Thermodynamic analysis of stable wetting states and wetting transition of micro/nanoscale structured surface
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Superhydrophobicity of biological surfaces with micro/nanoscale hierarchical roughness has recently been given great attention and widely reported in many experimental studies due to the unique wettability. For example, the dual-scale structure of the lotus leaf not only shows high contact angle and low contact angle hysteresis but also presents good stability and mechanical properties. Though lots of experimental studies on the wettability of artificial hierarchical rough surface have been carried out, a thorough analysis on the contribution of micro- and nano-scaled roughness to the metastable wetting states and their transition is still lack. In this paper, a thermodynamic approach is applied to analyze all the wetting states (including four stable wetting states and five transition states) of a water droplet on a surface with micro/nanoscale hierarchical roughness, and the corresponding free energy expressions and apparent contact angle equations are deduced. The stable wetting states are confirmed by the principle of minimum free energy. And the calculated results by these state equations can fit well with the experimental results reported in the literature when compared with the previous models. Meanwhile, the influence of micro/nanoscale roughness on the stable wetting states and metastable-stable transition has been analyzed thermodynamically. It is found that there is a synergistic effect of micro and nanoscale roughness on wettability, which nlay result in many different wetting states. There are four wetting states during increasing relative pitch of a microscaled structure at a given nanoscaled structure, but two wetting states can be obtained as increasing relative pitch of nanoscaled structure at a given microscaled structure. The change of nondimensional energy and nondimensional energy barrier in the metastable-stable transition process of water droplet wetting micro and nanoscaled structure is quantitatively analyzed. Results indicate that the micro-scaled structure is never wetted in a special size range of the nanoscaled structure, and the special size range is of great significance to enhance superhydrophobic stability of the microscaled structure. Furthermore, the existence of microscaled structure decreases the transition energy barrier of water droplet wetting nanoscaled structure, which is helpful for understanding the experimental results reported in the literature. Finally, all possible stable wetting states of water droplet no a surface with micro/nanoscale hierarchical roughness are discribed in a wetting map. A design principle of superhydrophobic surface with micro/nanoscale hierarchical roughness is put forward, which is helpful to ensure the size of micro/nanoscale structure in the “stable superhydrophobic region” and to provide a theoretical guidance in the preparation of superhydrophobic surface.Keywords:
Wetting transition
Metastability
Hysteresis
Lotus effect
Understanding wettability and mechanisms of wetting transition are important for design and engineering of superhydrophobic surfaces. There have been numerous studies on the design and fabrication of superhydrophobic and omniphobic surfaces and on the wetting transition mechanisms triggered by liquid evaporation. However, there is a lack of a universal method to examine wetting transition on rough surfaces. Here, we introduce force zones across the droplet base and use a local force balance model to explain wetting transition on engineered nanoporous microstructures, utilizing a critical force per unit length (FPL) value. For the first time, we provide a universal scale using the concept of the critical FPL value which enables comparison of various superhydrophobic surfaces in terms of preventing wetting transition during liquid evaporation. In addition, we establish the concept of contact line-fraction theoretically and experimentally by relating it to area-fraction, which clarifies various arguments about the validity of the Cassie-Baxter equation. We use the contact line-fraction model to explain the droplet contact angles, liquid evaporation modes, and depinning mechanism during liquid evaporation. Finally, we develop a model relating a droplet curvature to conventional beam deflection, providing a framework for engineering pressure stable superhydrophobic surfaces.
Wetting transition
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Superhydrophobic surfaces fabricated by laser irradiation on various materials have been reported recently to show excellent wetting properties. However, there are only limited works regarding the theoretical analysis and prediction of the wetting properties of different surface structures, especially the widely used pore array laser-texturing surfaces, whose fabrication process is simple and time-saving. Here we propose a two-dimensional thermodynamic structure model based on the actual pore array laser-texturing surfaces, and four wetting states are defined in our model. By minimizing the Gibbs free energy, equilibrium contact angle and contact angle hysteresis representing wetting properties are calculated, and the effects of defined parameters (intrinsic contact angle θY, pore space b, and pore depth H) on wetting properties are analyzed in detail to find out the critical transition conditions among different wetting states. Besides, actual pore array laser-texturing surfaces are fabricated for further validation, and the wetting properties in measurement are found to be in good agreement with those in prediction, indicating that our model is credible and can be used to guide the design of the pore array superhydrophobic laser-texturing surfaces.
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Hysteresis
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Micro-or nano-structurally roughened solid surfaces exhibit a rich variety of wetting behavior types, ranging from superhydro- or superoleophobicity to superhydro- or superoleophilicity. Depending on their material chemistry, the scale and morphology of their roughness or even the application of external electric fields, their apparent wettability can be significantly modified giving rise to challenging technological applications by exploiting the associated capillary phenomena at the micrometer scale. Certain applications, however, are limited by hysteretic wetting transitions, which inhibit spontaneous switching between wetting states, requiring external stimuli or actuation like thermal heating. The presence of surface roughness, necessary for the manifestation of the superhydrophobicity, induces multiplicity of wetting states and the inevitable hysteresis appears due to considerable energy barriers separating the equilibrium states. Here, by using continuum as well as mesoscopic computational analysis we perform a systems level study of the mechanisms of wetting transitions on model structured solid surfaces. By tracing entire equilibrium solution families and determining their relative stability we are able to illuminate mechanisms of wetting transitions and compute the corresponding energy barriers. The implementation of our analysis to 'real world' structured or unstructured surfaces is straightforward, rendering our computational tools valuable not only for the realization of surfaces with addressable wettability through roughness design, but also for the design of suitable actuation for optimal switching between wetting states.
