Influence of Bond Number on Behaviors of Liquid Drops Deposited onto Solid Substrates

The problem of spreading behaviors of pendant and sessile drops was studied experimentally and numerically under the action of gravity force and surface tension. Bond number was considered to be a main factor of the influence on shape behaviors of liquid drops. This study was performed in the framework of an experimental investigation of drop behaviors in microgravity onboard a Chinese satellite in future. The experiments were carried out in the Drop Tower of Beijing, which could supply about 3.6?s of microgravity (free-fall) time. The surface shape change of liquid drops was investigated and the contact angle variety in sessile and pendant drops were measured from normal gravity to microgravity. A sharp decrease and oscillatory variation of the contact angle for both sessile and pendant drops were found with the sudden decrease of Bond number. The succedent comparison between experimental and numerical results suggests that Bond number has a significant influence on the drop contact angle. Additionally, the drop shapes and the bulk flows inside sessile and pendant drops were analyzed numerically, and it was found that the bulk flows could affect the free-surface shape of liquid drops apparently. Comparison of the moving velocity of contact line between sessile and pendant drops indicated that the pendant drops had a faster response to Bond number.     

Sessile Drop in Microgravity: Creation, Contact Angle and Interface

We present in this paper the results obtained from a parabolic flight campaign regarding the contact angle and the drop interface behavior of sessile drops created under terrestrial gravity (1g) or in microgravity (μg). This is a preliminary study before further investigations on sessile drops evaporation under microgravity. In this study, drops are created by the mean of a syringe pump by injection through the substrate. The created drops are recorded using a video camera to extract the drops contact angles. Three fluids have been used in this study : de-ionized water, HFE-7100 and FC-72 and two heating surfaces: aluminum and PTFE. The results obtained evidence the feasibility of sessile drop creation in microgravity even for low surface tension liquids (below 15 mN m^− 1) such as FC-72 and HFE-7100. We also evidence the contact angle behavior depending of the drop diameter and the gravity level. A second objective of this study is to analyze the drop interface shape in microgravity. The goal of the these experiments is to obtain reference data on the sessile drop behavior in microgravity for future experiments to be performed in an French-Chinese scientific instrument (IMPACHT).     

Sessile Drop Wettability in Normal and Reduced Gravity

This paper presents initial work performed to develop a database of contact angles of sessile drops in reduced gravity. Currently, there is no database of wettability of sessile drops in reduced gravity. The creation of such a database is imperative for continued investigations of heat and/or mass transfer in reduced gravity and future engineering designs. In this research, liquid drops of water and ethanol were created on aluminum and PTFE substrates. The formed drops were characterized by their dimensions including contact angle, wetted perimeter and droplet shape in both normal gravity and reduced gravity. The droplets were recorded during testing with high definition video and the images obtained digitally analyzed, post-test, to determine their characteristics as a function of the experimental parameters. The Queensland University of Technology (QUT) Drop Tower Facility was utilized for the reduced gravity experimentation. For droplets with diameters above their capillary length, the changes in drop dimensions and/or wettability was observed. The Young-Laplace equation was validated to accurately predict the contact angle in reduced gravity for small droplets, however it was not adequate to describe the contact angle for larger drops (above the drops associated capillary length).     

Modulating contact angle hysteresis to direct fluid droplets along a homogenous surface

The shape and motion of drops on surfaces is governed by the balance between the driving and the pinning forces. Here we demonstrate control over the motion of droplets on an inclined surface by exerting control over the contact angle hysteresis. The external modulation of contact angle hysteresis is achieved through a voltage-induced local molecular reorganization within the surface film at the solid-liquid interface. We show that tuning contact angle hysteresis alone is sufficient to direct and deform drops when subjected to a constant external driving force, here gravity, in the absence of a pre-defined surface energy gradient or pattern. We also show that the observed stretching and contraction of the drops mimic the motion of an inchworm. Such reversible manipulation of the pinning forces could be an attractive means to direct drops, especially with the dominance of surface forces at micro-/nanoscale.     

