Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Pinning Effects of Wettability Contrast on Pendant Drops on Chemically Patterned Surfaces

The morphology and dynamics of the pendant drops attached to chemically patterned surfaces (pattern-pinned pendant drops) with different hydrophilic/hydrophobic contrasts were investigated experimentally and numerically. During the experiments, the evolution of the contact angle and the maximum drop volume were found to be different from those of traditional pendant drops, whose contact line is pinned on the edge of the tips (tip-pinned pendant drops), and the deviation is related to both the pattern radius and the wettability contrast. Then, a hypothesis was proposed to illustrate the behavior of the contact line after it reached the pattern boundary, based on the premise that the pattern boundary possessed a certain width or fuzziness. It was concluded that the special phenomena in this case were due to the movement of the contact line, and the maximum contact radius was presented as a key parameter for the pattern-pinned drops, which is directly related to the stability and the maximum volume of the drops. Furthermore, through a simulation study on pattern-pinned pendant drops, the vibration performance of the meniscus was revealed as a superposition of two vibration behaviors including a low-frequency vibration due to the inertia effects and a high-frequency vibration due to the surface tension gradient within the boundary region. In addition, the hypothesis proposed above was also verified. Finally, a forecasting model to predict the maximum contact radius for the pattern-pinned pendant drops was built for different liquids and pattern wettabilities. This allows us to effectively design and optimize chemically patterned surfaces to achieve a desired pinning function or a pendant drop with desired properties.

Understanding contact angle hysteresis on an ambient solid surface

We report a systematic study of contact angle hysteresis (CAH) with direct measurement of the capillary force acting on a contact line formed on the surface of a long glass fiber intersecting a liquid-air interface. The glass fiber of diameter 1-2μm and length 100-200μm is glued onto the front end of a rectangular cantilever beam, which is used for atomic force microscopy. From the measured hysteresis loop of the capillary force for 28 different liquids with varying surface tensions and contact angles, we find a universal behavior of the unbalanced capillary force in the advancing and receding directions and the spring constant of a stretched meniscus by the glass fiber. Measurements of the capillary force and its fluctuations suggest that CAH on an ambient solid surface is caused primarily by two types of coexisting and spatially intertwined defects with opposite natures. The contact line is primarily pinned by the relatively nonwetting (repulsive) defects in the advancing direction and by the relatively wetting (attractive) defects in the receding direction. Based on the experimental observations, we propose a "composite model" of CAH and relevant scaling laws, which explain the basic features of the measured hysteresis force loops.

Mechanical Strain Induced Tunable Anisotropic Wetting on Buckled PDMS Silver Nanorods Arrays

We report the fabrication of anisotropic superhydrophobic surface with dual-scale roughness by the deposition of silver nanorods arrays on prestretched poly(dimethylsiloxane) (PDMS) using oblique angle deposition and subsequent release of strain after the deposition, which resulted in the formation of microbuckles/wrinkles. The amplitude and periodicity of the wrinkles were tuned by varying the prestretching mechanical strain (ε) applied to the PDMS film from 0 to 30% prior to Ag nanorods deposition. The peaks and valleys in the surface topography of Ag nanorods arrays covered PDMS films lead to anisotropic wetting by water droplet. The droplet is free to move along the direction parallel to the wrinkles, but the droplet moving perpendicular to the wrinkles confront energy barrier leading to wetting anisotropy. The anisotropic wettability was tuned from 22 to 37° for 10-30% prestretched PDMS film. The dual scale roughness (nanorods on micro wrinkles) was found to be responsible for the superhydrophobicity (contact angle ∼155°) of the sample prepared for 30% prestretched PDMS film in perpendicular direction. The wetting behavior of the Ag nanorods PDMS film surface was reversibly tuned by applying the mechanical strain, which induces the change in the microscale roughness determined by amplitude (A) and periodicity (λ) of the buckles. Most interestingly, the water droplet also displayed the anisotropy in the roll-off angle. The effect of different A and λ on anisotropic wettability of Ag nanorods arrays/PDMS film was also demonstrated by lattice Boltzmann (LB) modeling. These findings may produce a promising way of controlling the direction of liquid flow such as in microfluidic devices and transportation of the microliter water droplets in a preset direction.

