Cold Solid Surface Research Articles

Numerical simulations of droplets impacting on a cold solid surface

Numerical simulations of droplets impacting on a cold solid surface

Influence of gravity on the freezing dynamics of drops on a solid surface

The influence of gravity on water droplet freezing on a cold solid surface has been investigated in this study. Experimental results over a range of Bond numbers, for both pendent and sessile droplets, show that gravity can significantly influence the freezing processes via shaping the initial droplet. Despite the significant difference in the initial droplet shape, some 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 proportional to its initial height.

Estimating the volume of frozen water droplets on a cold surface during the phase change with thermal image processing

In this paper, a new technique to estimate a frozen water droplet’s volume on a cold solid surface is presented, based on the contact angle and thermal images. The factors that can vary the contact angle, such as the temperature, surface roughness, and droplet size, are considered in the study. This technique can detect and obtain the volume of a single or a group of frozen droplets as soon as they are directly deposited on a cold hydrophilic surface and during the phase change from water to ice. The contact angle is pre-estimated, and the equivalent diameter is extracted from droplet's thermal image using image processing. From information on the contact angle and diameter of the deposited frozen droplet, the volume of the frozen droplet can be predicted. The evaluations show there is an average overestimation in droplets’ volumes of about 19%.

Effects of surface subcooling on the spreading dynamics of an impact water droplet

Spontaneous spreading of a liquid droplet upon a cold solid surface is ubiquitous in nature as well as critical to many industrial technologies, while the mechanism of which still remains elusive. The role of surface subcooling in a water droplet spreading behavior upon impacting on a smooth silicon surface has been experimentally investigated. Under the subcooling condition of the substrate, in the low Weber number region, the non-dimensional maximum spreading diameter decreases with the surface subcooling due to a larger viscosity dissipation and higher surface tension. However, in the case of a high Weber number, the maximum spreading factor first descends and then increases with the increasing surface subcooling. This non-monotonic tendency is attributed to the competition between the increased maximum fingering length and the reduced maximum interior spreading diameter with an increase of the surface subcooling. A sufficiently large Weber number is the prerequisite for forming fingering patterns, and a high subcooling reinforces them due to the enhanced deceleration caused by a larger surface tension and viscosity. The time at maximum spreading barely changes with the impact velocity and slightly decreases with the surface subcooling depending on the droplet size. An improved correlation of the time at maximum spreading as a function of the maximum spreading factor, droplet size, impact velocity, and surface subcooling is proposed.

Active control of the freezing process of a ferrofluid droplet with magnetic fields

Most existing studies of droplet freezing on cold solid surfaces focus on the use of different surface wettability and roughness which may be considered as passive methods. Here we report an active method using an applied magnetic field to control the deformation and freezing process of a sessile ferrofluid droplet on a cold surface. By changing the direction and magnitude of the magnetic field, we can elongate or squeeze the shape of ferrofluid droplets. Consequently, the droplet freezing time can be extended or shortened under the magnetic lift or squeezing conditions, respectively. Additionally, we use the modified Young-Laplace equation with consideration of an additional magnetic force effect to analyze the shape variation of a ferrofluid droplet with magnetic field, and also present a scaling analysis for the freezing time.

CO2 wetting on pillar-nanostructured substrates

CO2 capture by dropwise CO2 condensation on cold solid surfaces is a promising technology. Understanding the role of the nanoscale surface and topographical features of CO2 droplet wetting characteristics is of importance for CO2 capture by this technology, but this remains unexplored as of yet. Here, using large-scale molecular dynamics (MD) simulations, the contact angle and wetting behaviors of CO2 droplets on pillar-structured Cu-like surfaces are investigated for the first time. Dynamic wetting simulations show that, by changing the strength of the solid–liquid attraction a smooth Cu-like surface offers a transition from CO2-philic to CO2-phobic. By periodically pillared roughening of the Cu-like surfaces, however, a higher contact angle and a smaller spreading exponent of a liquid CO2 droplet are realized. Particularly, a critical crossover of CO2-philic to CO2-phobic can appear. The wetting of the pillared surfaces by a liquid CO2 droplet proceeds non-uniformly. A liquid CO2 droplet is capable of exhibiting a transition from the Cassie state to the Wenzel state with increasing increasing inter-pillar distance, and increasing pillar width. The wetting morphologies of the metastable Wenzel state of a CO2 droplet are very different from each other. The findings will inform the ongoing design of CO2-phobic solid surfaces for practical dropwise condensation-based CO2 capture applications.