Mesoscopic physics
Wetting transition
Hysteresis
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The current study reports the fabrication and characterization of superhydrophobic surfaces with increasing nanoroughness by decreasing silica nanoparticle size in a sol–gel matrix. Using small-angle X-ray scattering (SAXS) measurements allowed for the direct quantification of air entrapped at the interface, revealing for the first time that significant air remains on hierarchical surfaces despite observed droplet pinning through hysteresis measurements. Combining contact angle hysteresis and SAXS measurements of the surfaces immersed in sodium dodecylsulfate (SDS) solutions with Cassie and Tadmor's model, a series of predicted contact angles were generated, comparing wetting transition mechanisms based on wetting line advance, droplet adhesion/pinning, and interfacial air entrapment. The study provided confirmation of key theoretical assumptions on wetting of hierarchical surfaces: (i) Cassie wetting of the nanofeatures is the preferred wetting progression on hierarchical surfaces; and (ii) the presence of an intermediate petal state is dependent on the level of nanoroughness as compared to the microroughness.
Hysteresis
Small-angle X-ray scattering
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Wetting state transition regulated by surface roughness has increasing importance for its wide applications.
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以亲水性微观粗糙表面上不同几何形貌及分布的微柱阵列为对象, 讨论了液滴在亲水性粗糙表面上的润湿过程以及润湿状态的转变阶段. 从能量角度分别考察了微观粗糙结构几何形貌及分布、微柱几何参数、固体表面亲水性、接触角滞后作用等因素对液滴润湿状态转变的影响规律. 研究发现: 在亲水粗糙表面, 正方形微柱呈正六边形阵列分布时, 液滴更容易形成稳定的Cassie状态, 或者液滴仅发生Cassie状态向中间浸润状态的转变; 与此同时, 减小微柱间距、增大方柱宽度或圆柱直径、增大微柱高度、增强固体表面的亲水性将有利于液滴处于稳定的Cassie状态, 或阻止润湿状态向伪-Wenzel或Wenzel状态转变; 然而, 当液滴处于Cassie状态时, 较小的固-液界面面积分数或减弱固体表面亲水性能均有利于增大液滴的表观接触角, 因此在亲水表面设计粗糙结构时应综合考虑润湿状态稳定性和较大表观接触角两方面因素; 此外, 接触角滞后作用对于液滴状态的稳定性以及疏水性能的实现具有相反作用的影响. 研究结果为液滴在亲水表面获得稳定Cassie状态的粗糙结构设计方法提供了理论依据.
Microscale chemistry
Wetting transition
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The increasing interest in the superhydrophobic materials in the scientific world leads to the accumulation of a large amount of theoretical models of such surfaces, and the corresponding experimental data. The ordering of such information is required to create a unified approach to modeling surfaces with controlled hydrophobicity.The review includes a classification of the main significant characteristics of the hydrophobic properties of materials, namely, wetting, roll-off, and outflow wetting and inflow wetting angles in applying to smooth, as well as rough surfaces. Two fundamental wetting states of textured materials - Cassie-Baxter and Wentzel are described. Next, a set of mathematical models, which allow to calculate the above parameters based on structural and energy properties of the material surface is given. One of the most important characteristics of superhydrophobic materials - wetting state stability is described in the third part of the review, which presents corresponding analytical models, indicating the possible optimal types of the surface structure to achieve the specified state. For example, using irregularities with a reentrant geometry allows to achieve stable values of the wetting angle above 160°. At the same time, it is shown that for large-scale use of superhydrophobic materials, materials with the hierarchical (micro-nano) structure of irregularities are the most suitable.
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The ability to control wettability is important for a wide range of technological applications in which precise microfluidic handling is required. It is known that predesigned roughness at a micro- or nano- scale enhances the wetting properties of solid materials giving rise to super-hydrophobic or super-hydrophilic behavior. In this work, we study the dependence of the apparent wettability of a stripe-patterned solid surface on the stripe geometry, utilizing systems level analysis and mesoscopic Lattice-Boltzmann (LB) simulations. Through the computation of both stable and unstable states we are able to determine the energy barriers separating distinct metastable wetting states that correspond to the well-known Cassie and Wenzel states. This way the energy cost for inducing certain wetting transitions is computed and its dependence on geometric features of the surface pattern is explored.
Mesoscopic physics
Metastability
Lattice Boltzmann methods
Wetting transition
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Solid surface
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Superhydrophobic surfaces are extremely nonwetting by virtue of their surface chemistry and roughness. Applications for them are being pursued in coatings, microfluidics, textiles, and other areas. Most analyses of the wetting of superhydrophobic surfaces have focused on pillar geometries. However, mass-produced superhydrophobic surfaces are likely to have random topologies. A computational model for the wetting of rough one-dimensional surfaces is described, and applied to random, self-affine surfaces with various levels of roughness and intrinsic contact angles. It is found that all wetting properties are generally controlled by the Wenzel roughness parameter r, even when drops are in the suspended Cassie state. Superhydrophobicity is attained above a threshold value of r. Similar results are also found for the wetting of dual-scale surfaces.
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