Shape Of Contact Line Research Articles

Wind- and gravity-forced drop depinning

Liquid drops adhere to solid surfaces due to surface tension but can depin and run back along the surface due to wind or gravity forcing. This work develops a simple mechanistic model for depinning by combined gravity and high-Reynolds-number wind forcing and tests that model using water drops on a roughened aluminum surface. On non-inclined surfaces, drops depin at a constant critical Weber number, $W\!e_{\mathrm{crit}}=7.9$, for the present wettability conditions. On inclined surfaces, $W\!e_{\mathrm{crit}}$ decreases linearly with the product of the Bond number and the width-to-height aspect ratio of the unforced drop. The linear slope is different in distinct wind- and gravity-dominated forcing regimes above and below $W\!e_{\mathrm{crit}}=4$. Contact line shapes and drop profile shapes are measured at depinning conditions but do not adequately explain the differences between the two forcing regimes.

Effect of Contact Line Shape on Horizontal Shear Force of Water Droplet on Silicone Sheet

Effect of Contact Line Shape on Horizontal Shear Force of Water Droplet on Silicone Sheet

The effect of surface pattern property on the advancing motion of three-dimensional droplets

<p style='text-indent:20px;'>We investigate numerically the advancing motion of 3D droplets spreading on physically flat chemically heterogeneous surfaces with periodic structures. We use the Navier-Stokes-Cahn-Hilliard equations with the generalized Navier boundary conditions to model the motion of droplets. Based on a convex splitting scheme, we have done numerical simulations and compared the results between different surface patterns quantitatively. We study the effect of pattern property on the advancing motion of three phase contact lines, the critical volume at the contact line jump and the effective advancing angles. By increasing the volume of droplet slowly on heterogeneous surfaces with different pattern property, we find that the advancing contact line approaches an equiangular octagon for the patterned surface with periodic squares separated by channels and approaches a regular hexagon for the patterned surface with periodic circles in regular hexagonal arrays. The shape of three-phase contact line is much more determined by the macro structure of the pattern than the micro structure of the pattern in each period.

A data set characterizing thermal resistance at evaporation from sintered porous media

Passive cooling devices like heat pipes play an increasingly important role in a vast field of cooling applications. For optimal design of heat pipe-based cooling systems, it is crucial to perform reliable simulations which adequately account for thermal resistance of evaporation from the embedded capillary structure. In this study, a data set which provides thermal resistance for water evaporating from sintered porous media was obtained using a micro model. The open source software Surface Evolver was used to calculate 1638 liquid meniscus shapes in a cubic arrangement of sintered spheres for various porosities, water levels, and contact angles. A heat conduction model accounting for temperature dependent thermophysical fluid properties was developed to compute corresponding thermal resistances. Phase change at the liquid surface was modeled using expressions based on the thermal-energy-dominant limit of the statistic rate theory. The results show a significant dependence of thermal resistance on vapor temperature, wick geometry, contact angle, and the shape of contact line. 8316 data points suggest high vapor temperatures, small grain sizes, low porosities, and small contact angles for minimal thermal resistance. Furthermore, a method for utilizing the data set in device level macro models is outlined.

The interaction of inner and outer surface corners during spontaneous wetting

Real world surfaces can often be modeled as a collection of edges, corners, dents or spikes of varying roundness. These features exhibit individual spontaneous wetting behaviors comprising pinned contact lines, rivulets or cusps. If occurring in proximity to one another, as is often the case in applications, these wetting properties interact, resulting in an overall changed wetting pattern on the surface. Hence, there is considerable interest in understanding when, and to what extent, interactions occur, and how wetting then deviates from the wetting of isolated surface features.The present study addresses these questions by experimentally and theoretically studying the capillary interaction of sharp-edged 90° (outer) and 270° (inner) corners in proximity to one another. It is shown that the spontaneous wetting at the convex outer corner is influenced by the concave inner corner even when they are separated by a distance of several times the capillary length, while the wetting of the inner corner takes place unaffected by the outer corner, except when the separating distance is much smaller than the capillary length. The final contact line shape at the inner corner is measured and theoretically modeled for contact angles up to 90°.