Solidification dynamics of an impacted drop

This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In the first part, we establish a one-dimensional (1-D) solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamics of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1-D solidification set-up, using different liquids and substrates. In the 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 at its edge when the drop reaches its maximal diameter. The liquid film then remains still on the ice and keeps freezing. This configuration lasts until the contact line eventually unpins and the liquid film retracts on the ice. We measure and interpret this crucial time of freezing during which the main ice layer is built. Finally, we compare our 1-D model prediction to the thickness of this ice pancake and we find a very good agreement. This allows us to provide a general expression for the frozen drop’s main thickness, using the drop’s impact and liquid parameters.

A multicomponent multiphase enthalpy-based lattice Boltzmann method for droplet solidification on cold surface with different wettability

In this paper, a liquid droplet solidification contacting cold solid surface is modeled by a novel multicomponent multiphase enthalpy-based lattice Boltzmann method (LBM). The freezing process of liquid droplet coupled with thermal and mass transfer on cold flat surface with different wettability (θ = 160°, 135°, 60°, 20°) is investigated in detail. The solid volume fraction of droplet solidification with Fourier number are shown under different contact angles. The simulation results show that the solidification time for droplet contacting on a hydrophilic surface is much smaller than that of hydrophobic surface when liquid droplet shares the same initial radius.

Experimental and numerical study on the impact and freezing process of a water droplet on a cold surface

Ice accretion on cold solid surfaces presents hazards to a broad range of applications. It is quite essential to understand the dynamic and freezing mechanism of water droplets on a cold solid substrate for the prevention of ice accretion. In this study, the impact and freezing process of water droplets was studied experimentally and numerically. The effects of substrate temperature on the whole processes were investigated through changing the surface temperature from room temperature 25 °C to −30 °C. The results showed that the decrease of surface temperature led to the decrease of retraction rate, equilibrium droplet height after oscillation, freezing delay time and freezing time, while increased the final contact area due to the lower viscous dissipation energy. Also, a numerical model was developed to investigate the impact and freezing process of water droplets on an ultra-cold surface (−100 °C to −40 °C). The predicted droplet impact morphology, dynamic characteristics (spreading factor) and the propagation of freezing front were compared with experimental results, which exhibited good agreements. The numerical results suggested that the final contact area decreased slightly with the drastic decrease in surface temperature when the surface temperature is below −40 °C. Moreover, the influence of surface temperature on freezing front propagation and freezing time were analyzed in detail from the numerical results.

Deformation and breakup of a pendant drop with solidification

This paper presents a numerical simulation of deformation and breakup of a solidifying liquid drop pendant from a cold solid surface by an axisymmetric front-tracking method combined with an interpolation technique for enforcing the no-slip velocity boundary at the solid–fluid interface. Many dimensionless parameters such as the Prandtl number Pr, the Stefan number St, the Rayleigh number Ra, the Ohnesorge number Oh and the Bond number Bo are varied to reveal their effects on the process. Numerical results show that depending on the flow conditions, the liquid drop can break up while solidifying. Starting from non-breakup, increasing Bo (from 1.0 to 3.5) or Pr (from 0.01 to 3.16) causes the solidifying drop to break up into liquid drops that fall away from the solid surface. The transition from non-breakup to breakup also appears when decreasing St from 1.0 to 0.01, Ra from 1000 to 50, or Oh from 0.316 to 0.01. In addition, the effects of these parameters on the solidification time and the height of the solidified products are investigated. Moreover, the effects of volume change (in terms of the solid-to-liquid density ratio) upon solidification and the tri-junction (in terms of the growth angle) are introduced. We also present a phase diagram of Bo versus St that shows the region of the non-breakup-to-breakup transition.

Molecular dynamics simulation of freezing process of water droplets impinging on cold surface

The freezing of water droplet is a ubiquitous phenomenon in nature. Although the freezing process of water droplet impacting on cold surfaces is widely observed on a macroscopic scale, the study of freezing process on a micro-scale is still deficient, and it is definitely difficult to study micro-droplets and nano-droplets using experimental methods due to the obstacles in both generation and observation. For these reasons, simulation methods using molecular dynamics (MD) have been proposed to study micro-droplets and nano-droplets, as molecular dynamics can trace each atom, count up the collective behavior of a group of atoms and describe the detail interaction between atoms. In this paper, a three-dimensional model is established by molecular dynamics simulation to study the freezing process of water droplets impinging on a cold solid surface on a nanoscale. We select the micro-canonical ensemble (NVE) as a statistical system and the TIP4P/ice model as a potential energy function to simulate oxygen atoms, hydrogen atoms and water molecules. The LJ/126 model is used to simulate the interaction between water molecules and solid atoms. Different wettability walls are simulated by adjusting the potential energy parameters. For all the simulations, the velocity-rescale method is used to keep the temperature constant and the Verlet algorithm is adopted to solve the Newton equations. In the velocity-rescale method, the temperature is calculated by using the profile-unbiased thermostat. The freezing process inside the water droplet is determined by the temperature distribution of water molecules along the vertical direction, which is more concise than by the location coordinates of the microscopic atoms. Through the numerical experimentations, we find that when the surface temperature decreases, the completely freezing time of drops is reduced; meanwhile, the time required for water temperature to drop down to the wall temperature is increased. Moreover, the heat transfer inside the water droplet slows down with the decreasing of wall hydrophilicity while the total freezing time is prolonged.

