Water droplet freezing is a common phenomenon in our daily life. In both natural scenarios and industrial production, different surface inclinations bring distinctive deformation and freezing dynamics to frozen droplets. We explore the freezing of pendent and sessile droplets at different Bond number regimes. The effect of gravity on the droplet freezing process is analyzed by considering droplet morphology, freezing front dynamics, and freezing time. It is found that gravity can significantly influence droplet freezing processes via shaping the initial droplet, resulting in the flattening or elongation of pendent and sessile droplets, respectively. We show that the droplet initial geometry is the most important parameter and it completely controls the droplet freezing. Despite the significant difference in the initial droplet shape several remarkable similarities have been found for pendent and sessile droplets at small and large Bond numbers. The final height of a frozen droplet is found to be linearly proportional to its initial height. The time evolution of the ice-liquid-air contact line is found to reproduce the power-law $t^{0.5}$, but noticeably faster than the Stefan 1-D icing front propagation. As a consequence, the time to freeze a droplet is faster than predicted by the Stefan model and it is found to be dependent on the initial droplet height and base radius through a simple power-law.
Surface icing affects the safety and performance of numerous processes in technology. Previous studies mostly investigated freezing of individual droplets. The interaction among multiple droplets during freezing is investigated less, especially on nanotextured icephobic surfaces, despite its practical importance as water droplets never appear in isolation, but in groups. Here we show that freezing of a supercooled droplet leads to spontaneous self-heating and induces strong vaporization. The resulting, rapidly propagating vapor front causes immediate cascading freezing of neighboring supercool…
Understanding the dynamics during freezing of nanofluid droplets is of importance from a fundamental and practical viewpoint. While the freezing of a water droplet has been extensively studied, little information is available about the characteristics of freezing a nanofluid droplet. Here, we report unique shape changes observed during the freezing process of a nanofluid droplet. Instead of forming a pointy tip on the frozen deionized water droplet, we found that the top of a frozen nanofluid droplet exhibits a flat plateau shape and such plateau becomes larger with increasing nanoparticle con…
Polymer-Regulated Freezing of Water Droplets Revealed by Synchrotron X-ray Imaging and Raman Spectroscopy
Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）；Korea Polar Research Institute (KOPRI)（韩国极地研究所）；Pohang Accelerator Laboratory, Pohang University of Science and Technology (POSTECH)（浦项科技大学波项加速器实验室）；UNIST Research Center for Soft and Living Matter, Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院软体与生命物质研究中心）
We experimentally investigate the effect of freezing on the spreading of a water drop. Whenever a water drop impacts a cold surface, whose temperature is lower than 0°C, a thin layer of ice grows during the spreading. This freezing has a notable effect on the impact: at given Reynolds and Weber numbers, we show that lowering the surface temperature reduces the drop maximal extent. Using an analogy between this ice layer and the viscous boundary layer, which also grows during the spreading, we are able to model the effect of freezing as an effective viscosity. The scaling laws designed for visc…
Freezing or solidification of impacting droplets is omnipresent in nature and technology, be it a rain droplet falling on a supercooled surface, be it in inkjet printing where often molten wax is used, be it in added manufacturing or in metal production processes or in extreme ultraviolet lithography (EUV) for the chip production where molten tin is used to generate the EUV radiation. For many of these industrial applications, a detailed understanding of the solidification process is essential. Here, by adopting a totally new optical technique in the context of freezing, namely TIR (Total-Inte…
In this fluid dynamics video we show how a drop of water freezes into a singular shape when deposited on a cold surface. The process of solidification can be observed very clearly due to the change in refraction when water turns into ice. The drop remains approximately spherical during most of the process, with a freezing front moving upwards and smoothly following the interface. However, at the final stage of freezing, when the last cap of liquid turns into ice, a singular tip develops spontaneously. Interestingly, the sharp tip of the ice drop acts as a preferential site for deposition of wa…
A fluid droplet may exhibit self-propelled motion by modifying the wetting properties of the substrate. We propose a novel model for droplet propagation upon a terraced landscape of ordered layers formed as a result of surface freezing driven by the contact angle dependence on the terrace thickness. Simultaneous melting or freezing of the terrace edge results in a joint droplet-terrace motion. The model is tested numerically and compared to experimental observations on long-chain alkane system in the vicinity of the surface melting point.