Scaling analysis and SE simulation of the tilted cylinder-interface capillary interaction

The capillary interaction induced by a tilted cylinder and interface is the basic configuration of many complex systems, such as micro-pillar arrays clustering, super-hydrophobicity of hairy surface, water-walking insects, and fiber aggregation. We systematically analyzed the scaling laws of tilt angle, contact angle, and cylinder radius on the contact line shape by SE simulation and experiment. The following in-depth analysis of the characteristic parameters (shift, stretch and distortion) of the deformed contact lines reveals the self-similar shape of contact line. Then a general capillary force scaling law is proposed to incredibly grasp all the simulated and experimental data by a quite straightforward ellipse approximation approach.

A three-dimensional model for analyzing the anisotropic wetting behavior of striped surfaces

Anisotropic wetting shows potential application in advanced microfluidics and biosensors. This study proposes a three-dimensional (3-D) methodology using a finite element method to investigate the anisotropic wettability of striped surfaces. The variations of free energy (FE), free energy barrier (FEB), contact angle (CA), contact angle hysteresis (CAH), droplet shape and the three-phase contact line shape of an anisotropic droplet during the spreading process are explored. It is found that the droplet length and three-phase contact line length fluctuate by the increase of the droplet width and three-phase contact line width during the spreading process of droplet. In addition, a relatively small stripe width with higher free energy is necessary to achieve a large equilibrium CA and a small CAH or easily reach the equilibrium CA. The present methodology can be potentially used for designing architected surfaces with anisotropic wetting properties in microfluidic devices, lab-on-a-chip systems, and self-cleaning surfaces.

Droplets on Microdecorated Surfaces: Evolution of the Polygonal Contact Line

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 biomicroarrays 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 homogeneous 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 depinning 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 the 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 outward 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.

Conjugate heat transfer analysis for the effect of the eccentricity of hydrophobic dot arrays on pool boiling

Patterned wettability causes pinning of the contact line, which is the area responsible for the heat flux transition. A new parameter, “eccentricity,” which governs the contact line shape and length, can be used to control the shape of the bubbles. Initially, we placed four hydrophobic dots on a surface. When a high input heat flux was applied, the bubbles merged and the contact line pinned onto the hydrophobic dots, thus preserving the relatively long dumbbell-shaped contact line. Additionally, the heat transfer coefficient was found to be high at high eccentricity values because of the separation of the merging timing and the generation of metastable contact lines. Next, we placed 36 dots on the surface. The merging and pinning behavior and heat transfer coefficient revealed two stages of transition by the heat flux. From a low to intermediate heat flux, a high eccentricity became effective because the merging and pinning location moved from a marginal area to the entire surface. From the intermediate to high heat flux, large bubbles formed through the simultaneous merging of all the nucleated bubbles, and the eccentricity had almost no influence on the merging or pinning. Therefore, the pinning count minus the number of times the lines merged comprised the relevant data required to analyze the heat transfer coefficient variation with heat flux.

A methodology to determine the adhesion force of arbitrarily shaped drops with convex contact lines

The adhesion force of drops deposited on smooth solid surfaces can be found by integration along the contact line of the liquid–vapor surface tension acting on an infinitesimal contact line element, projected on the substrate plane (γ||). Approximate relations available in the literature are applicable only for drops with specific contact line shapes (e.g. circular, elliptical, parallel-sided, or contact lines with at least one axis of symmetry). However, in most applications drops are exposed to a combination of forces and the contact line may have any arbitrary shape. In this study, a model is developed to calculate the adhesion force of drops with arbitrary shape. The contact line shape and contact angle values are found using side view images taken at different azimuthal angles (around the drop). The model is applicable to drops of any shape, as long as contact line is convex, and takes into account the perspective errors during imaging.

The three-phase contact line shape and eccentricity effect of anisotropic wetting on hydrophobic surfaces

This paper experimentally evaluates the combined effects of eccentricity, relative spacing, and viewing directions on the wetting conditions and the three-phase contact line shapes of hydrophobic surfaces patterned with discrete micropillars. Different techniques to depict the tortuosity of the contact line between the water droplet and microstructured surfaces are presented. First, square micropillars with different values of normalized eccentricity, e*, and relative spacing, D*, were fabricated using a double casting replication technique. Subsequently, the contact angles were measured along different viewing angles by gradually rotating the sample from 0° to 180°. The contact angle distribution was found as a periodic function of the viewing angle whose period depends on the micropillar eccentricity. The results showed that anisotropy increases by increasing the micropillar eccentricity or decreasing the pillar relative spacing. However, the effect of changing the micropillar eccentricity was much more pronounced. Micropillars with e* = 0.75 and smaller D* showed maximum degrees of anisotropic wetting and droplet distortion corresponding to 7% and 15%, respectively. Using the measured droplet aspect ratio, corrugated shapes of the three-phase contact line of the micropillars were also reconstructed. Finally, a simple yet effective semi-analytical model, based on Fourier series curve-fitting of the experimental data, was developed to describe the equilibrium 3D shape of the droplet on anisotropic surfaces. Experimental and simulation results reveal that the degrees of anisotropic wetting and droplet distortion were directly proportional to the energy barriers of the system, resulting from the noncircular corrugated shape of the three-phase contact line. The obtained results may further shed light on the underlying mechanism influencing anisotropic wetting on micropatterned surfaces.

