Contact Line Research Articles

Complementary correlation between surface microbubble and droplet shapes

Previous atomic force microscopy studies have suggested that surface micro- and nanobubbles exhibit a flat shape. In this study, we directly observed surface microbubbles formed in an NH3BH3 solution using an optical microscope. No flat microbubbles were observed. Instead, on an SiO2/Si substrate, we discovered a relationship where the sum of the contact angle of a microbubble and the contact angle of a droplet equaled ∼180°. This relationship allowed us to control the shape of surface microbubbles by manipulating the wettability of the surface and the surface tension of the liquid, similar to droplet control. We were able to produce almost perfectly spherical microbubbles. Conversely, on a Cu foil, this relationship did not hold, although we still observed the formation of nearly spherical microbubbles. In this scenario, the shape of microbubbles appeared to be influenced by contact line pinning.

Hierarchical Ti3C2Tx MXene@Honeycomb nanocomposite with high energy efficiency for solar water desalination

The utilization of solar-driven interfacial evaporation holds immense promise in enhancing energy efficiency and establishing sustainable methods for seawater desalination and water purification. While designing the materials to achieve high evaporation efficiency, the tuning of materials with porosity and surface chemistry is very crucial. Novel sustainable materials are of great importance for solar water desalination applications since clean water production is utmost important in the current era. There exists a lack of exploration in modifying the surface wettability states of solar evaporators to expedite the vapor generation rates. In this study, we showcase a hydrophilic Ti3C2Tx MXene-coated carbonized honeycomb (CHC) (Ti3C2Tx MXene@CHC) nanocomposite-based hexagonal-shaped evaporator surface. This is the first-time report on the effective utilization of hierarchical CHC for the preparation of solar absorber comprising of Ti3C2Tx MXene@CHC nanocomposite, particularly for the solar water desalination. The Ti3C2Tx MXene@CHC nanocomposite evaporator achieves an impressive water evaporation rate of 1.6 kg m−2 h−1 with 90% efficiency under 1 sun illumination. The augmented thickness of the water layer in the hydrophilic surface of the Ti3C2Tx MXene@CHC nanocomposite helps in facilitating the rapid escape of water molecules. The relatively elongated contact lines in the hydrophobic region simultaneously ensure substantial water evaporation, significantly enhancing the water desalination process. The Ti3C2Tx MXene@CHC nanocomposite exceeds stringent quality benchmarks, signaling its potential for solar water desalination.

Mathematical model and generation analysis for crossed helical gear system

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

An analytical approach for determining contact angle hysteresis on smooth, micropillared, and micropored homogeneous surfaces

HypothesisNumerous theoretical models have been developed from various research perspectives, including free energy analysis, force balance, and contact line dynamics, to elucidate the contact angle hysteresis on solid surfaces, especially for superhydrophobic surfaces. However, these models can produce inconsistent predictions, and few of them account for contact angle hysteresis on smooth and microstructured surfaces simultaneously. TheoryFormulas for advancing and receding free energy barriers of drops on different solid surfaces were derived, and then these formulas were simplified by incorporating the geometric constraint equation of drops, leading to an establishment of analytical models. FindingsThis study presented a unified approach for deriving analytical models of contact angle hysteresis for various wetting systems, including drops on smooth homogeneous surfaces, Cassie drops on micropillared and micropored homogeneous surfaces, and Wenzel drops on micropillared homogeneous surfaces. The established models revealed a significant impact of frictional tension, and of the change in free energy during drop motion, on the free energy barriers. These models were fully derived thermodynamically without subsequent theoretical modifications and found to agree well with experimental results. Some of the models in this study were validated using other existing models, despite the models having been developed using completely different approaches.

Droplet Contact Line Dynamics after Impact on Solid Surface: Future Perspectives in Healthcare and Medicine

Droplet Contact Line Dynamics after Impact on Solid Surface: Future Perspectives in Healthcare and Medicine

Freezing and Capillarity

Ice structures such as accretion on airplanes, wires, or roadways; ice falls; ice stalactites; frozen rivers; and aufeis are formed by the freezing of capillary flows (drops, rivulets, and films). To understand these phenomena, a detailed exploration of the complex coupling between capillary flow and solidification is necessary. Among the many scientific questions that remain open in order to understand these problems are the confinement of the thermal boundary layer by the free surface, the interaction between a freezing front and a free surface, the effect of freezing on the contact line motion, etc. This review focuses mainly on water and ice, discussing the theoretical framework and recent developments in the main areas of the freezing–capillarity interaction. The text deeply explores the freezing of a moving drop or a rivulet and the fundamental problem of wetting water on ice. Additionally, it highlights some of the main open questions on the subject.

Forced Wetting of Shear-Thinning Fluids in Confined Capillaries.