Liquid body formation from a semispherical superhydrophobic well on a small incline

In this work, drop formation on a slightly inclined superhydrophobic substrate with liquid at various flow rates delivered through a semispherical well was investigated. Due to the initial dry well condition in the first drop produced, the inertial force from liquid filling allowed the well's edge hysteresis to be more readily breached, in which flow rates of 16 mL/min and above could create a jet that appeared to be able to "pierce" through the top of the semispherical drop without disrupting its form and growth very much. For subsequent drops, the well's edge hysteresis at flow rates of 14 mL/min and above helped to support an "egg" like form. In contrast, this form could not be developed on a similarly inclined superhydrophobic substrate without a well. The findings here assist to establish the flow rate ranges for consistent discrete volume delivery in biochemical analysis and serves as a means to conduct investigations to better reconcile the tendency of liquids to assume drops or develop jets.

The influence of topography on dynamic wetting

The paramount importance of wetting applications and the significant economic value of controlling wetting-based industrial processes has stimulated a deep interest in wetting science. In many industrial applications the motion of a complex liquid front over nano-textured surfaces controls the fate of the processes. However our knowledge of the impact of nano-heterogeneities on static and dynamic wetting is very limited. In this article, the fundamentals of wetting are briefly reviewed, with a particular focus on hysteresis and roughness issues. Present knowledge and models of dynamic wetting on smooth and rough surfaces are then examined, with particular attention devoted to the case of nano-topographical heterogeneities and solid-fluid-fluid systems.

Directed drop transport rectified from orthogonal vibrations via a flat wetting barrier ratchet

We introduce the wetting barrier ratchet, a digital microfluidic technology for directed drop transport in an open air environment. Cyclic drop footprint oscillations initiated by orthogonal vibrations as low as 37 μm in amplitude at 82 Hz are rectified into fast (mm/s) and controlled transport along a fabricated ratchet design. The ratchet is made from a simple wettability pattern atop a microscopically flat surface consisting of periodic semi-circular hydrophilic features on a hydrophobic background. The microfluidic ratchet capitalizes on the asymmetric contact angle hysteresis induced by the curved features to drive transport. In comparison to the previously reported texture ratchets, wetting barrier ratchets require 3-fold lower actuation amplitudes for a 10 μL drop, have a simplified fabrication, and can be made optically flat for applications where transparency is paramount.

Tuning kinetics to control droplet shapes on chemically striped patterned surfaces

The typically elongated shape of droplets on chemically microstriped surfaces has been suggested to depend strongly on the kinetics during deposition. Here, we unequivocally establish the importance of impact kinetics by comparing the geometry of pico- to microliter droplets deposited from an inkjet nozzle with those obtained by conventional deposition from a syringe. For large Weber numbers, the strongly enhanced spreading during the impact in combination with direction-dependent pinning of the contact line gives rise to more spherical droplets with a low aspect ratio. The impact energy can be minimized by the prolonged firing of small picoliter droplets to form larger droplets or, as shown in the past, by using high-viscosity liquids. In the first case, the impact energy is absorbed by the liquid already present, therewith reducing the impact diameter and consequently forming markedly more elongated droplets.

Simulating anisotropic droplet shapes on chemically striped patterned surfaces

The equilibrium shape of droplets on surfaces, functionalized with stripes of alternating wettability, have been investigated using simulations employing a finite element method. Experiments show that a droplet deposited on a surface with relatively narrow hydrophobic stripes compared to the hydrophilic stripes adopts a strongly elongated shape. The aspect ratio, the length of the droplet divided by the width, decreases toward unity when a droplet is deposited on a surface with relatively narrow hydrophilic stripes. The aspect ratio and the contact angle parallel to the stripes show unique scaling behavior as a function of the ratio between the widths of the hydrophobic and hydrophilic stripes. For a small ratio, the contact angle parallel to the stripes is low and the aspect ratio high, while for a large ratio, the contact angle parallel is high and the aspect ratio low. The simulations exhibit similar scaling behavior, both for the aspect ratio of the droplets and for the contact angles in the direction parallel to the stripes. Two liquids with different surface tensions have been investigated both experimentally and in simulations; similarities and differences between the findings are discussed. Generally, three parameters are needed to describe the droplet geometry: (i) the equilibrium contact angles on the hydrophilic and (ii) hydrophobic areas and (iii) the ratio of the widths of these chemically defined stripes. Furthermore, we derive a simple analytical expression that proves to be a good approximation in the quantitative description of the droplet aspect ratio.

Initial spreading kinetics of high-viscosity droplets on anisotropic surfaces

Liquid droplets on chemically patterned surfaces consisting of alternating hydrophilic and hydrophobic stripes exhibit an elongated shape. To assess the dynamics during droplet formation, we present experimental results on the spreading of glycerol droplets on such surfaces using a high-speed camera. Two spreading regimes are observed. Initially, in what is referred to as the inertial regime, the kinetics is dominated by the liquid and spreading is only weakly dependent on the specific surface properties. As such, liquid spreading is isotropic and the contact line maintains a circular shape. Our results reveal a remarkably long inertial regime, as compared to previous results and available models. Subsequently, in the viscous regime, interactions between the liquid and underlying pattern govern the dynamics. The droplet distorts from a spherical cap shape to adopt an elongated morphology that corresponds to the minimum energy configuration on stripe-patterned surfaces.