Spreading and arrest of a molten liquid on cold substrates.

Understanding the spreading and solidification of liquids on cold solid surfaces is a problem of fundamental importance and general utility. The physics of nonisothermal spreading followed by phase change is still a mystery. The present work focuses on the dynamics and thermal characteristics of liquid drop spreading and their subsequent arrest due to freezing. The spreading of liquid is recorded, and the evolution of the liquid spreading diameter and liquid-solid contact angle is measured from the recordings of a high-speed digital camera. After the initiation of solidification, the liquid drops are pinned to the substrate, showing fixed footprints and contact angles. A physical hypothesis using scaling is provided to explain the relationship between the arrested base diameter (D*) and arrested contact angle (θ*) with respect to the Stefan number (Ste). The experimental observations of solidified drops on cold substrates corroborate the derived physical theory.

Characteristics of Single Droplet Impact on Cold Plate Surfaces

Droplet collision with cold solid surfaces is a fundamental phenomenon observed in low-temperature processes. In this work, a single droplet impacting on a cold surface was investigated by analyzing changes in droplet shape and dimensions recorded with a high-speed camera. At low surface temperatures (−5°C and −10°C), the droplet spreads in a very short period upon impact and then retracts, but to a diameter larger than that at room temperature, dependent on surface material property and texture. Higher impact velocity expands the spreading diameter and promotes the retraction to an extent, but at lower surface temperature (i.e., −20°C) the droplet is quickly frozen with smaller change in diameter on the stainless-steel surface rather than on the Teflon plate. The change of droplet shape upon impacting on a 30° inclined surface was also studied. The surface texture of the stainless-steel plate produced by the polishing process has an obvious effect on the droplet dimension retraction. A proper selection of wall material and process conditions can alleviate or prevent wall deposition.

Turbulent flame–wall interaction: a direct numerical simulation study

A turbulent flame–wall interaction (FWI) configuration is studied using three-dimensional direct numerical simulation (DNS) and detailed chemical kinetics. The simulations are used to investigate the effects of the wall turbulent boundary layer (i) on the structure of a hydrogen–air premixed flame, (ii) on its near-wall propagation characteristics and (iii) on the spatial and temporal patterns of the convective wall heat flux. Results show that the local flame thickness and propagation speed vary between the core flow and the boundary layer, resulting in a regime change from flamelet near the channel centreline to a thickened flame at the wall. This finding has strong implications for the modelling of turbulent combustion using Reynolds-averaged Navier–Stokes or large-eddy simulation techniques. Moreover, the DNS results suggest that the near-wall coherent turbulent structures play an important role on the convective wall heat transfer by pushing the hot reactive zone towards the cold solid surface. At the wall, exothermic radical recombination reactions become important, and are responsible for approximately 70% of the overall heat release rate at the wall. Spectral analysis of the convective wall heat flux provides an unambiguous picture of its spatial and temporal patterns, previously unobserved, that is directly related to the spatial and temporal characteristic scalings of the coherent near-wall turbulent structures.

Numerical simulation of windshield defogging process

A suite of routines for the prediction of environment moist condensation and evaporation on solid surfaces is presented. The physical problem requires the solution of the airflow field along a (cold) solid surface, the evaluation of the unsteady conduction through the solid itself, and the development of a suitable model for the heat and mass transfer through the thin water layer on the fogged surface. The routines for the unsteady simulation of the water layer development are designed as a purely interfacial procedure, minimizing the exchange of information with both the flow and the conductive solver. This allows the coupling with different solvers. Here, the model is used in connection with a commercial computational fluid dynamics solver, in order to predict the defogging process of a car windshield. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow the local ratio of the wet surface to the dry surface to be defined for both the fogging and the defogging process.