Dynamic wetting in confined spaces is pivotal for the functional efficiency of biological organisms and offers significant potential for optimizing microdevices. The fluids encountered in such scenarios often exhibit shear-thinning behavior, which gives rise to complex interfacial phenomena. Here, we present an intriguing wetting phenomenon for shear-thinning fluids in confined capillary spaces. The employed shear-thinning fluids, carboxymethyl cellulose aqueous solutions with mass fractions of 0.5, 1.0, and 1.5 wt %, exhibit an intermediate state between ideal viscoelastic liquids, viscoelastic solids, and gel-like properties. We elucidate the geometric effect on its capillary wetting behavior, demonstrating that distortion of the moving contact line alters flow dynamics near the front corner, modifying the viscous resistance. This intricate interplay between the modified viscous resistance and the driving force results in a novel dynamic equilibrium distinct from that in Newtonian fluids. We further reveal that the viscous resistance in confined capillaries is controlled by both the morphology of the moving contact line and the shear-thinning exponent, particularly within the range of 0.7 to 1. This novel mechanism provides a pathway for manipulating the wetting dynamics of complex fluids in confined spaces.

Numerical analysis of the Thermal EHL line contact problem under intermittent motion

Abstract A mathematical model of time-varying thermal elastohydrodynamic lubrication (EHL) is developed using a sleeve chain as the object of study. The effects of thermal effect, load, speed, rest time and equivalent radius of curvature on its EHL are investigated using theoretical simulations. The results show that during intermittent motion, a portion of oil is entrapped in the contact zone at the end of the deceleration phase, after which this entrapped oil gradually moves out of the contact zone with the onset of speed, and a lower film of oil at the lubrication inlet passes through the center of the contact zone. In simple sliding intermittent motion, the temperature rise plays a crucial role in the variation of the oil film, particularly during the motion phases, and is an unavoidable factor. An increase in stop time reduces the film thickness and increases the following friction coefficient in the acceleration stage. An increase in the equivalent radius of curvature increases the film thickness and thermal rise in the contact zone as well as decreases the friction coefficient. Since the sleeve chain is one of the most commonly used mechanism in industry, high priority should be given to the lubrication design of this structure.

Evaluation of Scuffing Load Capacity of Helical Gear Based on the Tribo‐Dynamic Model

ABSTRACTThe scuffing load capacity of gear is closely related to the meshing temperature rise of tooth surface. The key to predict the temperature rise is to establish an accurate meshing temperature rise model. In the paper, a tribo‐dynamic model of helical gear is established through coupling of tooth surface lubrication parameters, and the influence of temperature rise on ambient temperature during meshing process is considered. Then, the effects of oil supply temperature, input speed and torque on tooth surface temperature rise, film thickness, friction excitation and gear dynamic characteristics are discussed. The results show that the temperature rise of the gear is higher during the engaging‐in and engaging‐out regions. Meanwhile, there is local high temperature at the end of the contact line due to the end effect. The vibration of gear along the off‐line‐of‐action direction is mainly determined by friction excitation. With the increase of oil supply temperature, input speed and torque, the risk of scuffing failure increases and the influence of oil supply temperature and input load is more significant. The conclusions of this paper may provide some valuable suggestions for the anti‐gluing failure design of gear in engineering.

Evaporation and viscous flow structure near a contact line pinned at a solid wedge

Evaporation and viscous flow structure near a contact line pinned at a solid wedge

Precursor-film-driven ultra-early depinning of the three-phase contact line

Hypothesis: Despite its importance in colloid and interface science, contact line pinning remains poorly understood, especially in the presence of a precursor film. We hypothesized that this is due to a lack of an experimental method capable of directly observing their physics at the nanoscale. MethodsUsing coherence scanning interferometry, we visualized the three-dimensional behavior of contact lines with a precursor film near a nanogroove structure composed of flat terrace surfaces and steps with an inclination angle of 30° while achieving nanoscale vertical resolution. FindingsWe found that even when the contact line is pinned at the edge of the step, the precursor film is not and advances beyond the edge. Furthermore, we discovered that the precursor film has two distinct effects on contact line motion. Specifically, the precursor film facilitates depinning when the contact line descends the step — a contact angle change was 0.9°, only 3.0% of the value predicted by a classical theory of contact angle at a solid edge. This ultra-early depinning is attributed to the formation of a new liquid film past the edge, driven by the progression of the precursor film that overcomes the pinning effect. In contrast, when the contact line ascends the step, the precursor film acts as a resistance to movement due to steric interaction.

Life beyond Fritz: On the Detachment of Electrolytic Bubbles.