Modelling unidirectional liquid spreading on slanted microposts

A lattice Boltzmann algorithm is used to simulate the slow spreading of drops on a surface patterned with slanted micro-posts. Gibb's pinning of the interface on the sides or top of the posts leads to unidirectional spreading over a wide range of contact angles and inclination angles of the posts. Regimes for spreading in no, one or two directions are identified, and shown to agree well with a two-dimensional theory proposed in Chu, Xiao and Wang. A more detailed numerical analysis of the contact line shapes allows us to understand deviations from the two dimensional model, and to identify the shapes of the pinned interfaces.

The role of wetting heterogeneities in the meandering instability of a partial wetting rivulet

Rivers are subject to a meandering instability caused by sediment transport. A liquid rivulet on an inclined plate in partial wetting conditions exhibits a similar instability at sufficiently high flow rates. It takes a sinuous shape: curves become bigger and bigger, growing by inertia from contact line defects. Meanders are eventually stationary because of the pinning force. The way the initial rivulet is created has consequences on the contact line's shape. We run experiments to study how the critical flow rate depends on initial conditions. We measure a strong dependence, in particular by modifying the initial state from which meanders are growing: it shows that the pinning force plays the main role in the meandering instability. This is in contrast with the previous approach in which only a balance is considered between inertia and a line tension of capillary origin. Because of wetting hysteresis, rivulets have the capacity to deform without any movement of the contact line. We show that the rivulet deforms in response to the centrifugal force. This deformation also helps us to understand how the critical flow rate depends on the initial rivulet shape.

General Methodology for Evaluating the Adhesion Force of Drops and Bubbles on Solid Surfaces

The shortcomings of the current formulation for calculating the adhesion force for drops and bubbles with noncircular contact lines are discussed. A general formulation to evaluate the adhesion force due to surface forces is presented. Also, a novel methodology, that is, IBAFA, image based adhesion force analysis, was developed to allow implementation of the general formulation. IBAFA is based on the use of multiple profile images of a drop. The images are analyzed (1) to accurately reconstruct the contact line shape, which is analytically represented by a Fourier cosine series, and (2) to measure contact angles at multiple locations along the contact line and determine the contact angle distribution based on a linear piecewise interpolation routine. The contact line shape reconstruction procedure was validated with both actual experiments and simulated experiments. The procedure for the evaluation of the adhesion force was tested using simulated experiments with synthetic drops of known shapes. A comparison with current methods showed that simplifying assumptions (e.g., elliptical contact line or linear contact angle distribution) used in these methods result in errors up to 76% in the estimated adhesion force. However, the drop adhesion force evaluated using IBAFA results in small errors on the order of 1%.

Understanding of sliding and contact angle results in tilted plate experiments

Tilted plate experimental methodology is studied in order to address misinterpretations and omissions that exist in the literature. The effect of methodology on subsequent sliding angle measurements is quantitatively assessed in two parts. The first part is a comparison of drop placement techniques in the conventional tilted plate method (drops placed on a level surface, then inclined). The second part is a comparison between the conventional tilted plate method and a modified method, in which the drop is placed on a surface that is already inclined. The first part of the study involved water drops placed on alkyl ketene dimmer (AKD) surfaces using a needle from above as well as below the surface (through a hole). For drops placed from below, three different drop locations (with respect to the hole in the surface) are included in the study. It was found that the drop placement technique had a statistically significant impact on sliding angle measurements, and the most consistent and unbiased measurements resulted when the drop was placed from below, with the hole leading (downhill from) the drop. The second part of the study involved water drops on both AKD (high contact angle hysteresis system) and fluorinated silicon (low contact angle hysteresis) surfaces. For either system, it was shown that sliding angles were lower when drops were placed on surfaces that were already inclined. Since the maximum and minimum contact angles were identical between the two experimental methods, the difference in adhesion was due to variation in contact line shape. The results of this study show that errors of 50–60% would result from using conventional tilted plate measurements to predict droplet mobility on fixed, inclined surfaces, such as those found in condensers. The important distinction between repellency (measured by the advancing contact angle) and drop mobility is also discussed. Further, it was observed that the advancing and receding contact angles do not always correspond to the maximum and minimum contact angles observed in a tilted plate experiment.

