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Topography-induced symmetry transition of droplets on quasi-periodically patterned surfaces
Abstract and Figures
Quasi-periodic structures of quasicrystals yield novel effects in diverse systems. However, there is little investigation on employing quasi-periodic structures in the morphology control. Here, we show the use of quasi-periodic surface structures in controlling the transition of liquid droplets. Although surface structures seem random-like, we find that on these surfaces, droplets spread to well-defined 5-fold symmetric shapes and the symmetry of droplet shapes spontaneously restore during spreading, hitherto unreported in the morphology control of droplets. To obtain physical insights into these symmetry transitions, we conduct energy analysis and perform systematic experiments by varying properties of both liquid droplet and patterned surface. The results show the dominant factors in determining droplet shapes to be surface topography and the self-similarity of the surface structure. Our findings significantly advance the control capability of the droplet morphology. Such a quasi-periodic patterning strategy can offer a new method to achieve complex patterns.
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... Besides research on periodically patterned surfaces with two-, four-and six-fold symmetry (Raj et al. 2014), it is noteworthy that quasiperiodically patterned surfaces have also been investigated (Chen, Yuan & Zhao 2018b). On such surfaces, the symmetry of the wetted area of droplets can decrease and restore spontaneously. ...
... As mentioned in § 1, the characterization method for rough surfaces, particularly for pillar-arrayed microstructured surfaces includes surface roughness, the pillar density, aspect ratios and symmetry. The definition of surface roughness, ro, is described as the ratio of the actual area of solid surface, S ac , to the projected area of solid surface, S p (Chen et al. 2018b), ...
... Such quasiperiodically patterned pillar-arrayed surfaces, employed to manipulate the morphology of wetting liquid droplets are illustrated in figure 4(a-c), with pillars represented as colourful dots. In figure 4(a-c), quasiperiodically patterned surfaces fabricated with circular pillars of five-fold, six-fold and eight-fold symmetry, respectively, are depicted (Chen et al. 2018b). Each colour denotes one kind of pillar. ...
Microstructured surfaces with pillar arrays are widely used to control the wetting morphology and spreading dynamics of droplets. In both simulations and experiments, it is shown that fabricating the surface with various microstructures is a very effective method for achieving the desired symmetry of the moving contact line. However, the method for characterizing miscellaneous pillar-arrayed microstructured surfaces is still insufficient. This paper presents the configurational entropy to characterize the microstructured surfaces with pillar arrays. By calculating the configurational entropy of pillar-arrayed microstructured surfaces, the relationship between the configurational entropy and the wetting morphology of droplets is obtained. For pillar-arrayed microstructured surfaces with the configurational entropy S > 0, the droplet wetting morphology may be much more complex than those with S = 0. The relationship is found to be consistent with the previous results. Furthermore, the wetting dynamics has been analysed. This study may be useful to understand the mechanism of droplet wetting on pillar-arrayed microstructured surfaces and provide insights for the design and manufacture of microstructured surfaces.
... Liquids in the Wenzel wetting state present a completely wetting solid-liquid contact area, desirable features for pesticide retention on plant surfaces 17 and boiling heat transfer 18 . Using highly enhanced capillarity and contact line pinning, spectacular properties of the Wenzel wetting state have been discovered, including directional and multilayer liquid spreading, as well as the formation of polygonal thin-liquid films and droplets [19][20][21][22][23][24][25][26][27][28] . For instance, Courbin et al. 20,21 investigated deposited liquids on microtextured surfaces satisfying the imbibition condition and showed that they can form square, hexagonal, octagonal, and circular-shaped thin-liquid films. ...
... The challenges lie in several aspects. First, liquid fronts can proceed spontaneously for complete and partial wetting cases [19][20][21][22][23][24][25][26][27][28] . However, thermodynamics suggests that capillary imbibition cannot take place on non-wetting surfaces 33 . ...