Stability of sessile and pendant liquid drops

The solution space of axisymmetric liquid drops attached to a horizontal plane is investigated, and the stability of hydrostatic shapes is assessed by a novel numerical linear stability analysis involving discrete perturbations. For a given contact angle and Bond number, multiple interfacial shapes exist with compact, lightbulb, hourglass, and more convoluted pearly shapes. It is found that more than one solution branch can be stable, and that negative curvature at the contact line of a pendant drop is not a prerequisite for instability. Numerical simulations based on the boundary-integral method for Stokes flow illustrate the process of unstable drop detachment. Unstable drops transform into elongated threads with a spherical head whose volume is determined by a Bond number expressing the significance of surface tension. A complementary investigation of the shape and stability of two-dimensional drops attached to a horizontal or inclined plane reveals that hydrostatic shapes are least stable in the inclined configuration and most stable in the pendant or sessile configuration.     

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.     

Experimental Investigation of Pendant and Sessile Drops in Microgravity

The experiments regarding the contact angle behavior of pendant and sessile evaporating drops were carried out in microgravity environment. All the experiments were performed in the Drop Tower of Beijing, which could supply about 3.6 s of microgravity (free-fall) time. In the experiments, firstly, drops were injected to create before microgravity. The wettability at different surfaces, contact angles dependance on the surface temperature, contact angle variety in sessile and pendant drops were measured. Different influence of the surface temperature on the contact angle of the drops were found for different substrates. To verify the feasibility of drops creation in microgravity and obtain effective techniques for the forthcoming satellite experiments, we tried to inject liquid to create bigger drop as soon as the drop entering microgravity condition. The contact angle behaviors during injection in microgravity were also obtained.     

Uniform Spread of High‐Speed Drops on Superhydrophobic Surface by Live‐Oligomeric Surfactant Jamming

Inkjet printing of water‐based inks on superhydrophobic surfaces is important in high‐resolution bioarray detection, chemical analysis, and high‐performance electronic circuits and devices. Obtaining uniform spreading of a drop on a superhydrophobic surface is still a challenge. Uniform round drop spreading and high‐resolution inkjet printing patterns are demonstrated on superhydrophobic surfaces without splash or rebound after high‐speed impacting by introducing live‐oligomeric surfactant adhesion. During impact, the live‐oligomeric surfactant molecules aggregate into dynamic, wormlike micelle networks, which jam at the solid–liquid interface by entangling with the surface micro/nanostructures to pin the contact line and jam at the spreading periphery to keep the uniform spreading lamellar shape. This efficient uniform spreading of high‐speed impact drops opens a promising avenue to control drop impact dynamics and achieve high‐resolution printing.     

Drop detachment and motion on fuel cell electrode materials

Liquid water is pushed through flow channels of fuel cells, where one surface is a porous carbon electrode made up of carbon fibers. Water drops grow on the fibrous carbon surface in the gas flow channel. The drops adhere to the superficial fiber surfaces but exhibit little penetration into the voids between the fibers. The fibrous surfaces are hydrophobic, but there is a substantial threshold force necessary to initiate water drop motion. Once the water drops begin to move, however, the adhesive force decreases and drops move with minimal friction, similar to motion on superhydrophobic materials. We report here studies of water wetting and water drop motion on typical porous carbon materials (carbon paper and carbon cloth) employed in fuel cells. The static coefficient of friction on these textured surfaces is comparable to that for smooth Teflon. But the dynamic coefficient of friction is several orders of magnitude smaller on the textured surfaces than on smooth Teflon. Carbon cloth displays a much smaller static contact angle hysteresis than carbon paper due to its two-scale roughness. The dynamic contact angle hysteresis for carbon paper is greatly reduced compared to the static contact angle hysteresis. Enhanced dynamic hydrophobicity is suggested to result from the extent to which a dynamic contact line can track topological heterogeneities of the liquid/solid interface.     

Contact Angle Singularity in 4He Crystals

Equilibrium shape of the interface between superfluid and crystalline ⁴He near the (0001) orientation is analyzed. We observe a singular dependence of the contact angle on the wall inclination with respect to the gravity. The energy of a step on the basal plane is measured. From the analysis of the meniscus profile the step-step interaction constant is estimated.      

