We investigate the evaporation of a droplet surrounded by superheated vapor with relative motion between phases. The evaporating droplet is a challenging process, as one must take into account the transport of mass, momentum, and heat. Here a lattice Boltzmann method is employed where phase change is controlled by a nonideal equation of state. First, numerical simulations are compared to the D-2 law for a vaporizing static droplet and good agreement is observed. Results are then presented for a droplet in a Lagrangian frame under a superheated vapor flow. Evaporation is described in terms of the temperature difference between liquid-vapor and the inertial forces. The internal liquid circulation driven by surface-shear stresses due to convection enhances the evaporation rate. Numerical simulations demonstrate that for higher Reynolds numbers, the dynamics of vaporization flux can be significantly affected, which may cause an oscillatory behavior on the droplet evaporation. The droplet-wake interaction and local mass flux are discussed in detail.
We investigate the Marangoni effects in a hexane droplet under evaporation and close to its critical point. A lattice Boltzmann model is used to perform 3D numerical simulations. In a first case, the droplet is placed in its own vapor and a temperature gradient is imposed. The droplet locomotion through the domain is observed, where the temperature differences across the surface is proportional to the droplet velocity and the Marangoni effect is confirmed. The droplet is then set under a forced convection condition. The results show that the Marangoni stresses play a major role in maintaining the internal circulation when the superheated vapor temperature is increased. Surprisingly, surface tension variations along the interface due to temperature change may affect heat transfer and internal circulation even for low Weber number. Other results and considerations regarding the droplet surface are also discussed.
The heat and mass transfer of deformable droplets in turbulent flows is crucial. to a wide range of applications, such as cloud dynamics and internal combustion engines. This study investigates a single droplet undergoing phase change in isotropic turbulence using numerical simulations with a hybrid lattice Boltzmann scheme. Phase separation is controlled by a non-ideal equation of state and density contrast is taken into consideration. Droplet deformation is caused by pressure and shear stress at the droplet interface. The statistics of thermodynamic variables are quantified and averaged over both the liquid and vapour phases. The occurrence of evaporation and condensation is correlated to temperature fluctuations, surface tension variation and turbulence intensity. The temporal spectra of droplet deformations are analysed and related to the droplet surface area. Different modes of oscillation are clearly identified from the deformation power spectrum for low Taylor Reynolds number Re, whereas nonlinearities are produced with the increase of Re A, as intermediate frequencies are seen to overlap. As an outcome, a continuous spectrum is observed, which shows a decrease in the power spectrum that scales as similar to f(-3) Correlations between the droplet Weber number, deformation parameter, fluctuations of the droplet volume and thermodynamic variables are also developed.
In this paper we consider a thermal multiphase lattice Boltzmann method (LBM) to investigate the heating and vaporization of a suspended droplet. An important benefit from the LBM is that phase separation is generated spontaneously and jump conditions for heat and mass transfer are not imposed. We use double distribution functions in order to solve for momentum and energy equations. The force is incorporated via the exact difference method (EDM) scheme where different equations of state (EOS) are used, including the Peng-Robinson EOS. The equilibrium and boundary conditions are carefully studied. Results are presented for a hexane droplet set to evaporate in a superheated gas, for static condition and under gravitational effects. For the static droplet, the numerical simulations show that capillary pressure and the cooling effect at the interface play a major role. When the droplet is convected due to the gravitational field, the relative motion between the droplet and surrounding gas enhances the heat transfer. Evolution of density and temperature fields are illustrated in details.
The experimental results of Xia and Steen for the contact line dynamics of a drop placed on a vertically oscillating surface are analyzed by numerical phase field simulations. The concept of contact line mobility or friction is discussed, and an angle-dependent model is formulated. The results of numerical simulations based on this model are compared to the detailed experimental results of Xia and Steen with good general agreement. The total energy input in terms of work done by the oscillating support, and the dissipation at the contact line, are calculated from the simulated results. It is found that the contact line dissipation is almost entirely responsible for the dissipation that sets the amplitude of the response. It is argued that angle-dependent line friction may be a fruitful interpretation of the relations between contact line speed and dynamic contact angle that are often used in practical computational fluid dynamics.
