Sprays are extensively used in industry, especially for fuels in internal combustion and gas turbine engines. An optimal fuel/air mixture prior to combustion is desired for these applications, leading to greater efficiency and minimal levels of emissions. The optimization depends on details regarding the different breakups, evaporation and mixing processes. Besides, one should take into consideration that these different steps depend on physical properties of the gas and fuel, such as density, viscosity, heat conductivity and surface tension.

In this thesis the phase change and surface tension of a droplet for different flow conditions are studied by means of numerical simulations.This work is part of a larger effort aiming to developing models for sprays in turbulent flows. We are especially interested in the atomization regime, where the liquid breakup causes the formation of droplet sizes much smaller than the jet diameter. The behavior of these small droplets is important to shed more light on how to achieve the homogeneity of the gas-fuel mixture as well as that it directly contributes to the development of large-eddy simulation (LES) models.

The numerical approach is a challenging process as one must take into account the transport of heat, mass and momentum for a multiphase flow. We choose a lattice Boltzmann method (LBM) due to its convenient mesoscopic natureto simulate interfacial flows. A non-ideal equation of state is used to control the phase change according to local thermodynamic properties. We analyze the droplet and surrounding vapor for a hydrocarbon fuel close to the critical point. Under forced convection, the droplet evaporation rate is seen to depend on the vapor temperatureand Reynolds number, where oscillatory flows can be observed. Marangoni forces are also present and drivethe droplet internal circulation once the temperature difference at the droplet surface becomes significant.In isotropic turbulence, the vapor phase shows increasing fluctuations of the thermodynamic variables oncethe fluid approaches the critical point. The droplet dynamics is also investigated under turbulent conditions, where the presence of coherent structures with strong shear layers affects the mass transfer between the liquid-vapor flow, showing also a correlation with the droplet deformation. Here, the surface tension and droplet size play a major role and are analyzed in detail.

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.

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 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.

We investigate the behavior of a fluid near the critical point by using numerical simulations of weakly compressible three-dimensional isotropic turbulence. Much has been done for a turbulent flow with an ideal gas. The primary focus of this work is to analyze fluctuations of thermodynamic variables (pressure, density, and temperature) when a non-ideal Equation Of State (EOS) is considered. In order to do so, a hybrid lattice Boltzmann scheme is applied to solve the momentum and energy equations. Previously unreported phenomena are revealed as the temperature approaches the critical point. Fluctuations in pressure, density, and temperature increase, followed by changes in their respective probability density functions. Due to the non-linearity of the EOS, it is seen that variances of density and temperature and their respective covariance are equally important close to the critical point. Unlike the ideal EOS case, significant differences in the thermodynamic properties are also observed when the Reynolds number is increased. We also address issues related to the spectral behavior and scaling of density, pressure, temperature, and kinetic energy.

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 droplet undergoing phase change in isotropic turbulence using numerical simulations with a hybrid lattice Boltzmann scheme. We solve the momentum and energy transport equations, where phase separation is controlled by a non-ideal equation of state and density contrast is taken into consideration. Deformation is caused by pressure and shear stress at the droplet interface. The statistics of thermodynamic variables is quantified and averaged in terms of the liquid and vapor 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 analyzed and related to the droplet surface area.Different modes of oscillation are clearly identified from the deformation power spectrum for low Taylor Reynolds number $Re_\lambda$, whereas nonlinearities are produced with the increase of $Re_\lambda$, as intermediate frequencies are seen to overlap. As an outcome a continuous spectrum is observed, which shows a decrease that scales as $\sim f^{-3}$.Correlations between the droplet Weber number, deformation parameter, fluctuations of the droplet volume and thermodynamic variables are also examined.

We investigate the behavior of a uid near the critical point by using numerical simulations of weakly compressible three-dimensional isotropic turbulence. Much has been done for a turbulent ow with an ideal gas. The primary focus of this work is to analyze uctuations of thermodynamic variables (pressure, density and temperature) when a non-ideal Equation Of State (EOS) is considered. In order to do so, a hybrid lattice Boltzmann scheme is applied to solve the momentum and energy equations. Previously unreported phenomena are revealed as the temperature approaches the critical point. These phenomena include increased uctuations in pressure, density and temperature, followed by changes in their respective probability density functions (PDFs). Unlike the ideal EOS case, signicant dierences in the thermodynamic properties are also observed when the Reynolds number is increased. We also address issues related to the spectral behavior and scaling of density, pressure, temperature and kinetic energy.