Gravity Effect on the Axisymmetric Drop Spreading

The flattening (spreading) of the axisymmetrical drop on a plane horizontal surface under action of gravity force at zero tangential force (no shear at the gas–liquid interface) is investigated analytically and numerically. We determine the exact profile of compressed drop assuming the condition of drop volume conservation. 2D time dependant numerical model, based on a finite difference method, has been developed to describe the hydrodynamics inside the drop. The energy and Navier–Stokes equations are solved within the drop’s analytical profile. Effects of surface tension and thermocapillarity are taken into account. The effect of gravity has been studied to define main features of the drop dynamics. In calculations vector of gravitational acceleration is oriented perpendicularly to the surface, the Bond number is changed in the range from Bo = 0 to Bo = 151.6. Our results show that the gravity has a significant effect on the drop spreading.     

Impact of Marangoni effects on the apparent contact angle — a numerical investigation

The influence of thermocapillary stress on the shape of the gas-liquid phase boundary is investigated numerically. We consider the case of a cold liquid meniscus at a heated solid wall in the absence of gravity. An “apparent contact angle” is defined geometrically and the deviation of this apparent contact angle from the prescribed static contact angle due to thermocapillary convection is studied. We observe an enlarged apparent contact angle compared to the isothermal case. Since a fixed static contact angle is used in the computations, we emphasize that this effect does not depend on the specific model of a dynamic contact angle.     

A novel methodology to study shape and surface tension of drops in Electric Fields

A novel methodology is introduced that can be used to study the behavior of conducting drops in electrostatic fields, when gravity effects are negligible. This methodology, called Axisymmetric Drop Shape Analysis — Electric Field (ADSA-EF), generates numerical drop profiles in the electrostatic field, for a given surface tension. Then, it calculates the true value of the surface tension by matching the theoretical profiles with the shape of the experimental drops, with the surface tension as an adjustable parameter. ADSA-EF can be employed for simulating drop shapes in the electric field, detecting the effect of an electric field on liquid surface tensions, and measuring surface tensions in microgravity, where current drop-shape techniques are not applicable. The predicted drop shapes in the electric field were compared with experimental images, indicating good agreement. Preliminary experiments according to ADSA-EF methodology suggested that the surface tension of water increases by about one percent in the electric field.     

基于平衡原理的液滴接触角估计方法

基于液滴表面力的平衡原理推导了一种新的液滴表面曲线方程,通过提取图像上的样本点,以牛顿-拉夫逊法拟合曲线方程为基础来获取接触角的估计值,从而得到了一种基于平衡原理的液滴接触角估计方法。通过JGW-360A接触角测定仪采集实测图像,针对水滴与不同材料的接触场景进行了实验,采用Canny法获取液滴边缘曲线并提取采样点,计算出液滴表面接触角。将该算法与传统的影像分析法进行了比较,在大角度下与传统影像类方法相比估计值差别约为0.2°~0.3°,实验结果验证了算法的有效性。     

Wetting characteristics of oxygen-containing iron melts on refractory oxides

As part of refractory erosion studies, the wetting behaviour of molten iron containing varying amounts of oxygen on refractory oxides was investigated by the sessile drop method. The oxides investigated in the present work were alumina, silica and mullite. The reactions were followed in static as well as dynamic modes, under isothermal conditions, through contact angle measurements. Other parameters investigated in the present study were temperature and oxygen partial pressure. For all substrates, the contact angles started decreasing due to the lowering of the surface tension of iron, as oxygen at constant partial pressure, came into contact with the surface of the drop. At a critical level of oxygen in the metal drop, a reaction product started forming at the drop/substrate interface and at this stage the contact angle dropped suddenly. In all cases there was a tendency for the contact angle to increase after this minimum. In the alumina case, the iron drop moved away from the reaction site, once the product layer had been formed at the interface, probably due to the imbalance in the surface forces. In the case of SiO₂ and mullite, liquid slags were formed. The substrates were analysed through SEM and EDS. The reaction products identified were in agreement with thermodynamic predictions. In the case of SiO₂, deep erosions were formed along the periphery of the drops, probably due to Marangoni flow. The possible mechanisms of the reactions and their impact on refractory erosion are discussed in the light of the present experimental results.     

