pressure, from micro- to nanoscales, and it can be further tuned using separated grooves. Our study highlights groove convexity as a key morphological feature for the design of second-level architectures for underwater air plastron restoration on hierarchical superhydrophobic surfaces.

Droplet Spreading and Adhesion on Spherical Surfaces

Adhesion of a liquid droplet to a solid surface is a result of solid surface interactions with surrounding fluids, affected by its wettability and morphology. Unfortunately, the direct measurements of adhesion forces are rarely reported in the scientific literature, especially for solids with curvatures. In this study, by using a high-sensitivity microelectronic mechanical balance which vertically deposits and then pulls liquid droplets, the spreading and adhesion forces for water and ethylene glycol droplets on spherical surfaces of polyethylene terephthalate (PET) with radii of curvature from 2 to 8 mm were recorded. Results show that the surface curvature does not affect the advancing and most-stable contact angles but affects the extent of spreading and maximum adhesion forces. The solid surface curvature affects both surface tension and Laplace pressure forces at the spreading point, whereas it mainly affects the Laplace pressure force at the maximum adhesion point.

Contact Time of Droplet Impact on Inclined Ridged Superhydrophobic Surfaces

Superhydrophobic surfaces decorated with macrostructures have attracted extensive attention due to their excellent performance of reducing the contact time of impacting droplets. In many practical applications, the surface is not perpendicular to the droplet impact direction, but the impacting dynamics in such scenarios still remain mysterious. Here, we experimentally investigate the dynamics of droplet impact on inclined ridged superhydrophobic surfaces and reveal the effect of We_n (the normal Weber number) and α (the inclination angle) on the contact time τ. As We_n increases, τ first decreases rapidly until a platform is reached; if We_n continues to increase, τ further reduces to a lower platform, indicating a three-stage variation of τ in low, middle, and high We_n regions. In the middle and high We_n regions, the contact time is reduced by 30 and 50%, respectively, and is dominated by droplet spreading/retraction in the tangential and lateral directions, respectively. A quantitative analysis demonstrates that τ in the middle and high We_n regions is independent of We_n and α, while the range of middle and high We_n regions is related to α. When α < 30°, increasing α narrows the middle We_n region and enlarges the high We_n region; when α ≥ 30°, the two We_n regions remain unchanged. In addition, droplet sliding is hindered by the friction and is affected by the droplet morphology in the high We_n region. Overall, the synergistic effect of the surface inclination and macrostructures effectively promotes the detachment of impacting droplets on superhydrophobic surfaces, which provides guidance for applications of superhydrophobic surfaces.

Topological Data Analysis of Nanoscale Roughness in Brass Samples

Rough surfaces possess complex topographies, which cannot be characterized by a single parameter. The selection of appropriate roughness parameters depends on a particular application. Large datasets representing surface topography possess orderliness, which can be expressed in terms of topological features in high-dimensional dataspaces reflecting properties such as anisotropy and the number of lay directions. The features are scale-dependent because both sampling length and resolution affect them. We study nanoscale surface roughness using 3 × 3, 4 × 4, and 5 × 5 pixel patches obtained from atomic force microscopy (AFM) images of brass (Cu Zn alloy) samples roughened by a sonochemical treatment. We calculate roughness parameters, correlation length, extremum point distribution, persistence diagrams, and barcodes. These parameters of interest are discussed and compared.

Lubricant-Mediated Strong Droplet Adhesion on Lubricant-Impregnated Surfaces

Lubricant-impregnated surfaces have recently emerged as a new type of multifunctional coating with a promising capability in exhibiting low friction or contact angle hysteresis. However, lubricant-infused surfaces severely suffer from the tensile droplet-lubricant adhesion. In this study, we show that lubricant-infused surfaces allow for a strong tensile droplet adhesion, which results in the generation of an offspring residual droplet when a droplet detaches from the surface. Such tensile liquid-liquid adhesion and the corresponding liquid residue are solely mediated by the lubricant, independent of the underlying surface topography. We reveal how the lubricant film mediates droplet adhesion by measuring the maximum adhesion force and liquid residue and theoretically analyzing Laplace pressure force from the droplet shape and surface tension force depending on the contact line. Further, the presence of lubricant-induced adhesion considerably compromises the advantages of lubricant-infused surfaces in some applications. The lubricant-triggered tensile adhesion hampers the loss-free droplet transfer away from the surfaces in the photoelectrically and magnetically driven droplet manipulation. In addition, we demonstrate that the lubricant-triggered adhesion plays a dominant role in attenuating the efficiency of fog harvesting by impeding the shedding of the intercepted droplets by comparing the onset time, droplet radius, and collection efficiency. These findings advance our fundamental understanding of droplet adhesion on lubricant-infused surfaces and significantly benefit the design of lubricant-infused surfaces for various applications.

Open Problems in Wetting Phenomena: Pinning Retention Forces

We review existing explanations for drop pinning and the origin of the force required to initiate the sliding of a drop on a solid surface (depinning). Theories that describe these phenomena include de Gennes', Marmur's, Furmidge's, the related Furmidge-Extrand's, and Tadmor's theory. These theories are all well cited but generally do not address each other, and usually papers that cite one of them ignore the others. Here, we discuss the advantages and disadvantages of these theories and their applicability to different experimental systems. Thus, we link different experimental systems to the theories that describe them best. We describe the force laws that can be deduced should these theories be united and the major open problems that remain. We describe a physical meaning that can be extracted from retention force measurements, specifically, the interfacial modulus that describes the tendency of a solid to conform to the liquid. This has implications for various wetting phenomena such as adhesion robustness, drug penetration into biological tissues, and solid robustness/resilience versus solid degradation over time as a result of its contact with a liquid.

Droplet Characteristics at the Maximum Adhesion on Curved Surfaces

For applications involving droplet detachment from solid surfaces, it is vital to study the droplet characteristics (e.g., contact angle and base width) when the droplet is experiencing the maximum force that detaches the droplet (maximum adhesion state). Historically, such investigations were mainly conducted on flat two-dimensional surfaces and the characteristics on curved surfaces with the third dimension remain unknown. Thus, the generalized description of such characteristics has not been established yet. Here, by vertically pulling liquid droplets using a microbalance, we study the droplet characteristics at the maximum adhesion on curved homogeneous surfaces. Variables in this study include liquid surface tension, initial droplet base area, and the asymmetry in solid surface curvature. Results show that the contact angle is identical everywhere along the droplet perimeter on curved surfaces irrespective of the asymmetry in surface curvature. In addition, we found that the droplet base is nonaxisymmetric (not circular) at the maximum adhesion, opposing previous understanding that was formulated for flat surfaces. As a result, we propose a more generalized and quantitative description of the droplet characteristics at the maximum adhesion, derived from the component of the surface tension force acting along the droplet perimeter.