In the present paper we present a phenomenological description of droplet dynamics in a bifurcating channel that is based on three-dimensional numerical experiments using the Phase Field theory. Droplet dynamics is investigated in a junction, which has symmetric outflow conditions in its daughter branches. We identify two different flow regimes as the droplets interact with the tip of the bifurcation, splitting and non-splitting. A distinct criterion for the flow regime transition is found based on the initial droplet volume and the Capillary (Ca) number. The Rayleigh Plateau instability is identified as a driving mechanism for the droplet breakup close to the threshold between the splitting and non-splitting regime.
Inkjet technology has been recognized as one of the most successful and promising micro-system technologies. The wide application areas of printer heads and the increasing demand of high quality prints are making ink consumption and print see-through important topics in the inkjet technology. In the present study we investigate numerically the impact of ink droplets onto a porous material that mimics the paper structure. The mathematical framework is based on a free energy formulation, coupling the Cahn-Hilliard and Navier Stokes equations, for the modelling of the two-phase flow. The case studied here consists of a multiphase flow of air-liquid along with the interaction between a solid structure and an interface. In order to characterize the multiphase flow characteristics, we investigate the effects of surface tension and surface wettability on the penetration depth and spreading into the paper-like structure.
This paper presents a technology for dispensing droplets through thin liquid layers. The system consists of a free liquid film, which is suspended in a frame and positioned in front of a piezoelectric printhead. A droplet, generated by the printhead, merges with the film, but due to its momentum, passes through and forms a droplet that separates on the other side and continues its flight. The technology allows the dispensing, mixing and ejecting of picolitre liquid samples in a single step. This paper overviews the concept, potential applications, experiments, results and a numerical model. The experimental work includes studying the flight of ink droplets, which ejected from an inkjet print head, fly through a free ink film, suspended in a frame and positioned in front of the printhead. We experimentally observed that the minimum velocity required for the 80 pl droplets to fly through the 75 ± 24 lm thick ink film was of 6.6 m s-1. We also present a numerical simulation of the passage of liquid droplets through a liquid film. The numerical results for different initial speeds of droplets and their shapes are taken into account. We observed that during the droplet-film interaction, the surface energy is partially converted to kinetic energy, and this, together with the impact time, helps the droplets penetrate the film. The model includes the Navier- Stokes equations with continuum-surface-tension force derived from the phase-field/Cahn-Hilliard equation. This system allows us to simulate the motion of a free surface in the presence of surface tension during merging, mixing and ejection of droplets. The influence of dispensing conditions was studied and it was found that the residual velocity of droplets after their passage through the thin liquid film well matches the measured velocity from the experiment.
Computations of the turbulent flow through plane asymmetric diffusers for opening angles from 8degrees to 10degrees have been carried out with the explicit algebraic Reynolds stress model (EARSM) of Wallin and Johansson [J. Fluid Mech. 403 (2000) 89]. It is based on a two-equation platform in the form of a low-Re K - omega formulation, see e.g. Wilcox [Turbulence Modeling for CFD, DCW Industries Inc., 1993]. The flow has also been studied experimentally for the 8.5degrees opening angle using PIV and LDV. The models under-predict the size and magnitude of the recirculation zone. This is, at least partially, attributed to an over-estimation of the wall normal turbulence component in a region close to the diffuser inlet and to the use of damping functions in the near-wall region. By analyzing the balance between the production and dissipation of the turbulence kinetic energy we find that the predicted dissipation is too large. Hence, we can identify a need for improvement of the modeling the transport equation for the turbulence length-scale related quantity.