A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperatur…
A drop of water that freezes from the outside-in presents an intriguing problem: the expansion of water upon freezing is incompatible with the self-confinement by a rigid ice shell. Using high-speed imaging we show that this conundrum is resolved through an intermittent fracturing of the brittle ice shell and cavitation in the enclosed liquid, culminating in an explosion of the partially frozen droplet. We propose a basic model to elucidate the interplay between a steady build-up of stresses and their fast release. The model reveals that for millimetric droplets the fragment velocities upon ex…
We have studied the splashing dynamics of water drops impacting granular layers. Depending on the drop kinetic energy, various shapes are observed for the resulting craters. Experimental parameters that have been considered are : the size of the millimetric droplets; the height of the free fall, ranging from 1.5 cm to 100 cm; and the diameter of the grains. As the drop is impacting the granular layer, energy is dissipated and a splash of grain occurs. Meanwhile, surface tension, inertia and viscosity compete, leading to strong deformations of the drop which depend on the experimental condition…
In this work a numerical model for two-dimensional axisymmetric continuous freezing by impingement of processed meat or similar products in food industry moving along a conveyor belt is presented. The model represents a more computationally efficient alternative to solve conjugate heat transfer between a fluid and a solid, accompanied by phase change in some constituents of the solid phase. In the model presented here it is assumed that the solid can be represented as an homogeneous medium, with its thermophysical properties depending on the temperature. The impingement freezing model is conce…
The effect of freezing on contact line motion is a scientific challenge in the understanding of the solidification of capillary flows. In this letter, we experimentally investigate the spreading and freezing of a water droplet on a cold substrate. We demonstrate that solidification stops the spreading because the ice crystals catch up with the advancing contact line. Indeed, we observe the formation and growth of ice crystals along the substrate during the drop spreading, and show that their velocity equals the contact line velocity when the drop stops. Modelling the growth of the crystals, we…
In a recent paper [S. Khrapak, Molecules {\bf 25}, 3498 (2000)] the longitudinal and transverse sound velocities of conventional Lennard-Jones systems at the liquid-solid coexistence were calculated. It was shown that the sound velocities remain almost invariant along the liquid-solid coexistence boundary lines and that their magnitudes are comparable with those of repulsive soft sphere and hard sphere models at the fluid-solid phase transition. This implies that attraction does not affect the magnitude of sound velocities at the fluid-solid phase transition. This paper provides further eviden…
This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1D solidification setup, using different liquids and substrates. In a second part, we show that during the actual drop spreading, a thin layer of ice develops between the water and the substrate, and pins the contact line …
We present a simple experiment that demonstrates how a water drop hanging from a Plexiglas surface (pendant drop) experiences a lateral retention force that is comparable to, and in some cases larger than, the lateral retention force on a drop resting on top of the surface (sessile drop). The experiment also affords a simple demonstration of the Coriolis effect in two dimensions.
The behavior of a magnetic fluid drop lying on a solid horizontal surface and surrounded by a nonmagnetic liquid under the action of a uniform magnetic field which is rotating in a vertical plane with low frequency (of the order of 1 Hz) has been investigated experimentally. Shape deformation and translatory motion of the drop were observed and studied. The drop translation velocity for different field amplitudes and field frequencies has been measured.
Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer…
Gravitational settling of a droplet in air onto a soft substrate is a ubiquitous event relevant to many natural processes and engineering applications. We study this phenomenon by developing a three-phase lubrication model of droplet settling onto a solid substrate coated by a thin soft layer represented by a viscous film, an elastic compressible layer and an elastic sheet supported by a viscous film. By combining scaling analysis, analytical methods, and numerical simulations we elucidate how the resulting droplet dynamics is affected by the nature of the soft layer. We show that these soft l…
A diffuse-interface model for N-phase flows with liquid-solid phase change
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology（华中科技大学工程建模与科学计算湖北省重点实验室）；The State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology（华中科技大学智能装备与技术国家重点实验室）
The impact of nanometer sized drops on solid surfaces is studied using molecular dynamics simulations. Equilibrated floating drops consisting of short chains of Lennard-Jones liquids with adjustable volatility are directed normally onto an atomistic solid surface where they are observed to bounce, stick, splash or disintegrate, depending on the initial velocity and the nature of the materials involved. Drops impacting at low velocity bounce from non-wetting surfaces but stick and subsequently spread slowly on wetting surfaces. Higher velocity impacts produce an prompt splash followed by disint…
The dynamic frictional force between solid surfaces in relative motion differs from the static force needed to initiate motion, but this distinction is not usually thought to occur for liquid drops moving on a solid. Recent experiments [Gao, et al., Nature Phys. {\bf 114}, 191 (2018)] have challenged this view, and claim to observe an analog of solid-on-solid friction for sliding drops. We use molecular dynamic simulations to investigate the forces that moving liquids exert on solids in several situations. In contrast to the indirect techniques required in laboratory experiments, the forces in…
We investigate freely expanding sheets formed by ultrasoft gel beads, and liquid and viscoelastic drops, produced by the impact of the bead or drop on a silicon wafer covered with a thin layer of liquid nitrogen that suppresses viscous dissipation thanks to an inverse Leidenfrost effect. Our experiments show a unified behaviour for the impact dynamics that holds for solids, liquids, and viscoelastic fluids and that we rationalize by properly taking into account elastocapillary effects. In this framework, the classical impact dynamics of solids and liquids as far as viscous dissipation is negli…
