Phase field theory is widely used to model multi-phase flows. A drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy. In this paper, the spontaneous behaviour of a drop on a flat surface is investigated. It is found that there exists a critical radius dependent on the contact angle, the domain size and the interface width, below which the droplet will eventually disappear. In particular, the critical radius can be very large when the contact angle is hydrophilic. The theoretical prediction of the critical radius is verified numerically by simulating a drop on a surface with various contact angles, the domain sizes and the interface widths.
Conventional wetting theories on rough surfaces with Wenzel, Cassie-Baxter, and Penetrate modes suggest the possibility of tuning the contact angle by adjusting the surface texture. Despite decades of intensive study, there are still many experimental results that are not well understood because conventional wetting theory, which assume an infinite droplet size, has been used to explain measurements of finite-sized droplets. In this study, we suggest a wetting theory that is applicable to any droplet size based on the free energy landscape analysis of various wetting modes of finite-sized drop…
Soft surfaces impacted by liquid droplets trap more air underneath than their rigid counterpart. The extended lifetime of the air film not only facilitates bouncing behaviours of the impacting droplets but also increases the possibility of an interaction between the air film itself and the air cavity formed inside the droplets by capillary waves. Such interaction may cause rupture of the trapped air film by a so-called dimple inversion phenomenon and suppress bouncing. In this work, we systematically investigate the relation between air cavity collapse and air film rupture for water droplets i…
The levitation of a volatile droplet on a highly superheated surface is known as the Leidenfrost effect. Wetting state during transition from full wetting of a surface by a droplet at room temperature to Leidenfrost bouncing, i.e., zero-wetting at high superheating, is not fully understood. Here, visualizations of droplet thermal and wetting footprint in the Leidenfrost transition state are presented using two optical techniques: mid-infrared thermography and wetting sensitive total internal reflection imaging under carefully selected experimental conditions, impact Weber number < 10 and dropl…
Although realizing wetting transitions of droplets spontaneously on solid rough surfaces is quite challenging, it is becoming a key research topic in many practical applications which require highly efficient removal of liquid. We report wetting transitions of condensed droplets occurring spontaneously on pillared surfaces with two-tier roughness owing to excellent superhydrophobicity. The phenomenon results from further decreased Laplace pressure on the top side of the individual droplet when its size becomes comparable to the scale of the micropillars, which leads to a surprising robust spon…
We demonstrate droplet manipulation using electric signals to induce the liquid to wet or dewet on a hydrophilic conductive substrate in the air without adding layers. In this phenomenon, the contact angle changes more than 15° or -20° by using the ionic surfactant mediated droplets, with only \pm3 volts of the actuation voltage.
We simulate gravity driven dynamics of partially wetting droplets moving along a fibre using the lattice Boltzmann method. For the so-called clamshell morphology, we find three possible dynamic regimes upon varying the droplet Bond number and the fibre radius: compact droplet, droplet breakup and droplet oscillation. For small Bond numbers, in the compact droplet regime, the droplet reaches a steady state and its velocity scales linearly with the driving body force. A similar scaling law can also be observed for the barrel morphology. For higher Bond numbers, in the droplet breakup regime, sat…
A mesh-dependent relation for the slip number in the Navier-slip with friction boundary condition for computations of impinging droplets with sharp interface methods is proposed. The relation is obtained as a function of Reynolds number, Weber number and the mesh size. The proposed relation is validated for several test cases by comparing the numerically obtained wetting diameter with the experimental results. Further, the computationally obtained maximum wetting diameter using the proposed slip relation is verified with the theoretical predictions. The relative error between the computational…
The impact of droplets on solids or weakly-deformable surfaces can lead to non-wetting outcomes, depending on the control parameters. Here, we perform experiments and develop a simple model to understand the impact dynamics by varying three important drop parameters: the Ohnesorge number $\mathcal{O}h$, the Bond number $\mathcal{B}o$ and the Weber number $\mathcal{W}e$. The model suggests that the droplet dynamics is captured by only two non-dimensional groups, namely $\ \mathcal{O}h$ and $ξ= \mathcal{B}o/\sqrt{\mathcal{W}e}$. For $ξ\ll 1$, the droplet dynamics is fully dominated by $\mathcal{…