We study the sedimentaion of finite-size particles in a quiescent wall-boundedNewtonian and shear-thinning fluids. The problem is studied numerically bymeans of direct numerical simulations with the presence of the particles ac-counted for with an immersed boundary method. The supensions are Non-Brownian rigid spherical particles with particle to fluid density ratio ρ p /ρ f =1.5; three different solid volume fractions Φ = 1%, 5% and 20% are considered.The Archimedes number is kept constant to Ar = 36 for all shear-thinning fluidcases, while it is changed to Ar = 97 for the Newtonian fluid to reproduce thesame terminal velocity of a single particle sedimenting in the shear-thinningfluid. We show that the mean settling velocities decrease with the particle con-centration as a consequence of the hindering effect and that the mean settlingspeed is always larger in the shear thinning fluid than in the Newtonian one.This is due to the decrease of the mean viscosity of the fluid which leads to alower drag force acting on the particles. We show that particles tend to formaggregates in the middle of the channel in a shear-thinning fluid, preferentiallypositioning in the wake of neighboring particles or aside them, resulting in lowerlevels of fluctuation in the gravity direction than in a Newtonian fluid.

Purpose - In welding there is an intricate coupling between the composition of the material and the shape and depth of the weld pool. In certain materials, the weld pool may not penetrate the material easily, so that it is difficult or impossible to weld, while other seemingly quite similar materials may be well suited for welding. This is due to the convective heat transfer in the melt where the flow is driven primarily by surface tension gradients. This paper aims to study how surface active agents affect the flow and thus the welding properties by surveying some recent 3D simulations of weld pools. Design/methodology/approach - Some basic concepts in the modelling of flow in a weld pool are reviewed. The mathematical models for a convecting melt, with a detailed model for the surface tension and the Marangoni stress in the presence of surfactants, are presented. The effect of the sign of the Marangoni coefficient on the flow pattern, and thus, via melting and freezing, on the shape of the weld pool, is discussed. Findings - It is seen that it is beneficial to have surfactants present at the pool surface, in order to have good penetration. Results from a refined surface tension model that accounts for non-equilibrium redistribution of surfactants are presented. It is seen that the surfactant concentration is significantly modified by the fluid flow. Thereby, the effective surface tension and the Marangoni stresses are altered, and the redistribution of surfactants will affect the penetration depth of the weld pool. Originality/value - The importance of surfactants for weld pool shapes, and in particular the convective redistribution of surfactants, is clarified.

In this experimental work, a proportional feedback control was applied to attenuate an oscillatory thermocapillary flow in an open cylindrical container (annular configuration) filled with silicon oil with high Prandt1 number (Pr = 14 at 25 degrees C). The control was realized by locally heating the free surface with two point source heaters strategically positioned in different azimuthal positions. The heaters were actuated using the local temperature signals fed back from paired sensors. It is suggested that the shortcoming of the control performance accompanied with the amplification of the harmonic frequency components is due to the coupling of the fundamental and the harmonic modes caused by the local control. A remedy is demonstrated to validate the suggestion, where the coupling can be attenuated by increasing the azimuthal length of the actuation region.

We consider preconditioned iterative solution methods to solve the algebraic systems of equations arising from finite element discretizations of multiphase flow problems, based on the phase-field model. The aim is to solve coupled physics problems, where both diffusive and convective processes take place simultaneously in time and space. To model the above, a coupled system of partial differential equations has to be solved, consisting of the Cahn-Hilliard equation to describe the diffusive interface and the time-dependent Navier-Stokes equation, to follow the evolution of the convection field in time. We focus on the construction and efficiency of preconditioned iterative solution methods for the linear systems, arising after conforming and non-conforming finite element discretizations of the Cahn-Hilliard equation in space and implicit discretization schemes in time. The non-linearity of the phase-separation process is treated by Newton's method. The resulting matrices admit a two-by-two block structure, utilized by the preconditioning techniques, proposed in the current work. We discuss approximation estimates of the preconditioners and include numerical experiments to illustrate their behaviour.

In this work we consider preconditioned iterative solution methods for numerical simulations of multiphase flow problems, modelled by the Cahn-Hilliard equation. We focus on diphasic flows and the construction and efficiency of a preconditioner for the algebraic systems arising from finite element discretizations in space and the theta-method in time. The preconditioner utilizes to a full extent the algebraic structure of the underlying matrices and exhibits optimal convergence and computational complexity properties. Large scale umerical experiments are included as well as performance comparisons with other solution methods.

In this work we consider preconditioned iterative solution methods for numerical simulations of multiphase flow problems, modelled by the Cahn-Hilliard equation. We focus on the construction and efficiency of various preconditioning techniques and the effect of two discretization methods - conforming and non-conforming finite elements spaces - on those techniques.

