Adjustable Capillary Forces Through Wetting State Changes in Liquid Bridges: Regulation via Trapezoidal Microstructures

In this paper, we propose a microscale liquid oscillator using electrowetting-on-dielectric (EWOD). Specifically, a mesoscale liquid bridge (LB) between two horizontal surfaces with EWOD is considered. When EWOD is applied, the solid surface becomes more hydrophilic, and hence the contact angle (CA) is reduced. Following the activation of EWOD, the LB can remain connected or it can break into either symmetric or asymmetric shapes depending on the initial liquid volume and wettability of the two surfaces. The LB dynamics activated by EWOD is studied using the multibody dissipative particle dynamics (MDPD) method. Our numerical results show that the behavior of an LB under EWOD can be interpreted via three modes. In the first mode, the LB does not break after applying EWOD. In the second mode, the LB breaks and does not reform. The third mode happens when, depending on the interplay of the volume of the liquid and CA manipulation, the LB continuously breaks, recoils, and reforms. For asymmetric cases, it was observed that the LB may completely detach from one surface and may not reform. It was also observed that decreasing the wettability of a surface, for cases with a continuous breaking and reformation behavior, increases the connecting time interval and decreases the breaking time interval in one break-reform cycle. The results provided in this investigation facilitate fundamental understanding of LB dynamics and their application for the design of microscale liquid oscillators using EWOD.

The angle of repose does affect the behavior of granular materials and has a wide range of applications. The addition of a small amount of liquid can dramatically change the properties of granular media, leading to an increase in the repose angle. This change is mainly attributed to the capillary force resulting from the liquid bridge when the small amount of water was introduced. The capillary force as an attractive force increases the interaction between particles and becomes a dominant factor affecting the angle of repose because it is usually stronger than gravity. In this paper, a new discrete element method (DEM) model was developed in which the capillary force was calculated by the liquid bridge model based on toroidal approximation. The developed DEM model linked the microscopic liquid bridge volume to the macroscopic water content and it also considered the effect of liquid bridge breakage and formation on capillary force. The numerical model was first validated by comparing the experimental and numerical results. Then, the effects of surface tension, volume of the liquid bridge, and the contact angle are studied numerically. Finally, the empirical equation between water content and angle of repose is given under the present simulation conditions. This work will provide a deep understanding for the effect of capillary on the angle of repose.

Rupture distance and shape of the liquid bridge with rough surface

Effects of the interaction between neighboring droplets on the stability of nanoscale liquid bridges

Pendular bond strength between unequal-sized spherical particles

Capillary forces are commonly encountered in nature because of the spontaneous condensation of liquid from surrounding vapor, leading to the formation of a liquid bridge. In most cases, the advent of capillary forces by condensation leads to undesirable events such as an increase in the strength of granules, which leads to flow problems and/or caking of powder samples. The prediction and control of the magnitude of capillary forces is necessary for eliminating or minimizing these undesirable events. The capillary force as a function of the separation distance, for a liquid bridge with a fixed volume in a sphere/plate geometry, was calculated using different expressions reported previously. These relationships were developed earlier, either on the basis of the total energy of two solid surfaces interacting through the liquid and the ambient vapor or by direct calculation of the force as a result of the differential gas pressure across the liquid bridge. It is shown that the results obtained using these methodologies (total energy or differential pressure) agree, confirming that a total-energy-based approach is applicable, despite the thermodynamic nonequilibrium conditions of a fixed volume bridge rupture process. On the basis of the formulas for the capillary force between a sphere and a plane surface, equations for the calculation of the capillary force between two spheres are derived in this study. Experimental measurements using an atomic force microscope (AFM) validate the formulas developed. The most common approach for transforming interaction force or energy from that of sphere/plate geometry to that of sphere/sphere geometry is the Derjaguin approximation. However, a comparison of the theoretical formulas derived in this study for the interaction of two spheres with those for sphere/plate geometry shows that the Derjaguin approximation is only valid at zero separation distance. This study attempts to explain the inapplicability of the Derjaguin approximation at larger separation distances. In particular, the area of a liquid bridge changes with the separation distance, H, and thereby does not permit the application of the "integral method," as used in the Derjaguin approximation.

The rupture of a liquid bridge has many applications while the rupture of a gaseous bridge is gaining importance in the use of bubbles to affect the speed of liquid flow over surfaces. Here, comparative experiments were conducted for liquid and gaseous bridges dispensed at fixed volumes of 6 μL on silicone (hydrophobic) and silane coated glass (hydrophilic) surfaces and with the dispensing tip retracted at different speeds. With the liquid bridge, increasing the retracting speed left behind lower volumes on the substrate. The pinch off position and the contact line radius were factors that determined the volume. The bridge first entered into a receding state before being able to restore toward equilibrium in a relaxation process closer to rupture. On silicone the contact angle was able to undergo higher degrees of hysteresis with faster tip retraction speeds due to the lower free surface energy. With gaseous bridges, only a very small volume was left behind on the silane coated glass while the volume deposited on silicone could be tuned from almost none at low retraction speeds to virtually the entire gaseous volume bridge at high retraction speeds. The tip and neck distances from the substrate increased with tip speed until 0.5 mm/s on the silicone surface, but, beyond that, the position remained invariant until rupture. With the progress toward rupture for the gaseous bridge, the contact angle advanced rather than receded and there was no relaxation stage that brought the contact angle back toward equilibrium before rupture. Overall the gaseous bridges responded very differently to tip retraction than the liquid bridges.