Flexural gravity wave scattering by a nearly vertical porous wall

Two-dimensional linear flexural gravity wave scattering by a nearly vertical porous wall is analyzed through a simplified perturbational analysis. A continuous semi-infinite ice sheet of uniform thickness is assumed to be floating over water of infinite depth. The ice sheet, with inclusion or exclusion of compressive stress, has either a free edge or a clamped edge at the porous wall. The first-order correction to the reflected flexural gravity wave amplitude is obtained by two different methods. The first method involves an application of Green’s theorem, and the second method involves a first kind integral equation. The integral equation method proves to be robust as it provides a complete solution in all cases of the problem, whereas the first method fails to produce the same when the ice sheet with a free edge is under compressive stress. The strain in the ice sheet and shear force along the ice sheet are computed and explained graphically for suitable parameters and a particular wall shape function.     

Effect of contact resistance on steady MHD flows through circular pipes having constant conductivity and finite wall thickness

The steady flow of viscous, electrically conducting liquids through circular pipes having finite wall thickness and conductivity under an applied uniform transverse magnetic field is considered. A uniform contact resistance at the solid/liquid interface is taken into account. An exact solution and its numerical calculations are presented.     

Iron Burning in Pressurised Oxygen Under Microgravity Conditions

An investigation of cylindrical iron rods burning in pressurised oxygen under microgravity conditions is presented. It has been shown that, under similar experimental conditions, the melting rate of a burning, cylindrical iron rod is higher in microgravity than in normal gravity by a factor of 1.8 ± 0.3. This paper presents microanalysis of quenched samples obtained in a microgravity environment in a 2.0 s duration drop tower facility in Brisbane, Australia. These images indicate that the solid/liquid interface is highly convex in reduced gravity, compared to the planar geometry typically observed in normal gravity, which increases the contact area between liquid and solid phases by a factor of 1.7 ± 0.1. Thus, there is good agreement between the proportional increase in solid/liquid interface surface area and melting rate in microgravity. This indicates that the cause of the increased melting rates for cylindrical iron rods burning in microgravity is altered interfacial geometry at the solid/liquid interface.     

MHD Effect on Interfacial Deformation of Thermocapillary Convection in Two-Layer System

Steady thermocapillary convection with deformable interface in a two-layer system is simulated by the second-order projection method combined with the level set method, in which the three-stage Runge–Kutta technique and second-order semi-implicit Crank–Nicholson technique are employed to temporally update the convective and diffusion terms, respectively. The level set approach is employed to implicitly capture the interface. The continuum surface force tension model is used to simulate the Marangoni effect. Simulations are conducted for both fixed angle and fixed points at the contact between the interface and the end walls. The numerical results show that, the interface bulges out near the hot wall and bulges in near the cold wall, due to the Marangoni effect. With Marangoni number increasing, the deformability of interface increases. The contact condition of interface with the end walls is important for the prediction of thermocapillary convection characteristics, and the contact points fixed condition is more close to real condition.     

Drop spreading and drifting on a spatially heterogeneous film: capturing variability with asymptotics and emulation

A liquid drop spreading over a thin heterogeneous precursor film (such as an inhaled droplet on the mucus-lined wall of a lung airway) will experience perturbations in shape and location as its advancing contact line encounters regions of low or high film viscosity. Prior work on spatially one-dimensional spreading over a precursor film having a random viscosity field (Xu and Jensen, Proc R Soc A 472:20160270, 2016) has demonstrated how viscosity fluctuations are swept into a narrow region behind the drop’s effective contact line, where they can impact drop dynamics. In this paper, we investigate two-dimensional drops, seeking to understand the relationship between the statistical properties of the precursor film and those of the spreading drop. Assuming the precursor film is much thinner than the drop and viscosity fluctuations are weak, we use asymptotic methods to derive explicit predictions for the mean and variance of drop area and the drop’s lateral drift. For larger film variability, we use Gaussian process emulation to estimate the variance of outcomes from a restricted set of simulations. Stochastic drift of the droplet is predicted to be the greatest when the initial drop diameter is comparable to the correlation length of viscosity fluctuations.