Wetting 101 degrees

We review our 2006-2009 publications on wetting and superhydrophobicity in a manner designed to serve as a useful primer for those who would like to use the concepts of this field. We demonstrate that the 1D (three-phase, solid/liquid/vapor) contact line perspective is simpler, more intuitive, more useful, and more consistent with facts than the disproved but widely held-to-be-correct 2D view. We give an explanation of what we believe to be the reason that the existing theoretical understanding is wrong and argue that the teaching of surface science over the last century has led generations of students and scientists to a misunderstanding of the wetting of solids by liquids. We review our analyses of the phenomena of contact angle hysteresis, the lotus effect, and perfect hydrophobicity and suggest that needlessly complex theoretical understandings, incorrect models, and ill-defined terminology are not useful and can be destructive.

Modeling the corrugation of the three-phase contact line perpendicular to a chemically striped substrate

We model an infinitely long liquid bridge confined between two plates chemically patterned by stripes of the same width and different contact angle, where the three-phase contact line runs, on average, perpendicular to the stripes. This allows us to study the corrugation of a contact line in the absence of pinning. We find that, if the spacing between the plates is large compared to the length scale of the surface patterning, the cosine of the macroscopic contact angle corresponds to an average of cosines of the intrinsic angles of the stripes, as predicted by the Cassie equation. If, however, the spacing becomes on the order of the length scale of the pattern, there is a sharp crossover to a regime where the macroscopic contact angle varies between the intrinsic contact angle of each stripe, as predicted by the local Young equation. The results are obtained using two numerical methods, lattice Boltzmann (a diffuse interface approach) and Surface Evolver (a sharp interface approach), thus giving a direct comparison of two popular numerical approaches to calculating drop shapes when applied to a nontrivial contact line problem. We find that the two methods give consistent results if we take into account a line tension in the free energy. In the lattice Boltzmann approach, the line tension arises from discretization effects at the diffuse three phase contact line.

An attempt to correct the faulty intuition perpetuated by the Wenzel and Cassie "laws"

We respond to a recent report in this journal that criticizes our experiments, which disproved the Wenzel and Cassie theories. The criticism is that we measured contact angles "with drops that were too small, ignoring the indications of existing theoretical understanding." We take a step back to give an explanation of what we believe to be the reason that the "existing theoretical understanding" is wrong. We explain that the teaching of surface science has led generations of students and scientists to a misunderstanding of the wetting of solids by liquids. This continues as evidenced by this recent criticism and numerous recent papers. We describe several demonstrations that were designed to help teachers, students, and scientists overcome the widespread learning disability that is rooted in their faulty intuition and to help them regard wetting from the perspective of lines and not areas.

Asymmetric wetting of patterned surfaces composed of intrinsically hysteretic materials

Wetting of chemically heterogeneous surfaces is modeled using a phase field theory. We focus on a chemically heterogeneous surface composed of squares of one component material embedded in another. Unlike previous studies where the component materials were characterized only by an equilibrium contact angle, in this paper each of the component materials is constitutively allowed to exhibit hysteresis. Using this approach, we investigate the effect of heterogeneity length scale on observed macroscopic behavior. Cassie theory is found to be applicable only in the limit of vanishing length scale. For surfaces with a finite heterogeneity length scale, the advancing and receding contact angles deviate from Cassie theory. We find that this deviation and its length scale dependence are asymmetric and depend on the wetting properties of the embedded material relative to the contiguous substrate.

Scaling of anisotropic droplet shapes on chemically stripe-patterned surfaces

We present an experimental study of the tunable anisotropic wetting behavior of chemically patterned anisotropic surfaces. Asymmetric glycerol droplet shapes, arising from patterns of alternating hydrophilic (pristine SiO2) and hydrophobic (fluoroalkylsilane self-assembled monolayers) stripes with dimensions in the low-micrometer range, are investigated in relation to stripe widths. Owing to the well-defined small droplet volume, the equilibrium shape as well as the observed contact angles exhibit unique scaling behavior. Only the relative width of hydrophilic and hydrophobic stripes proves to be a relevant parameter. Our results on morphologically flat, chemically patterned surfaces show similarities with those of experiments on topographically corrugated substrates. They are discussed in terms of the energetics at the liquid-solid interface.