Contact Line Shape on Ultrahydrophobic Post Surfaces

In this work, we investigate the configuration of the contact line of a water drop lying on an ultrahydrophobic post surface using the numerical algorithm Surface Evolver. For the special situation of Cassie wetting, we propose a modified definition of the contact line as the line in space where the meniscus starts to curve upward out of the plane of the composite surface. In our simulations, it is found that the contact line is very strongly distorted, indicating a strong tendency of the drop to "ball up" in those areas where it is not in contact with the solid surface. The distortion of the contact line corresponds to a pronounced deformation of the liquid-air interface around the base of the drop. We discuss the consequences of this distortion for the definition and practical measurement of the contact angle on ultrahydrophobic surfaces.

Quasistatic relaxation of arbitrarily shaped sessile drops

We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid. We have shown rigorously in the case of quasi-static relaxation using the standard mechanical description of dissipative system dynamics that the introduction of a dissipation term proportional to the contact line length leads to the well-known local relation between the contact line velocity and the dynamic contact angle at every point of an arbitrary contact line shape. A numerical code is developed for three-dimensional drops to study the dependence of the relaxation dynamics on the initial drop shape. The available asymptotic solutions are tested against the obtained numerical data. We show how the relaxation at a given point of the contact line is influenced by the dynamics of the whole drop which is a manifestation of the nonlocal character of the contact line relaxation.

Thermodynamics of soft anisotropic contact lines.

Contact lines arising from the intersection of interfaces between liquids and nematic liquid crystals are representative models of soft anisotropic contact lines. This paper presents the thermodynamics of soft anisotropic contact lines and the derivation of the one dimensional (1D) Gibbs-Duhem adsorption equation. Consistency between the 1D Gibbs-Duhem equation and the classical equations of lineal nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic line Gibbs-Duhem equation reveals the presence of couplings between curvature, torsion, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for contact line shape and orientation selection. The ability of an adsorbed solute to orient the director and to bend and twist the contact line is predicted. The thermodynamic origin of preferred orientation at a straight contact line is established.

Thickness Control of Colloidal Crystals with a Substrate Dipped at a Tilted Angle into a Colloidal Suspension

When a glass substrate is dipped into a colloidal suspension, the contact line shape is changed with the angle of tilt. These variations in the contact line shape indicate a possibility for thickness control of colloidal crystals. Thus, we have investigated how the thickness of colloidal crystals is changed with specific tilted angles (−10°, 0°, 10°, 20°, and 30°, respectively). As a glass substrate is tilted more (from −10° to 30°), a smoother and thicker contact line is formed and thicker colloidal crystals are obtained. In addition, it is possible to explain why multiple contact line patterns are formed on the glass substrate. It was found that to fabricate three-dimensional colloidal crystals with an even surface, the evaporation rate of water should be reduced and/or the glass substrate should be tilted over 10° in our cases.

Spreading of Large Drops on Patterned Surfaces

We report an experimental study of the shape of large liquid drops spreading on surfaces with patterns of wettability. The patterns are sets of disks of a material less wettable than the rest of the plane substrate. When few defects are present, or when the average distance between defects is large compared to the capillary length, the drop edge is a set of circular arcs connecting the pinning points. When the density of defects is smaller than the capillary length, the contact line shape is more complex and we analyze its morphology through a kind of box counting method. The roughness of the contact line is maximum when the average distance between defects is comparable to two times the defects size. Setting the non-wetting defects on a periodic or almost periodic array produces drops with faceted edges. The transition between circular and faceted drops can be understood as a competition between the tension of the drop edge and the local force exerted on the contact line by the defects. Although the drops are grown at a fixed flow rate, the motion of the contact line is irregular, with jumps between pinning sites. In some cases, the jumps of the contact line are correlated in space, leading to avalanchesand large scale motions of the drop.