This paper describes an experiment of using an existing hardware platform, the Reactable, to help designing the interaction between three different sound models and instrument interfaces. The aim was to test if prototyping could be facilitated by interacting with models of control actions derivedfrom performance gestures on an intermediate interface. The Reactable isa tangible table-top electronic musical instrument, and the software models include a DJ scratch interface, a virtual turntable, a physics-based sound model representing a bow-and-string interaction, and a physics-based friction sound model for sonification of the user gestures. The interaction was evaluated by two experts: one Reactable musician and one DJ. Their task was to practice expressive, musical performances. Data from the performers were collected through questionnaires and video recordings. The advantages of usinga single, versatile, hardware setup as a designer tool for various interface tasks are discussed. It is suggested how this hardware can be described as an alternative mapping layer.
This paper investigates noise annoyance from wind turbines of different sizes and in different acoustic surroundings. A listening test was conducted where wind turbine noises were rated alone and together with background sounds from a deciduous forest, a busy city and road traffic. A magnitude production procedure was implemented which showed high correlation between repeated measurements and the results were analysed using A-weighted sound levels, signal-to-noise ratios and time varying loudness and partial loudness. Ratings for wind turbine sound heard alone showed no coherent statistically significant differences between wind turbine types, neither for A-weighted sound levels nor loudness. The masking test indicate that road traffic noise is a superior masker compared to forest sound. However, these effects where only statistically significant at low sound levels, below the range 35–45 dB(A), where noise guidelines for wind turbine noise usually are stipulated.
A Volume of Fluid (VOF) method is applied to study the interaction between two liquid drops with the same initial diameter in uniform flow. Various arrangements of the drops are studied, based on two parameters, namely the initial separation distance and the angle between the line connecting the centres of the drops and the free-stream direction. Initial separation distances of 1.5–5 drop diameters, and angles between β=0∘ and 90° are considered. Simulations for a Weber number of We=20, two Reynolds numbers Re=20 and 50, and density and viscosity ratios in the range ρ*=20–80 and μ*=0.5–50 are performed. The movement of the secondary drop with respect to the primary drop, and estimates on the time required for the breakup of the secondary drop as compared to those observed for single drops are evaluated. It is found that the drops collide only in cases corresponding to the shortest initial displacements, while in others they deform and break up independently, similarly or identically to single drops. The same behaviour is reflected in the time required for breakup. Cases where the drops behave independently show breakup times close to those observed for single drops.
A Volume of Fluid (VOF) method is applied to investigate the deformation and breakup of an initially spherical drop in the bag- and shear breakup regimes, induced by steady disturbances. The onset of breakup is sought by studying steady-shape deformations while increasing the Weber number until breakup occurs. A parameter study is carried out applying different material properties and a wide range of drop Reynolds numbers in the steady wake regime. Density ratios of liquid to gas of 20, 40, and 80, viscosity ratios in the range 0.5-50, and Reynolds numbers between 20 and 200 are investigated for a constant Weber number of 20. The critical Weber number is found to be 12, in agreement with observations of earlier studies. For Weber number of 20 varying density, viscosity ratios and Reynolds numbers, interesting mixed breakup modes are discovered. Moreover, a new regime map including all modes observed is presented. A criterion for the transition between bag-and shear breakup is defined relating the competing inertial and shear forces appearing in the flow. Furthermore, results on breakup times and the time history of the drag coefficient are presented; the latter is concluded to be a potential parameter to indicate the occurrence of breakup. (C) 2014 Elsevier Ltd. All rights reserved.
We present a modeling approach that enables numerical simulations of a boiling Van der Waals fluid based on the diffuse interface description. A boundary condition is implemented that allows in and out flux of mass at constant external pressure. In addition, a boundary condition for controlled wetting properties of the boiling surface is also proposed. We present isothermal verification cases for each element of our modeling approach. By using these two boundary conditions we are able to numerically access a system that contains the essential physics of the boiling process at microscopic scales. Evolution of bubbles under film boiling and nucleate boiling conditions are observed by varying boiling surface wettability. We observe flow patters around the three-phase contact line where the phase change is greatest. For a hydrophilic boiling surface, a complex flow pattern consistent with vapor recoil theory is observed.