We present an experimental study on detachment characteristics of hydrogen bubbles during electrolysis. Using a transparent (Pt or Ni) electrode enables us to directly observe the bubble contact line and bubble size. Based on these quantities we determine other parameters such as the contact angle and volume through solutions of the Young-Laplace equation. We observe bubbles without ("pinned bubbles") and with ("spreading bubbles") contact line spreading and find that the latter mode becomes more prevalent if the concentration of HClO4 is ≥0.1 M. The departure radius for spreading bubbles is found to drastically exceed the value predicted by the well-known formula of W. Fritz [Phys. Z. 1935, 36, 379-384] for this case. We show that this is related to the contact line hysteresis, which leads to pinning of the contact line after an initial spreading phase at the receding contact angle. The departure mode is then similar to a pinned bubble and occurs once the contact angle reaches the advancing contact angle of the surface. A prediction for the departure radius based on these findings is found to be consistent with the experimental data.

Spreading of rotating liquid annular ring with hysteresis effects

The spreading of a liquid, subjected to centrifugal forces or an air jet, leads to a lowering of the liquid height at the center. If the system is partially wetting, experiments show a break up of the liquid and the appearance of a dry patch at the center. In this article, the spreading of a liquid droplet or a liquid film, featuring a dry patch at the center, is investigated. Via a generalized Tanner’s law, we allow for a contact-angle hysteresis in partially wetting systems. By means of the lubrication approximation, an analytical quasi-steady solution can be derived in the limit of small capillary numbers. We find a power-law regime for the spreading, in which at least one of the contact lines follows a power law in time, almost independent of both static contact angles. The influence of the static contact angles remains restricted to the beginning of the spreading and to transition periods. Four different types of spreading can be identified, namely spreading (i) with a very thin central liquid layer, (ii) as annular ring with central dry patch, (iii) into a static equilibrium, and (iv) with closing of the central dry patch. In a flow map, these types of spreading are mapped as function of both static contact angles. Moreover, the dependency from gravitational and centrifugal forces is investigated and included in the flow map. For a perfectly wetting system, a disjoining-pressure correction in combination with Tanner’s law prohibits negative liquid heights at the center. Hereby, the magnitudes of the Hamaker constants have a negligible influence and arbitrary-small values can be used, since the dynamics of the contact line remains controlled by Tanner’s law.

Geometric Parameter Optimization for Axial Modification in Helical Gear Form Grinding

During the axial modification in helical gear form grinding, the contact line between the grinding wheel and the gear constantly changes, and the additional radial motion can cause a “tooth surface twist” phenomenon. An optimization method for tooth surface twist error was proposed to address this. Based on the gear meshing principles, a mathematical model for axial modification in form grinding was established to solve for the instantaneous contact lines at various positions on the actual modified tooth surface. By analyzing the influence of the grinding wheel installation angle on the axial modification contact line, an optimization model was constructed to reduce the twist of the transverse profile, reduce the twist of the flank profile, reduce the helix deviation, and improve the form grinding efficiency. The practical implications of this research are significant, as the Particle Swarm Optimization (PSO) algorithm was employed to optimize the form grinding parameters, leading to a method that effectively reduced tooth surface twist error and improved the form grinding accuracy of the modified tooth surface.

Model interpretation and microscopic characteristics of collapsibility evolution of compacted loess under dry-wet cycles

The evolution of loess microstructure exerts a direct impact on its collapse evolution during dry and wet (DW) cycles. In this study, a hydro-mechanical coupling numerical model considering DW cycles and mechanical loading was established by extending the Barcelona Basic model, meanwhile combining with the test results to reveal the effect of DW cycling on the collapse deformation and strength response of loess. Additionally, the microscopic mechanism of loess collapse evolution was revealed through microscopic tests. Results indicated DW cycles caused the net compaction of loess, with the first DW cycle exerting the most significant effect on its deformation, consequently deteriorating the loess. Wetting under constant loading leads to a collapse of macrostructures formed by aggregates. Moreover, DW cycles transformed the structural units from line and surface contact to point. The basic structural units exhibited obvious grade properties, in which DW cycles trigger the collapse of compound aggregates, with the number of relatively stable mononuclear aggregates and intergranular pores increasing. DW cycles in an open environment induced the loss of cementing materials such as soluble salts and reduced the bonding strength among basic structural units. This subsequently tended to weaken the structural properties of loess and decreased the mechanical properties.

A coupled local front reconstruction and immersed boundary method for simulating 3D multiphase flows with contact line dynamics in complex geometries

Multi-phase flows in the presence of complex solid geometries are encountered widely throughout industrial processes to intensify mass and heat transfer processes. The efficiency of these processes relies largely on the predominant fluid dynamics regime inside the reaction vessel (e.g. trickle bed, bubble column reactor). The prevailing flow structure is influenced by many factors including the nature of the fluid-solid interactions (i.e. wetting or non-wetting). Such flows are often studied using front-capturing techniques to capture the fluid-fluid interface in combination with an auxiliary model to account for fluid-solid interactions. However, these front-capturing methods have difficulties in accurately representing the interface. Therefore, we adopted a front-tracking method: the Local Front Reconstruction Method (LFRM). In this study, LFRM is coupled with the Immersed Boundary method to incorporate the no-slip boundary condition at the solid surface. The model performance is assessed using droplet spreading simulations, where the equilibrium droplet shape (i.e. radius, height, and outline), the interfacial pressure difference, and the surface tension force are compared to analytical solutions and literature data. The results show an excellent match with the analytical solutions, and additionally superior performance to state-of-the-art volume tracking models.