Different types of plant leaves exhibit a broad spectrum of wetting behaviour because of their different pubescence, wax layer, scales, veins, etc. The wetting tension is used to express the wetting of a leaf with βsf = σf. cos θ (σf = the surface tension of a liquid and θ= the contact angle of a liquid to the surface of a leaf). Three different methods are used for measuring contact angles: the contact angle goniometer method, the meniscus rise method and the Wilhelmy plate method. All three methods are based on completely independent theories and produce absolutely uniform contact angles on smooth paraffin surfaces. Closed cup systems which could be thermostatted were used for making the measurements. Substantial differences in the contact angles become apparent when contact angle measurements on roughened and smooth firm surfaces are compared, as for example contact angles on smooth and roughened paraffin surfaces. If the figures for the contact angles on a smooth surface are 90° or > 90°, they will be bigger on a roughened surface; if they are <90° on a smooth surface, they will be smaller on a roughened surface. These results obtained with paraffin were confirmed by contact angle measurements made on plant leaves. The contact angles, measured on plant leaves with the help of the three different measuring methods, show a high degree of uniformity.

On the identification of liquid surface properties using liquid bridges

In the present study, we investigated the evaporation process and deposition pattern of saline droplet on a copper substrate with different roughness under 40 °C ambient temperature. These four substrates are classified as smooth surface and rough surface based on their droplet contact angles. It has been found in this study that the evaporation pattern of droplets has a strong relationship to substrate roughness. The thickness boundary of the evaporation pattern on a smooth surface is larger than that on a rough surface and the particles are closer to boundary and the tendency is more obvious on a smooth surface. The below factors contribute to the result. On the smooth surface, the contact angle of droplet increases as the roughness decreases. On the rough surface, the contact angle increases as the roughness increases. With contact angle decreasing, the evaporation rate at the boundary increases leading to the particles at the boundary more easily sedimentate. Moreover, the capillary flow is hindered by increasing the substrate roughness, while the Marangoni flow remains constant, resulting in more particles remain in the center of the droplet on the rough surface. To sum up, the coffee-ring formation is suppressed by increasing the substrate roughness on a copper substrate under 40 °C temperature.

The changes of wetting state of water droplet on the solid surface featuring pillared structures are quantitatively studied by Coarse Grained simulation. Our results demonstrate that wetting state changes with the different topography (surface roughness), and it depends on the intrinsic hydrophilic/hydrophobic property of surface as well. Only if the contact angle of water droplet on the smooth surface is larger than 93.13°, the wetting state translates from the Wenzel state to the Cassie state on the rough surface with certain pillar height and width, and the contact angle climb up to the highest point and then remain almost unchanged with the increasing of pillar height and the same pillar distance. However, the wetting state does not change if the contact angle on the smooth surface is 85.1° or less, no matter what pillar structure the surface has. Additionally, the contact angles will remain almost unchanged if the pillar height is higher than a certain value. Our simulation results provide a quantitative understanding about the wetting state of water droplet on solid rough surfaces, and the results show the wetting state can be controlled by combining rough structure design and hydrophilic/hydrophobic property change of surfaces.

The Effect of Drop (Bubble) Size on Advancing and Receding Contact Angles for Heterogeneous and Rough Solid Surfaces as Observed with Sessile-Drop and Captive-Bubble Techniques

The stability of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart (the so-called liquid bridge model) is considered. For a weightless liquid bridge that is a right circular cylinder, the well-known Rayleigh stability limit holds, and the liquid column becomes unstable when its length is larger than its circumference. Many perturbations from this ideal configuration have been studied in the past, but the supporting disk shape has always been assumed circular. In this Brief Communication the influence of noncircular supports on stability limits of almost cylindrical liquid bridges is analyzed through an asymptotic analysis. Closed form expressions for the stability limits are presented.

Influence mechanism of liquid bridge evaporation on the dynamic behaviour of dust particles on solar photovoltaic panels

It is common knowledge that a fluid motion can be initiated both by the volume (buoyancy) forces, due to density variations in presence of a gravity field, and the surface (capillary) forces, due to variations of surface tension along a fluid/fluid interface. Involving in motion the surface and the near-surface layers the capillary forces gives rise to a volumetric flow generally known as the Marangoni convection. In turn, inhomogeneity of the surface tension may result from its dependence on temperature or concentration of the dissolved surfacetension active (surfactant) component. Such convection, thermocapillary or solutocapillary one, respectively, plays an important role in hydrodynamics and heat/mass transfer of inhomogeneous multi-phase media with the liquid/liquid interface or the free surface between liquid and gas. The Marangoni convection has a marked effect on the intensity of many technological processes encountered in food, chemical, oil, metallurgical and other industries, including those proceeding in microgravity conditions where the gravitational mechanisms of convective motion are weakened or absent. Particular interest on research in this field has quickened in recent years due to new achievements in the development of space technologies and life-support and survival systems for orbital stations. Marangoni phenomena is a problem of great application value for such areas as ecology (purification of water surface from petroleum products), meteorology, biology (motion of bacteria and microbodies), medicine (spreading of pulmonic surfactants during aerosol inhalation in treatment of lung diseases) and so on. Despite the global abundance of the Marangoni convection the direct experimental investigation of the Marangoni flows in the so-called pure form is a challenging task. The reason is that under normal terrestrial conditions the existence of temperature and concentration gradients in a fluid also leads to development of the gravitational Rayleigh convection with considerably higher intensity than that of the Marangoni convection. Hence the latter proves to be almost suppressed by a more severe convective driving mechanism or veiled by its action. At the same time, under certain conditions, the surface forces may dominate over the buoyancy ones. Such conditions are realized, for example, in shallow layers and fluid films, liquid bridges and zones confined between solid surfaces, and also for small insoluble drops or gas bubbles suspended in liquids. In the past decades, the Marangoni convection in such systems has been the subject of intensive investigation. However, most of the studies are concerned with thermocapillary variant of the Marangoni