... Second, a comparison of the cross-sectional areas of the pillars and the arrangements of the arrays revealed that the shapes of the droplet patterns demonstrated in Fig. 1b-e were consistent with those of the liquid films created on wetting microtextured surfaces 20,25 . Third, remarkably different from the wetting case [19][20][21][22][23][24][25][26][27][28] , when the confinement is removed, the polygonal droplet reverts back to its initial spherical shape (Supplementary Discussion 3, Supplementary Fig. 5), which shows a good reversibility of the wetting state transition. Moreover, there is a robust reproducibility of the polygonal droplet pattern when the confinement is repeatedly imposed and removed (Supplementary Discussion 4, Supplementary Figs. 6 and 7). ...
Understanding the interactions between liquids and solids is important for many areas of science and technology. Microtextured surfaces have been extensively studied in microfluidics, DNA technologies, and micro-manufacturing. For these applications, the ability to precisely control the shape, size and location of the liquid via textured surfaces is of particular importance for the design of fluidic-based systems. However, this has been passively realized in the wetting state thanks to the pinning of the contact line, leaving the non-wetting counterpart challenging due to the low liquid affinity. In this work, confinement is imposed on droplets located on well-designed shapes and arrangements of microtextured surfaces. An active way to shape non-wetting water and liquid metal droplets into various polygons ranging from triangles, squares, rectangles, to hexagons is developed. The results suggest that energy barriers in different directions account for the movement of the contact lines and the formation of polygonal shapes. By characterizing the curvature of the liquid-vapour meniscus, the morphology of the droplet is correlated to its volume, thickness, and contact angle. The developed liquid-based patterning strategy under active regulation with low adhesion looks promising for low-cost micromanufacturing technology, DNA microarrays, and digital lab-on-a-chip.
... The aperiodic structures, which are ordered without translation symmetry observed in many natural materials (25), can provide a large design space and abundant structural and physical properties compared to periodic ones (26). In particular, aperiodic structures generated by deterministic mathematical rules (deterministic aperiodic structures) have recently attracted significant attention in engineering applications such as droplet dynamics, acoustic and optical wave transport, and photonics (27)(28)(29)(30)(31)(32)(33)(34)(35) due to their simplicity and geometrical freedom of design. However, the tunable and scalable printing of 3D aperiodic structures remains a difficult challenge due to time-consuming and costly fabrication techniques, thereby limiting the applications of aperiodic structures. ...
... In addition, the structures can transform into quasicrystals with higher rotational symmetry or aperiodic albeit regular symmetry (i.e., lattice-dependent symmetry breaking). Therefore, these structures are a promising tool for exploring the diverse physics including the investigation of liquid droplet dynamics (30), wave transport, and controlling the properties of wave patterns, which are relevant to several areas of acoustic metasurfaces (27), chiral structures (28), wave localization (31,32), and tunable multiband responses of quasi-lattice metasurfaces (33). ...
The limitation of projection microstereolithography in additive manufacturing methods is that they typically use a single-aperture imaging configuration, which restricts their ability to produce microstructures in large volumes owing to the trade-off between image resolution and image field area. Here, we propose an integral lithography based on integral image reconstruction coupled with a planar lens array. The individual microlenses maintain a high numerical aperture and are used to create digital light patterns that can expand the printable area by the number of microlenses (103 to 104), thereby allowing for the scalable stereolithographic fabrication of 3D features that surpass the resolution-to-area scaling limit. We extend the capability of integral lithography for programmable printing of deterministic nonperiodic structures through the rotational overlapping or stacking of multiple exposures with controlled angular offsets. This printing platform provides new possibilities for producing periodic and aperiodic microarchitectures spanning four orders of magnitude from micrometers to centimeters.
... The engineered fluidic-based system, which uses topographic [18][19][20] and chemical [21][22][23] heterogeneities to modulate wetting phenomena and thus control the shape of drops, is of increasing significance due to its flexibility and fluidity. 24,25 Even for the same wettability pattern, the drop can transit dynamically to different shapes during its spreading 26,27 or dissolution. 28,29 This method has been applied to a vast spectrum of substrate types 21,30 and works for drop sizes down to femtoliter or submicron scale, 31,32 providing a low-cost fabrication choice for micromechanical devices, 33,34 capsulation for integrated circuits, 35,36 lab-on-chip parts, 37,38 and 3D electrodes, 39,40 among other uses. ...