Droplet spreading and transport phenomenon is ubiquitous and has been studied by engineered surfaces with a variety of topographic features. To obtain a directional bias in dynamic wetting, hydrophobic surfaces with a geometrical asymmetry are generally used, attributing the directionality to one-sided pinning. Although the pinning may be useful for directional wetting, it usually limits the droplet mobility, especially for small volumes and over wettable surfaces. Here, we demonstrate a pinning-less approach to rapidly transport millimeter sized droplets on a partially wetting surface. Placing droplets on an asymmetrically structured surfaces with micron-scale roughness and applying symmetric horizontal vibration, they travel rapidly in one direction without pinning. The key, here, is to generate capillary-driven rapid contact-line motion within the time-scale of period of vibration. At the right regime where a friction factor local at the contact line dominates the rapid capillary motion, the asymmetric surface geometry can induce smooth and continuous contact-line movement back and forth at different speed, realizing directional motion of droplets even with small volumes over the wettable surface. We found that the translational speed is selective and strongly dependent on the droplet volume, oscillation frequency, and surface pattern properties, and thus droplets with a specific volume can be efficiently sorted out.
In this paper, we numerically study particle formation in the rapid expansion of supercritical solution (RESS) process in a two dimensional, axisymmetric geometry, for a benzoic acid + CO2 system. The fluid is described by the classical Navier-Stokes equation, with the thermodynamic pressure being replaced by a generalized pressure tensor. Homogenous particle nucleation, transport, condensation and coagulation are described by a general dynamic equation, which is solved using the method of moments. The results show that the maximal nucleation rate and number density occurs near the nozzle exit, and particle precipitation inside the nozzle might not be ignored. Particles grow mainly across the shocks. Fluid in the shear layer of the jet shows a relatively low temperature, high nucleation rate, and carries particles with small sizes. On the plate, particles within the jet have smaller average size and higher geometric mean, while particles outside the jet shows a larger average size and a lower geometric mean. Increasing the preexpansion temperature will increase both the average particle size and standard deviation. The preexpansion pressure does not show a monotonic dependency with the average particle size. Increasing the distance between the plate and the nozzle exit might decrease the particle size. For all the cases in this paper, the average particle size on the plate is on the order of tens of nanometers.
The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular motion close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and contact angles. We use a simple-point-charge/extended water model. This model provides a very small slip and a more realistic representation of the molecular physics than Lennard-Jones models. The Cahn-Hilliard phase-field model and the volume-of-fluid model are calibrated against the drop displacement from molecular dynamics reference data. It is shown that the calibrated continuum models can accurately capture droplet displacement and droplet break-up for different capillary numbers and contact angles. However, we also observe differences between continuum and atomistic simulations in describing the transient and unsteady droplet behaviour, in particular, close to dynamical wetting transitions. The molecular dynamics of the sheared droplet provide insight into the line friction experienced by the advancing and receding contact lines. The presented results will serve as a stepping stone towards developing accurate continuum models for nanoscale hydrodynamics.
Auditory masking of unwanted sounds by wanted sounds has been suggested as a tool for outdoor acoustic design. Anecdotal evidence exists for successful applications, for instance the use of fountain sounds for masking road traffic noise in urban parks. However, basic research on auditory masking of environmental sounds is lacking. Therefore, we conducted two listening experiments, using binaural recordings from a city park in Stockholm exposed to traffic noise from a main road and sound from a large fountain located in the center of the park. In the first experiment, 17 listeners assessed the loudness of the road traffic noise and fountain sounds from recordings at various distances from the road, with or without the fountain turned on. In the second experiment, 16 listeners assessed the loudness of systematic combinations of a singular fountain sound and a singular road traffic noise. The results of the first experiment showed that the fountain sound reduced the loudness of road traffic noise close to the fountain, and that the fountain sound was equally loud or louder than the road traffic noise in a region 20-30 m around the fountain. This suggests that the fountain added to the quality of the city park soundscape by reducing the loudness of the (presumably unwanted) traffic noise. On the other hand, results from the second experiment showed that road traffic noise was harder to mask than fountain sound, and that the partial loudness of both sources was considerably less than expected from a model of energetic masking. This indicates that auditory processes, possibly related to target-masker confusion, may reduce the overall masking effect of environmental sounds.