Dynamics of a stick-jump contact line of water drops on a strip surface

In this study, we prepared microscale periodic rough structures consisting of parallel strips on a silicon surface. The width of each strip was equal to the gap between the strips, and the silicon surface was silanized with perfluorooctyltrichlorosilane. We studied the wetting characteristics of water drops as they advanced and receded on patterned surfaces in a direction perpendicular to the strip. Water drops were observed to advance or recede in a smooth manner when the strip width was smaller than 32 microm but in a stick-jump manner when the strip width was larger than 50 microm. The regular strip-patterned substrates enabled us to deduce the relationship between the stick-jump behavior and the feature size of the substrate. For surfaces on which water drops showed stick-jump behavior, the oscillation amplitude of the contact angle decreased with decreasing strip width. In addition, the jumping distances of the contact lines, for both advancing and receding water drops, were nearly equal to the strip period. A 2D model was applied to analyze the contact line motion on the patterned surfaces, which showed reasonable agreement with the experimental results.

A Cassie-like law using triple phase boundary line fractions for faceted droplets on chemically heterogeneous surfaces

We present experimental contact angle data for surfaces, which were surface-engineered with a hydrophobic micropattern of hexagonal geometry. The chemically heterogeneous surface of the same hexagonal pattern of defects resulted in faceted droplets of hexagonal shape. When measuring the advancing contact angles with a viewing position aligned parallel to rows of defects, we found that an area averaged Cassie-law failed in describing the data. By replacing the area fractions by line fractions of the triple phase boundary line segments in the Cassie equation, we found excellent agreement with data.

Wetting on axially-patterned heterogeneous surfaces

Contact angle variability, leading to errors in interpretation, arises from various sources. Contact angle hysteresis (history-dependent wetting) and contact angle multiplicity (corrugation of three-phase contact line) are irrespectively the most frequent causes of this uncertainty. Secondary effects also derived from the distribution of chemical defects on solid surfaces, and so due to the existence of boundaries, are the known "stick/jump-slip" phenomena. Currently, the underlying mechanisms in contact angle hysteresis and their connection to "stick/jump-slip" effects and the prediction of thermodynamic contact angle are not fully understood. In this study, axial models of smooth heterogeneous surface were chosen in order to mitigate contact angle multiplicity. For each axial pattern, advancing, receding and equilibrium contact angles were predicted from the local minima location of the system free energy. A heuristic model, based on the local Young equation for spherical drops on patch-wise axial patterns, was fruitfully tested from the results of free-energy minimization. Despite the very simplistic surface model chosen in this study, it allowed clarifying concepts usually misleading in wetting phenomena.

Effect of three-phase contact line topology on dynamic contact angles on heterogeneous surfaces

Cassie-Baxter theory has traditionally been used to study liquid drops in contact with microstructured surfaces. The Cassie-Baxter theory arises from a minimization of the global Gibbs free energy of the system but does not account for the topology of the three-phase contact line. We experimentally compare two situations differing only in the microstructure of the roughness, which causes differences in contact line topology. We report that the contact angle is independent of area void fraction for surfaces with microcavities, which correspond to situations when the advancing contact line is continuous. This result is in contrast with Cassie-Baxter theory, which uses area void fraction as the determining parameter, regardless of the type of roughness.

Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasistatically increased and decreased. We consider both two (cylindrical drops) and three (spherical drops) dimensions using analytical and numerical approaches to minimize the free energy of the drop. In two dimensions, we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions, this behavior persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions, we identify analytically the advancing and receding contact angles on the different surfaces, and we use numerical insights to argue that these provide bounds for the three-dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.

Interaction forces between talc and pitch probed by atomic force microscopy

Colloidal wood resin components present in pulp are collectively called "pitch". The presence of pitch may cause severe problems due to deposits in and on the paper machine. There is thus a need for controlling pitch aggregation and adsorption. To be able to develop more efficient pitch control systems, one needs to develop the understanding of pitch-pitch interactions and of the interactions between pitch and other materials. With this general goal in mind, we present methods for preparing geometrically well-defined pitch particles attached to atomic force microscopy tips. This has enabled us to investigate the interactions between pitch and talc, an additive commonly used for pitch control. We have used model pitch particles consisting of one component only (abietic acid), a mixture of components (collophonium), and particles prepared from real pitch deposits. We show that the forces acting between pitch and talc are attractive and, once the initial approach is made, exert this attraction out to large distances of separation. We present evidence that the formation of bridging air bubbles or cavities is responsible for this interaction.