... Surfaces constructed with micro/nano-structures are usually more hydrophobic or hydrophilic [28][29][30] . If the cavities between micro-/nano-pillars or micro-/nano-pores is fully filled with liquid, the droplet is in the Wenzel (W) wetting state. ...
Wettability and evaporation of dilute sodium dodecyl sulfate (SDS) droplets on micropillar-arrayed polydimethylsiloxane (PDMS) were experimentally studied. It was found that the apparent, advancing and receding contact angles all decreased with the increase of initial SDS concentration and wettability of dilute SDS droplets depended on both SDS concentration and surface roughness. Due to the adhesion between the droplets and the micropillars, all evaporation began with constant contact radius (CCR) mode. It is more interesting that short-time spontaneous spreading was found to follow the CCR stage for dilute SDS droplets evaporating on the patterned surface with sparser micropillars, which can be attributed to the transition from the Cassie-Baxter wetting state to the Wenzel wetting state (CB-W transition). Such a transition has been experimentally observed and a theoretical model was developed to qualitatively elucidate the spontaneous spreading.
... Furthermore, some open questions remain that need to be addressed, for example, what are the criteria that account for the morphology transition from the circular shape to the square shape during compression and the transition from the Cassie-Baxter wetting state to the SP wetting state? It would be interesting to explore the dynamics of the transition, as well as the variation of the morphology of the droplet and the motion of the solid-liquid-vapor threephase contact lines [39,40]. However, our experiments suggest that in order to guarantee the occurrence of the SP wetting state, the area fraction and the pillar height of the micropillared substrate should have large values. ...
When a water droplet on a micropillar-structured hydrophobic surface is submitted to gradually increased pressure, the Cassie-Baxter wetting state transforms into the Wenzel wetting state once the pressure exceeds a critical value. It has been assumed that the reverse transition (Wenzel-to-Cassie-Baxter wetting state) cannot happen spontaneously after the pressure has been removed. In this paper, we report a new wetting-state transition. When external pressure is exerted on a droplet in the Cassie-Baxter wetting state on textured surfaces with high micropillars to trigger the breakdown of this wetting state, the droplet penetrates the micropillars but does not touch the base of the surface to trigger the occurrence of the Wenzel wetting state. We have named this state the suspended penetration wetting state. Spontaneous recovery from the suspended penetration wetting state to the initial Cassie-Baxter wetting state is achieved when the pressure is removed. Based on the experimental results, we built models to establish the penetration depth that the suspended penetration wetting state could achieve and to understand the energy barrier that influences the equilibrium position of the liquid surface. These results deepen our understanding of wetting states on rough surfaces subjected to external disturbances and shed new light on the design of superhydrophobic materials with a robust wetting stability.
... The transition between the ordered and disordered case by itself constitutes and interesting problem [13]. Breaking symmetry of droplets may occur during both spreading [22] and receding, and it can result in unusual effects, such as the self-propulsion [23]. ...
Self-assembled clusters of condensed water microdroplets can levitate over a locally heated layer of water. Large clusters form hexagonally ordered (honeycomb) structures similar to colloidal crystals, while small (from one to several dozens of droplets) clusters possess special symmetry properties. Small clusters may demonstrate 4-fold, 5-fold, and 7-fold symmetry which is absent from large clusters and crystals. The symmetry properties of small cluster configurations are universal, i.e., they do not depend on the size of the droplets and details of interaction between the droplets. The small cluster configurations may be compared with other types of symmetric objects in geometry.
The extent to which a droplet pins on a textured substrate is determined by the dynamics of contact line and the liquid-vapor interface. However, the synergistical contribution of contact line...
The surface of Salvinia had superhydrophobicity and kept good compressive stability, which was mainly attributed to the dense microscopic eggbeater structure villi on the surface. By means of force equilibrium, a theoretical model was established to analyze the interface mechanical behaviors when a droplet infiltrates the microstructures. Based on the minimum energy principle, a theoretical model was presented to analyze the process of a droplet spreading on the surface of Salvinia reaching a steady state. Combined with numerical simulations, it was found that the superhydrophobicity and compressive stability of the Salvinia were dependent on the morphological and geometric parameters of the microstructure (edge angle φ, number of branching n, width W and spacing D, etc.). By adjusting these geometrical parameters, the surface of the biomimetic structure can maintain a stable Cassie state at 0.63 kPa pressure, and the apparent contact angle is controllable in the range of 121° - 169.8°. The research results provide a theoretical foundation for the structural design of superhydrophobic surfaces with high stability and tunable wettability.