Dynamic wetting problems are fundamental to understanding the interaction between liquids and solids. Even in a superficially simple experimental situation, such as a droplet spreading over a dry surface, the result may depend not only on the liquid properties but also strongly on the substrate-surface properties; even for macroscopically smooth surfaces, the microscopic geometrical roughness can be important. In addition, because surfaces may often be naturally charged or electric fields are used to manipulate fluids, electric effects are crucial components that influence wetting phenomena. We investigate the interplay between electric forces and surface structures in dynamic wetting. Although surface microstructures can significantly hinder spreading, we find that electrostatics can “cloak” the microstructures, that is, deactivate the hindering. We identify the physics in terms of reduction in contact-line friction, which makes the dynamic wetting inertial force dominant and insensitive to the substrate properties.
Enhancement of boiling heat transfer on biphilic (mixed-wettability) surfaces faces a sudden reversal at low pressures, which is brought about by excessive contact-line spreading across the wetting heterogeneities. We employ the diffuse-interface approach to numerically study bubble expansion on a heating surface that consists of opposing wettabilities. The results show a dramatic shift in the dynamics of a traversing contact line across the wettability divide under different gravities, which correspond to variable bubble growth rates. Specifically, it is found that the contact-line propagation tends to follow closely the rapidly expanding bubble at low gravity, with only a brief interruption at the border between the hydrophobic and hydrophilic sections of the surface. Only when the bubble growth becomes sufficiently weakened at high gravity does the contact line get slowed down drastically to the point of being nearly immobilized at the edge of the hydrophilic surface. The following bubble expansion, which faces strong limitations in the direction parallel to the surface, features a consistent apparent contact angle at around 66.4 degrees, regardless of the wettability combination. A simple theoretical model based on the force-balance analysis is proposed to describe the physical mechanism behind such a dramatic transition in the contact-line behavior.
In this paper, we numerically study pool boiling of a binary (water and nitrogen) mixture on a surface endowed with a combination of hydrophobicity and hydrophilicity (i.e., the so called biphilic surface). Here we adopt a numerical approach based on the phase field theory, where the vapor-liquid interface is assumed to be of a finite thickness (hence diffusive in nature) and requires no explicit tracking schemes. The theoretical modeling of two-phase heat and mass transfer in water diluted with nitrogen demonstrates the signiant impact of impurities on bubble dynamics. The simulations show that locally high concentrations of nitrogen gas within the vapor bubble is essential to weakening the condensation effect, which results in sustained bubble growth and ultimately (partial) departure from the surface under the artificially enlarged gravity. Simply increasing the solubility of nitrogen in water, however, turns out to be counterproductive because possible re-dissolution of the aggregated nitrogen by the bulk water could deprive the bubble of vital gas contents, leading instead to continuous bubble shrinkage and collapse. Additionally, it is found that with the significant accumulation of nitrogen, the bubble interface is increasingly dominated by a strong interfacial thermocapillary flow due to the Marangoni effect.