Solidification contact angles of molten droplets deposited on solid surfaces

Droplet impact and equilibrium contact angle have been extensively studied. However, solidification contact angle, which is the final contact angle formed by molten droplets impacting on cold surfaces, has never been a study focus. The formation of this type of contact angle was investigated by experimentally studying the deposition of micro-size droplets (∼39 μm in diameter) of molten wax ink on cold solid surfaces. Scanning Electron Microscope (SEM) was used to visualize dots formed by droplets impacted under various impact conditions, and parameters varied included droplet initial temperature, substrate temperature, flight distance of droplet, and type of substrate surface. It was found that the solidification contact angle was not single-valued for given droplet and substrate materials and substrate temperature, but was strongly dependent on the impact history of droplet. The angle decreased with increasing substrate and droplet temperatures. Smaller angles were formed on the surface with high wettability, and this wetting effect increased with increasing substrate temperature. Applying oil lubricant to solid surfaces could change solidification contact angle by affecting the local fluid dynamics near the contact line of spreading droplets. Assuming final shape as hemispheres did not give correct data of contact angles, since the final shape of deposited droplets significantly differs from a hemispherical shape.

Novel ultra-rapid freezing particle engineering process for enhancement of dissolution rates of poorly water-soluble drugs

An ultra-rapid freezing (URF) technology has been developed to produce high surface area powders composed of solid solutions of an active pharmaceutical ingredient (API) and a polymer stabilizer. A solution of API and polymer excipient(s) is spread on a cold solid surface to form a thin film that freezes in 50 ms to 1 s. This study provides an understanding of how the solvent’s physical properties and the thin film geometry influence the freezing rate and consequently the final physico-chemical properties of URF-processed powders. Theoretical calculations of heat transfer rates are shown to be in agreement with infrared images with 10 ms resolution. Danazol (DAN)/polyvinylpyrrolidone (PVP) powders, produced from both acetonitrile (ACN) and tert-butanol (T-BUT) as the solvent, were amorphous with high surface areas (∼28–30 m 2/g) and enhanced dissolution rates. However, differences in surface morphology were observed and attributed to the cooling rate (film thickness) as predicted by the model. Relative to spray-freezing processes that use liquid nitrogen, URF also offers fast heat transfer rates as a result of the intimate contact between the solution and cold solid surface, but without the complexity of cryogen evaporation (Leidenfrost effect). The ability to produce amorphous high surface area powders with submicron primary particles with a simple ultra-rapid freezing process is of practical interest in particle engineering to increase dissolution rates, and ultimately bioavailability.

Numerical simulation of glass fogging and defogging

A numerical procedure for the prediction of fogging and defogging phenomena is presented. The simulation involves the solution of an air flow field along a cold solid surface, the evaluation of the unsteady conduction through the solid itself, and a model for the heat and mass transfer within the thin water layer on the fogged surface. A suite of routines for the unsteady simulation of the water layer evolution is coupled with an equal order finite element Navier Stokes solver and a finite volume conduction code. The procedure is fully independent of the numerical details of the solid and fluid domain solvers. Two different coupling approaches may be followed: A loose one, where the Navier Stokes solution is used only for a steady state estimate of the heat transfer coefficient, or a close one, where the Navier Stokes, conduction and water layer codes are iterated simultaneously. The latter is required for the problem of natural convection, where temperature (and thus the energy balance of the water layer) and flow field are coupled. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow to define the local ratio between wet and dry surface for both the fogging and defogging process. As a case study, a comparison with experimental data for a complete fogging and defogging cycle of a glass lens in natural convection is presented.

Direct numerical simulation of non-premixed flame-wall interactions

The overall objective of this paper is to illustrate how detailed numerical modelling may be used to bring basic information on fundamental problems in combustion science. We consider in the following the interaction of non-premixed flames with cold solid wall surfaces. Flame-wall interactions are an important feature in many combustion systems, that result in significant changes in the flame and wall dynamics: the flame strength is reduced near cold wall surfaces, leading possibly to (partial or total) quenching, while the gassolid heat flux takes peak values at flame contact. The questions of turbulent fuel-air-temperature mixing, flame extinction and wall surface heat transfer are here studied using direct numerical simulation (DNS). The DNS configuration corresponds to an ethylene-air diffusion flame stabilized in the near-wall region of a chemically-inert solid surface. Simulations are performed with adiabatic or isothermal wall boundary conditions, and with different turbulence intensities. The simulations feature flame extinction events resulting from excessive wall cooling, and convective heat transfer up to 90 kW/m2. The structure of the simulated wall flames is studied in terms of a classical mass mixing variable, i.e. the fuel-airbased mixture fraction, and a less familiar heat loss variable, i.e. the excess enthalpy variable, introduced to provide a measure of non-adiabatic behavior due to wall cooling.

Quantum one-phonon-assisted adsorption of light atoms on cold solid surfaces

Quantum-mechanical one-phonon-assisted sticking of on LiF and NaF is considered under -matrix formalism. The bound-state energies, lifetimes and corresponding surface temperatures at which the sticking takes place are evaluated and compared with the experimental results. The exact -matrix approach is found to give better results even for Morse-potential parameters.