We report an idealized numerical study of a melting and freezing solid adjacent to a turbulent, buoyancy-affected shear flow, in order to improve our understanding of topography generation by phase changes in the environment. We use the phase-field method to dynamically couple the heat equation for the solid with the Navier-Stokes equations for the fluid. We investigate the evolution of an initially-flat and horizontal solid boundary overlying a pressure-driven turbulent flow. We assume a linear equation of state for the fluid and change the sign of the thermal expansion coefficient, such that…
When a droplet is brought in contact with an undercooled surface, it wets the substrate and solidifies at the same time. The interplay between the phase transition effects and the contact-line motion, leading to its arrest, remains poorly understood. Here we reveal the early solidification patterns and dynamics of spreading hexadecane droplets. Total internal reflection (TIR) imaging is employed to temporally and spatially resolve the early solidification behaviour. With this, we determine the conditions leading to the contact-line arrest. We quantify the overall nucleation behaviour, \textit{…
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…
Understanding flow patterns and coupled transport phenomena during evaporation of droplets loaded with colloidal particles is central to design technical applications such as organizing proteins/DNA on a solid surface. We review recent reports on evaporating sessile droplets of colloidal suspensions on a solid surface. Starting from the classical mechanism of formation of a ring-like deposit, we discuss the influence of several problem parameters. Notably, thermal or solutal Marangoni effect, particle size, particle concentration, particle shape, substrate wettability, pH of the suspension etc…
The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$, and the ratio of surface tension to elastic modulus $γ/E$. We show that the contact angles undergo two transitions upon changing the substrates from rigid to soft. The microscopic wetting angles deviate from Young's law when $γ/Ea \gg 1$, while the apparent macroscopic angle only changes in the very soft limit $γ/ER \gg 1$. The el…
A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a pinned contact line. The Navier-Stokes equations in cylindrical coordinates were solved inside the droplet. Galerkin weight residual approach and velocity pressure formulation was used to discretise the governing equations. Six node triangular mesh and quadratic shape functions were used to obtain higher accuracy solutions. Radial velocity profiles in axial…
Drop-surface interaction is predominant in nature as well as in many industrial applications. Freezing rain is the frequent origin of ice accretion on surfaces. Superhydrophobic surfaces show potential for anti-icing applications as they exhibit complete drop rebounce. Nonetheless, drop shedding has to take place before freezing for effective functioning. Recently, introducing a macro-ridge to break the hydrodynamic symmetry, has been shown to reduce the residence time on the surface of a bouncing drop. However, for a practical application the surface must be decorated with a series of ridges …
Phase change under reduced environmental pressures is key to understanding liquid discharge and propulsion processes for aerospace applications. A representative case is the sessile water droplets exposed to high vacuum, which experience complex phase change and transport phenomena that behave so differently than that under the atmosphere. Here, we demonstrate a previously unexplored aspect of the mechanism governing icing droplet self-launching from superhydrophobic surfaces when exposed to low pressures (~100 Pa). In contrast to the previously reported recalescence-induced local overpressure…
Solid state convection can take place in the rocky or icy mantles of planetary objects and these mantles can be surrounded above or below or both by molten layers of similar composition. A flow toward the interface can proceed through it by changing phase. This behaviour is modeled by a boundary condition taking into account the competition between viscous stress in the solid, that builds topography of the interface with a timescale $τ_η$, and convective transfer of the latent heat in the liquid from places of the boundary where freezing occurs to places of melting, which acts to erase topogra…
We present a fluid dynamics video which illustrates a kinetic-dominated phase change just prior to solidification inception for a static drop situated on a cold solid substrate. This metastable stage initiated from solid-vapor-liquid interface and propagates through drop volume at much faster speeds than solidification growth stage.
We predict and analyze the drying time of respiratory droplets from a COVID-19 infected subject, which is a crucial time to infect another subject. The drying of the droplet is predicted by diffusion-limited evaporation model for a sessile droplet placed on a partially-wetted surface with a pinned contact line. The variation of droplet volume, contact angle, ambient temperature, and humidity are considered. We analyze the chances of the survival of the viruses present in the droplet, based on the lifetime of the droplets in several conditions, and find that the chances of survival of the virus…
Capillary filling dynamics of liquid n-tetracosane (n-C24H50) in a network of cylindrical pores with 7 and 10 nm mean diameter in monolithic silica glass (Vycor) exhibit an abrupt temperature-slope change at Ts=54 deg C, ~4 deg C above bulk and ~16 deg C, 8 deg C, respectively, above pore freezing. It can be traced to a sudden inversion of the surface tension's T slope, and thus to a decrease in surface entropy at the advancing pore menisci, characteristic of the formation of a single solid monolayer of rectified molecules, known as surface freezing from macroscopic, quiescent tetracosane melt…
This paper investigates the properties of a three dimensional shear flow overpassing a hemispherical droplet resting on a plane wall. The exact solution is computed as a function of the viscosity ratio between the droplet and the surrounding fluid and generalizes the solution for the hemispherical no-slip bump given in an earlier paper by Price (1985). Several expressions including the torque and the force acting on the drop will be considered as well as the importance of the deformations on the surface for small Capillary numbers.
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations describing the drop shapes are found in both cases. A case of good wetting is considered to determine the profiles of the sessile and inclined drops. The generalization of the boundary conditions for the contact angle hysteresis of the drop on an inclined surface is discussed. The limit of the inclination angle at which the drop begins to run down the inclined plane …