The last two decades have witnessed an explosion of interest in the field of droplet-based microfluidics for their multifarious applications. Despite rapid innovations in strategies to generate small-scale liquid transport on these devices, the speed of motion is usually slow, the transport distance is limited, and the flow direction is not well controlled because of unwanted pinning of contact lines by defects on the surface. We report a new method of microscopic liquid transport based on a unique topological structure. This method breaks the contact line pinning through efficient conversion of excess surface energy to kinetic energy at the advancing edge of the droplet while simultaneously arresting the reverse motion of the droplet via strong pinning. This results in a novel topological fluid diode that allows for a rapid, directional, and long-distance transport of virtually any kind of liquid without the need for an external energy input.
The authors acknowledge support from the Innovative electronic Manufacturing Research Centre (IeMRC) through the EPSRC funded flagship project SMART MICROSYSTEMS (FS/01/02/10), Knowledge Transfer Partnership No KTP010548, EPSRC project EP/L026899/1, EP/F063865/1; EP/F06294X/1, EP/P018998/1, the Royal Society-Research Grant (RG090609) and Newton Mobility Grant (IE161019) through Royal Society and NFSC, the Scottish Sensing Systems Centre (S3C), Royal Society of Edinburgh, Carnegie Trust Funding, Royal Academy of Engineering-Research Exchange with China and India, UK Fluidic Network and Special Interest Group-Acoustofluidics, the EPSRC Engineering Instrument Pool. We also acknowledge the National Natural Science Foundation of China (Nos. 61274037, 51302173), the Zhejiang Province Natural Science Fund (No. Z11101168), the Fundamental Research Funds for the Central Universities (No. 2014QNA5002), EP/D03826X/1, EP/ C536630/1, GR/T24524/01, GR/S30573/01, GR/R36718/01, GR/L82090/01, BBSRC/E11140. ZXT acknowledges the supports from the National Natural Science Foundation of China (61178018) and the NSAF Joint Foundation of China (U1630126 and U1230124) and Ph.D. Funding Support Program of Education Ministry of China (20110185110007) and the NSAF Joint Foundation of China (Grant No. U1330103) and the National Natural Science Foundation of China (No. 11304209). NTN acknowledges support from Australian Research Council project LP150100153. This work was partially supported by the European Commission through the 6th FP MOBILIS and 7th FP RaptaDiag project HEALTH-304814 and by the COST Action IC1208 and by the Ministerio de Economía y Competitividad del Gobierno de España through projects MAT2010-18933 and MAT2013-45957R.
Assembly of nanoparticles into controllable micro or nanocurve circuits by a feasible strategy is demonstrated. The curves, with various tortuosity morphologies, have tunable resistive strain sensitivity, which can be integrated into a multi-analysis flexible sensor. The curve-based sensor could run complicated facial expression recognition, and would contribute practical applications on skin micromotion manipulation auxiliary apparatuses for paraplegics.
This paper presents a fractal model to describe wettability on multiscale randomly rough surfaces. Hydrophobic or superhydrophobic surfaces produced using processes such as electrodeposition and etching lead to the creation of random roughness at multiple length scales on the surface. This paper considers the description of such surfaces with a fractal asperity model based on the Weierstrass-Mandelbrot (W-M) function, where the fractal parameters are uniquely determined from a power spectrum of the surface. Using this description, a model is presented to evaluate the apparent contact angle in the different wetting regimes. The model is predictive in that it does not use any empirical or correlatory fitting of parameters to experimental data. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. The contact angle is found be strongly dependent on the range of asperity length scale and weakly dependent of the fractal dimension for a surface with stable Cassie state. Based on the fractal description, desired surface roughness characteristics for generating superhydrophobicity on a particular substrate are also derived.