To understand the non-equilibrium relaxation dynamics of a liquid droplet on a switchable substrate the interplay of different length- and time-scales needs to be understood. We present a method to map the microscopic information, resulting from a molecular dynamics simulation, to a mesoscopic scale, reflected by a thin film model. After a discussion of the mapping procedure we first analyze the relaxation of a liquid droplet upon switching the wettability of the substrate. Further, we show that a nearly identical mapping procedure can be used for the description of two coalescing droplets. Wi…
Microstructured surfaces that control the direction of liquid transport are not only ubiquitous in nature, but they are also central to technological processes such as fog/water harvesting, oil-water separation, and surface lubrication. However, a fundamental understanding of the initial wetting dynamics of liquids spreading on such surfaces is lacking. Here, we show that three regimes govern microstructured surface wetting on short time scales: spread, stick, and contact line leaping. The latter involves establishing a new contact line downstream of the wetting front as the liquid leaps over …
The classical wetting models, such as the Wenzel and Cassie-Baxter have been extensively used to quantify the wettability of laser-textured surfaces. However, these models do not provide any description of the corresponding droplet dynamics. In this work, we propose a detailed continuum-level modelling to study the wetting dynamics of a water droplet on Ti-6Al-4V alloy. The calculations are performed for flat surfaces and surfaces with various reliefs. The calculated evolutions of the droplet spreading parameter for flat surfaces, surfaces with triangular reliefs and one with two different per…
We present a hybrid microtextured surface with heterogeneous hydrophilic-hydrophobic regions for condensing water vapor while maintaining anti-wetting behavior. Fluid dynamics videos are shown demonstrating the difference between condensation on a homogeneous hydrophobic structure and the same structure with hybrid wetting regions.
An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier--Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surfactant-dependent surface tension and dynamic cont…
The superhydrophobic leaves of a lotus plant and other natural surfaces with self-cleaning function have been studied intensively for the development of artificial biomimetic surfaces. Surface roughness generated by hierarchical structures is a crucial property required for superhydrophobicity and self-cleaning. Here, we demonstrate a novel self-cleaning mechanism of textured surfaces attributed to a spontaneous coalescence-induced wetting transition. We focus on the wetting transition as it represents a new mechanism, which can explain why droplets on rough surfaces are able to change from th…
Cassie-Wenzel transition induced by localized freezing after droplet impact on supercooled micro-patterned surfaces
State Key Laboratory of Engines, Tianjin University（天津大学内燃机国家重点实验室）；National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, Huazhong University of Science and Technology（华中科技大学引力中心、教育部物理量测量重点实验室）；National Industry-Education Platform of Energy Storage, Tianjin University（天津大学国家储能产教融合平台）
A liquid drop impacting a dry solid surface with sufficient kinetic energy will splash, breaking apart into numerous secondary droplets. This phenomenon shows many similarities to forced wetting, including the entrainment of air at the contact line. Because of these similarities and the fact that forced wetting has been shown to depend on the wetting properties of the surface, existing theories predict splashing to depend on wetting properties as well. However, using high-speed interference imaging we observe that at high capillary numbers wetting properties have no effect on splashing for var…
We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving, spreading droplet. The model describes well the physics of droplet spreading -- including Tanner's Law for the evolution of the contact line. The model can be configured to describe complete wetting or partial wetting, and we explore both cases numerically. In the case of partial wetting, the model also admits analytical solutions for the droplet profile, whic…
Surface wettability has a huge influence on its functional properties. For example, to minimize smudging, surfaces should be able to repel oil droplets. To quantify surface wettability, the most common approach is to measure the contact angles of a liquid droplet on the surface. While well-established and relatively easy to perform, contact angle measurements are crude and imprecise; moreover, they cannot spatially resolve surface heterogeneities that can contribute to surface fouling. To address these shortcomings, we report on using an Atomic Force Microscopy (AFM) technique to quantitativel…
Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the cont…
Directed motion of liquid droplets is of considerable importance in various industrial processes. Despite extensive advances in this field of research, our understanding and the ability to control droplet dynamics at high temperature remain limited, in part due to the emergence of complex wetting states intertwined by the phase change process at the triple-phase interfaces. Here we show that two concurrent wetting states (Leidenfrost and contact boiling) can be manifested in a single droplet above its boiling point rectified by the presence of asymmetric textures. The breaking of the wetting s…