The correlation correlation between the fluctuating particle and gas velocity in isotropic turbulence is studied with a set of stochastic differential equations taking into account both particle-particle collisions and the particle feedback on the turbulence. The principal aim of this work is to use the Langevin equations to formulate closures for two-fluid gas-particle flow models. Using Ito calculus we derived solutions for the turbulent kinetic energy of the particle phase and the particle-gas velocity correlations. If particle-particle collisions and particle feedback on the turbulence are neglected the new relations approach the ones derived by Tchen and Hinze but if these effects are included additional terms in the relations appear. In this study we only use a very simple model for the particle-particle collisions. The new relation and the classical relation of Tchen and Hinze for the particle turbulent kinetic energy as well as a relation based on the kinetic theory of granular flows have been implemented in a two-fluid model for turbulent gas-particle flow in a channel in order to make comparison for different particle Stokes numbers. Results show that while the two-fluid model using Hinze's relations only gives good results for small Stokes numbers, the new relation yields significant improvements for a large range of Stokes numbers.
An Eulerian model was developed for turbulent gas-particle flow that takes into account the influence of particles on the gas-phase turbulence. For the description of the particle-phase stress the kinetic theory of granular flow and the simpler Hinze model were adopted. A K-ω model was used as the gas phase turbulence model. The difference between one- and two-way coupling was investigated for different particle volume fractions and particle diameters. It was found that particles with a much higher density than the fluid substantially affect the gas-phase in turbulent channel flow for particle volume fractions as low as 10 -4. The models with the particle-phase stress described by the kinetic theory of granular flow and the simpler Hinze model produce similar results for particles with small response times but deviate for larger response times. The study shows that two-way coupling and the turbophoretic effect must be taken into account in models even at relatively low particle volume fractions.
Dissolutive wetting is investigated numerically using a diffuse-interface model that incorporates fluid flow, solute diffusion and phase change. A range of materials parameters are investigated: (1) permitting recovery of the hydrodynamic limit by suppressing the dissolution of the substrate and (2) evaluating the role of diffusion. The time history of droplet size, droplet concentration and angles between the interfaces are given. For cases in which convection dominates, the dynamics of spreading agrees with a known hydrodynamic model for spreading of inert fluids. A phase change increases wetting speed, due to a condensation that takes place near the triple junction. There is also a strong dependence of the wetting kinetics on the solute diffusivities. Details of composition changes during spreading are also discussed, such as the composition path of the bulk liquid probed at different locations in the drop. Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Liquid wetting of a surface is omnipresent in nature and the advance of micro-fabrication and assembly techniques in recent years offers increasing ability to control this phenomenon. Here, we identify how surface roughness influences the initial dynamic spreading of a partially wetting droplet by studying the spreading on a solid substrate patterned with microstructures just a few micrometers in size. We reveal that the roughness influence can be quantified in terms of a line friction coefficient for the energy dissipation rate at the contact line, and that this can be described in a simple formula in terms of the geometrical parameters of the roughness and the line-friction coefficient of the planar surface. We further identify a criterion to predict if the spreading will be controlled by this surface roughness or by liquid inertia. Our results point to the possibility of selectively controlling the wetting behavior by engineering the surface structure.
We conduct numerical experiments on viscoelastic droplets hitting a flat solid surface. The results present time-resolved non-Newtonian stresses acting in the droplet. Comparing with the simulation of the impact of a Newtonian droplet, the effects of viscoelasticity on droplet behaviors such as splashing, the maximum spreading diameter and deformation are analyzed. With detailed information on the contact line region, we demonstrate how the contact line behaves according to the transition of the fluid property from elasticity dominated to shear-thinning dominated when a droplet expands and contracts on the substrate. The propose of this work is to discuss whether and how the elasticity in an impinging droplet takes effect.
Non-Newtonian droplet dynamics commonly exist in microfluidic systems. We report simulations of viscoelastic (VE) droplets traveling in a two dimensional capillary bifurcation channel. A numerical system combining phase field method, VE rheology, and Stokes flow equations is built. As a generic microfluidic two-phase problem, we study how a non-Newtonian droplet that approaches a channel bifurcation will behave. We identify conditions for when a droplet will either split into two or be directed into one of the branches. In particular, we study the importance of the non-Newtonian properties. Our results reveal two different non-Newtonian mechanisms that can enhance splitting and non-splitting of droplets with respect to Newtonian droplets, depending on the size of droplet and capillary number.