Interaction of liquids with surfaces is ubiquitous in our physical environment as well as many engineering applications. Recent advances on this topic have not only provided us with valuable insight into nature's design, but also enabled improved fluidic manipulation for liquid-based printing applications such as bio-microarrays for protein and DNA sequencing, multicolor polymer-based LED displays, inkjet printing, and solder droplet printing, among others. For example, droplet contact lines which are typically circular on a smooth and homogenous surface when deposited on a microdecorated surface may take various common polygonal shapes such as squares, rectangles, hexagons, octagons and dodecagons. These polygonal contact line shapes are highly stable due to the local energy barriers associated with the anisotropy in de-pining contact angles. In addition to the knowledge of the eventual contact line shapes, liquid-based printing applications would require accurate prediction of temporal evolution of contact line on these surfaces. In this work, we model and validate the evolution of droplets on microdecorated surfaces with microgoniometry experiments reported in literature. We show that various metastable contact line shapes are formed in-between the well-known stable polygonal contact line shapes usually observed in experiments. We elucidate that the movement of the contact line between adjacent micropillars can primarily be categorized as primary zipping and transition zipping. Primary zipping occurs when the contact line moves radially outwards to the next row of pillars, often resulting in the formation of a metastable contact line shape. Conversely, metastable droplet attains stable polygonal contact line shape via transition zipping wherein the contact line advances sideways. We believe that the current simulation approach can be effectively utilized for designing optimized textured surfaces for applications where control over liquid supply via surface design is required.
Recently, piezoelectric thin films including zinc oxide (ZnO) and aluminium nitride (AlN) have found a broad range of lab-on-chip applications such as biosensing, particle/cell concentrating, sorting/patterning, pumping, mixing, nebulisation and jetting. Integrated acoustic wave sensing/microfluidic devices have been fabricated by depositing these piezoelectric films onto a number of substrates such as silicon, ceramics, diamond, quartz, glass, and more recently also polymer, metallic foils and bendable glass/silicon for making flexible devices. Such thin film acoustic wave devices have great potential for implementing integrated, disposable, or bendable/flexible lab-on-a-chip devices into various sensing and actuating applications. This paper discusses the recent development in engineering high performance piezoelectric thin films, and highlights the critical issues such as film deposition, MEMS processing techniques, control of deposition/processing parameters, film texture, doping, dispersion effects, film stress, multilayer design, electrode materials/designs and substrate selections. Finally, advances in using thin film devices for lab-on-chip applications are summarised and future development trends are identified.
The wettability and evaporation of water-ethanol binary droplets on the substrate with micro-pyramid cavities are studied by controlling initial ethanol concentrations. The droplets form octagonal initial wetting areas on the substrate. As the ethanol concentration increases, the side ratio of the initial wetting octagon increases from 1.5 at 0% of ethanol concentration to 3.5 at 30% of ethanol concentration. The increasing side ratio indicates that the wetting area transforms from an octagon to a square if we consider the octagon as a square with its four corners cut. The droplets experience a pinning-depinning transition during the evaporation. The pure water sessile droplet evaporation demonstrates three stages from the constant contact line (CCL) stage, then the constant contact angle (CCA) stage, to the mixed stage. An additional mixed stage is found between the CCL and CCA stages in the evaporation of water-ethanol binary droplets due to the anisotropic depinning along the two different axes of symmetry of the octagonal wetting area. The droplet depinning occurs earlier on the patterned surface as the ethanol concentration increases.
Hemiwicking refers to the spreading of a liquid on a rough hydrophilic surface driven by capillarity. Here, we construct scaling laws to predict the velocity of hemiwicking on a rough substrate and experimentally corroborate them with various arrangements and dimensions of micropillar arrays. At the macroscopic scale, where the wetting front appears parallel to the free surface of the reservoir, the wicking distance is shown to grow diffusively, i.e. like
with
t
being time. We show that our model is consistent with pillar arrays of a wide range of pitch-to-height ratios, either square or skewed. At the microscopic scale, where the meniscus extension from individual pillars at the wetting front is considered, the extension distance begins to grow like
t
but the spreading slows down to behave like
when the meniscus is far from the pillar. Our microscopic flow modelling allows us to find pillar spacing conditions under which the assumption of densely spaced pillars is valid.