Strongly Different Adhesion Reduction for 1D or 2D Random Fractal Roughness, and an Extension of the BAM Model to Anisotropic Surfaces

The influence of roughness on adhesion has been studied since the time of Fuller and Tabor, but recently there has been debate about how roughness exactly seems to kill (but sometimes enhance!) adhesion, particularly with reference to the accepted model of fractal roughness. We show that the Persson–Tosatti criterion does not depend on anisotropy of the surface for a typical power law PSD if written in terms of rms roughness and magnification. Instead, a very simple extension of the Bearing Area Model (BAM) of Ciavarella to anisotropic fractal surface shows a weak but clear dependence on the anisotropy, with higher adhesion in the 1D case, showing better agreement than the Persson–Tosatti criterion to actual numerical results of Afferrante Violano and Dini. However, neither of the two models permit to capture the strong hysteresis found in experiments between loading and unloading, which is very likely to enhance adhesion more as we move from the isotropic to the full 1D case. This suggests the mechanism of load amplification along contact lines and the associated elastic instabilities, is not captured by either the Persson–Tosatti or the BAM model applied to anisotropic surfaces.

Exceptional anisotropic superhydrophobicity of sword-lily striated leaf surface and soft lithographic biomimicking using polystyrene replica

Herein, we report unusually high anisotropic superhydrophobicity, unidirectional self-cleaning, and biomimicking of adaxial sword-lily (Gladiolus hortulanus) leaf comprising three distinct levels of surface textures. Observably, the static anisotropic wetting and rolling of water droplets are more favourable in the parallel (or, striation) direction than in the perpendicular direction. Inspired from such water repellency of the sword lily leaf surface, here bio-mimicked polystyrene (PS) leaf construct is developed through a soft lithographic technique. Considering different water droplet sizes (4–10 μl) on natural lily leaf and bio-mimicked PS construct surfaces, the respective parallel (θ ||) and perpendicular (θ ⊥) water contact angles (WCAs) stand at, θ || ∼143°–147°, θ ⊥ ∼156°–169°; and θ || ∼130°–139°, θ ⊥ ∼142°–145°. Moreover, the specimens under study exhibit roll-off angles ranging, α || ∼8°–23° (α ⊥ ∼16°–41°) and α || ∼21°–49° (α ⊥ ∼40°–55°) along parallel (and perpendicular) directions; respectively. A noticeable difference in α ⊥ and α || values can be ascribed to the profound three-phase contact line (TCL) pinning along the perpendicular direction taking advantage of striation as means of barrier. The roll-off angles can also alter due to a variation in the droplet volume. The unusual anisotropic superhydrophobicity and unidirectional droplet roll-off can be attributed to the entrapped air within the micro-nano texture beneath the water droplet along with the pinning effect in the perpendicular direction caused by the striated heights.

Experimental Investigation of Oil Film Variation in Finite Line Contact Under Intermittent Motion

Experimental Investigation of Oil Film Variation in Finite Line Contact Under Intermittent Motion

Synthesis and Characterization of Monolayer Colloidal Sheets.

Sheet-like colloidal assemblies represent model systems to investigate the structure and properties of two-dimensional materials. Here, we report a simple yet versatile method for the preparation of colloidal monolayer sheet-like assemblies that affords control over the size, crystalline order, flexibility, and defect density. The protocol that we report relies on self-assembly of colloids as a sessile drop of dispersion is evaporated on an oil-covered substrate. In this case, the contact line continually moves as the drop shrinks. Polyethyleneimine polymer-covered micrometer-sized colloidal particles are transported to the air-water interface and assemble to form a monolayer sheet as the drop dries. Cross-linking the polymer renders the colloidal assembly permanent. Interestingly, monodisperse colloidal particles form disordered assemblies when dried from low concentration dispersions, while polycrystalline ordered assemblies form at higher concentrations. We demonstrate that increasing the cross-linker to polymer ratio decreases the flexibility of the assembly. Introduction of different-sized colloidal particles in a sheet leads to increased disorder. Removal of sacrificial particles from the sheet allowed the introduction of "holes" in the sheets. Thus, these colloidal sheets are models for probing the effects of disorder, doping, and vacancies in two-dimensional systems.