A drop impacting on a solid surface deforms before the liquid makes contact with the surface. We directly measure the time evolution of the air layer profile under the droplet using high-speed color interferometry, obtaining the air layer thickness before and during the wetting process. Based on the time evolution of the extracted profiles obtained at multiple times, we measure the velocity of air exiting from the gap between the liquid and the solid, and account for the wetting mechanism and bubble entrapment. The present work offers a tool to accurately measure the air layer profile and quan…
Anisotropically wetting substrates enable useful control of droplet behavior across a range of applications. Usually, these involve chemically or physically patterning the substrate surface, or applying gradients in properties like temperature or electrical field. Here, we show that a flat, stretched, uniform soft substrate also exhibits asymmetric wetting, both in terms of how droplets slide and in their static shape. Droplet dynamics are strongly affected by stretch: glycerol droplets on silicone substrates with a 23\% stretch slide 67\% faster in the direction parallel to the applied stretc…
Modelling wetting-bouncing transitions of droplet impact on random rough surfaces
State Key Laboratory of Mesoscience and Engineering, Institute of Process Engineering, Chinese Academy of Sciences（中国科学院过程工程研究所介科学工程国家重点实验室）；School of Civil Engineering, University of Sydney（悉尼大学土木工程学院）；School of Chemical Engineering, University of Chinese Academy of Sciences（中国科学院大学化学工程学院）
Young's law fails on soft solid and liquid substrates where there are substantial deformations near the contact line. On liquid substrates, this is captured by Neumann's classic analysis, which provides a geometrical construction for minimising the interfacial free energy. On soft solids, the total free energy includes an additional contribution from elasticity. A linear-elastic model incorporating an out-of-plane restoring force due to solid surface tension was recently shown to accurately predict the equilibrium shape of a thin elastic film due to a large sessile droplet. Here, we extend thi…
The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to measure the temperature at the solid-liquid interface, with a time and space resolution of 100 μs and 20 μm, respectively. Isopropanol droplets with micro- and nanoliter volumes are considered. A finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well…
The directional movement and rebound behaviours of two droplets simultaneously impacting a designed flat surface with wettability difference is investigated based on the three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model. The effects of several factors, such as wettability difference, Weber number and droplet spacing on the directional movement and rebound behaviours are investigated in detail. The numerical results show that the unbalanced Young 's force caused by the wetting difference will cause the droplets to rebound or migrate laterally toward to the side wit…
This paper reports the dynamic wetting behavior and heat transfer characteristics for impinging droplets on heated bi-phobic surfaces (superhydrophobic matrix with hydrophobic spots). A non-patterned superhydrophobic and a sticky hydrophobic surface acted as control wettability surfaces. As expected, differences in wetting and heat transfer dynamics were noticeable for all surfaces, with the most pronounced variation during the receding phase. During spreading, inertia from the impact dominated the droplet dynamics and heat transfer was dominated by convection at the contact line and internal …
We present high speed video of Cassie-Baxter to Wenzel drop transition during gentle deposition of droplets where the modest amount of energy is channeled via rapid deceleration into a high water hammer pressure.
We investigate the impact velocity beyond which the ejection of smaller droplets from the main droplet (splashing) occurs for droplets impacting a smooth surface. We examine its dependence on the surface wetting properties and droplet surface tension. We show that the splashing velocity is independent of the wetting properties of the surface, but increases roughly linearly with increasing surface tension of the liquid. A preexisting splashing model is considered that predicts the splashing velocity by incorporating the air viscosity. The model is consistent with our data, but the calculation i…
Place a droplet of mineral oil on water and the oil will spread to cover the water surface in a thin film -- a phenomenon familiar to many, owing to the rainbow-faced puddles left behind leaking buses on rainy days. In this paper we study the everted problem: an aqueous droplet deposited onto a deep layer of silicone oil. As it is energetically favourable for the oil phase to spread to cover the droplet surface completely, the droplet is ultimately engulfed in the oil layer. We present a detailed study of engulfment dynamics, from the instant the droplet first impacts the oil surface until it …
We study the flow close to an advancing contact line in the limit of small capillary number. To take into account wetting effects, both long and short-ranged contributions to the disjoining pressure are taken into account. In front of the contact line, there is a microscopic film corresponding to a minimum of the interaction potential. We compute the parameters of the contact line solution relevant to the matching to a macroscopic problem, for example a spreading droplet. The result closely resembles previous results obtained with a slip model.
There is a huge interest in developing super-repellent surfaces for anti-fouling and heat transfer applications. To characterize the wetting properties of such surfaces, the most common approach is to place a millimetric-sized droplet and measure its contact angles. The adhesion and friction forces can then be indirectly inferred from the Furmidge's relation. While easy to implement, contact angle measurements are semi-quantitative and cannot resolve wetting variations on a surface. Here, we attach a micrometric-sized droplet to an Atomic Force Microscope cantilever to directly measure adhesio…
On the hydrodynamic behaviour of the immersed boundary -- lattice Boltzmann method for wetting problems
The Cyprus Institute（塞浦路斯研究所）；Tor Vergata University of Rome（罗马托维塔大学）；Télécom Paris, IP Paris（巴黎电信学院，巴黎理工学院）；CNR - Istituto per le Applicazioni del Calcolo（意大利国家研究委员会计算应用研究所）；Inria and LIX (École Polytechnique), IP Paris（法国国家信息与自动化研究所与LIX实验室（巴黎综合理工学院），巴黎理工学院）；University of Cyprus（塞浦路斯大学）
The wetting properties of immiscible two-phase systems are crucial in a wide range of applications, from lab-on-a-chip devices to field-scale oil recovery. It has long been known that effective wetting properties can be altered by the application of an electric field; a phenomenon coined as electrowetting. Here, we consider theoretically and numerically a single droplet sitting on an (insulated) conductor, i.e., within a capacitor. The droplet consists of a pure phase without solutes, while the surrounding fluid contains a symmetric monovalent electrolyte, and the interface between them is imp…
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs
The University of Western Ontario（西安大略大学）；Cold Spring Harbor Laboratory（冷泉港实验室）；Brown University（布朗大学）；University of Maryland（马里兰大学）；Clemson University（克莱姆森大学）；US Army Research Laboratory（美国陆军研究实验室）
We consider the flotation of deformable, non-wetting drops on a liquid interface. We consider the deflection of both the liquid interface and the droplet itself in response to the buoyancy forces, density difference and the various surface tensions within the system. Our results suggest new insight into a range of phenomena in which such drops occur, including Leidenfrost droplets and floating liquid marbles. In particular, we show that the floating state of liquid marbles is very sensitive to the tension of the particle-covered interface and suggest that this sensitivity may make such experim…
We experimentally investigate impact dynamics of a microliter water droplet on a hydrophobic microgrooved surface. The surface is fabricated using photolithography and high-speed visualization is employed to record the time-varying droplet shapes in transverse as well as longitudinal direction. The effect of the pitch of the grooved surface and Weber number on droplet dynamics and impact outcome are studied. At low pitch and Weber number, the maximum droplet spreading is found to be greater in the longitudinal direction than the transverse direction to the grooves. The preferential spreading i…
Universal mapping of drop impact spreading from wetting to Leidenfrost regimes
Institute of Thermal Science and Power Systems, School of Energy Engineering, Zhejiang University（浙江大学能源工程学院热科学和动力系统工程研究所）；Department of Mechanical and Aerospace Engineering, Princeton University（普林斯顿大学机械与航空航天工程系）；State Key Laboratory of Clean Energy Utilization, Zhejiang University（浙江大学清洁能源利用国家重点实验室）
The interplay between phase separation and wetting of multicomponent mixtures is ubiquitous in nature and technology and recently gained significant attention across scientific disciplines, due to the discovery of biomolecular condensates. It is well understood that sessile droplets, undergoing phase separation in a static wetting configuration, exhibit microdroplet nucleation at their contact lines, forming an oil ring during later stages. However, very little is known about the dynamic counterpart, when phase separation occurs in a non-equilibrium wetting configuration, i.e., spreading dropl…