We report experiments on control of thermocapillary instabilities at high temperature differences, in an annular geometry. Previous studies [Phys. Fluids 14, 3039 (2002)] showed that a reasonable control of oscillatory instability could be achieved by optimizing a local heating feedback process. We conducted experiments with a basic flow converging from periphery to center. This constitutes a more unstable configuration than previously, and enables appearance of higher-order instabilities and chaos. Applying successfully local feedback control to the periodic state close to the threshold, we extend the process to higher temperature differences, where nonlinear as well as proportional/derivative control laws are necessary to obtain a significant decrease of the temperature fluctuations. Finally, proportional control allows us to synchronize a chaotic state, to a periodic one.

This paper introduces and experimentally verifies a method for robust, active control of friction reduction in microchannels, enabling new flow control applications and overcoming previous limitations with regard to sustainable liquid pressure. The air pockets trapped at a

superhydrophobic micrograting during liquid priming are coupled to an actively controlled pressure source, allowing the pressure difference over the air/liquid interface to be dynamically adjusted. This allows for manipulating the friction reduction properties of the surface, enabling active control of liquid mass flow through the channel. It also permits for sustainable air lubrication at theoretically unlimited liquid pressures, without loss of superhydrophobic properties. With the non-optimized grating used in the experiment, a difference in liquid mass flow of 4.8 % is obtained by alternatively collapsing and recreating the air pockets using the coupled pressure source, which is in line with a FE analysis of the same geometry. A FE analysis of a more optimized geometry predicts a mass flow change of over 30%, which would make possible new microfluidic devices based on local friction control. It is also experimentally shown that our method allows for sustainable liquid pressure 3 times higher than the Laplace pressure of a passive device.

Dynamic wetting of a solid surface is a process that is ubiquitous in Nature, and also of increasing technological importance. The underlying dissipative mechanisms are, however, still unclear. We present here short-time dynamic wetting experiments and numerical simulations, based on a phase field approach, of a droplet on a dry solid surface, where direct comparison of the two allows us to evaluate the different contributions from the numerics. We find that an important part of the dissipation may arise from a friction related to the motion of the contact line itself, and that this may be dominating both inertia and viscous friction in the flow adjacent to the contact line. A contact line friction factor appears in the theoretical formulation that can be distinguished and quantified, also in room temperature where other sources of dissipation are present. Water and glycerin-water mixtures on various surfaces have been investigated where we show the dependency of the friction factor on the nature of the surface, and the viscosity of the liquid.

We report experiments on the rapid contact-line motion present in the early stages of capillary-driven spreading of drops on dry solid substrates. The spreading data fail to follow a conventional viscous or inertial scaling. By integrating experiments and simulations, we quantify a contact-line friction mu(f) which is seen to limit the speed of the rapid dynamic wetting. A scaling based on this contact-line friction is shown to yield a universal curve for the evolution of the contact-line radius as a function of time, for a range of fluid viscosities, drop sizes, and surface wettabilities.

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.

Liquid infiltrated solids have been proposed as functional solvent-phobic surfaces for handling single and multiphase flows. Implementation of such surfaces alters the interfacial transport phenomenon as compared to a dry substrate. To better understand the interface characteristics in such systems we study experimentally the dynamics of a pendant water drop in air that contacts a substrate coated by thin oil films. At short times the water drop is deformed by the oil that spreads onto the water-air interface, and the dynamics are characterized by inertial and viscous regimes. At late times, the the oil film under the drop relaxes either to a stable thin film or ruptures. In the thin film rupture regime, we measure the waiting time for the rupture as a function of the drop equilibrium contact angle on a dry substrate and the initial film height. The waiting time is rationalized by lubrication theory, which indicates that long-range intermolecular forces destabilize the oil-water interface and is the primary mechanism for the film drainage.

The viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results.

The impact of a solid object on a free liquid surface is quite complex. This problem has challenged researchers for centuries and remains of interest today. Recently Duez et al. [1] published experimental results on the splash when a solid sphere enters a liquid Surprisingly, a small change in the surface chemistry of the object can turn a big splash into an inconspicuous disappearance and vice versa. We study this problem by solving the Navier-Stokes together with the Cahn-Hilliard equations, [2, 3], which allows us to simulate the motion of a free air-water surface in detail, in the presence of surface tension and dynamic wetting. Quantitative computational modeling of dynamic wetting is difficult in itself, but here the use of this tool allows us to study in detail how the wetting properties determine whether a splash appears or not. Our simulated results are compared with the experiments of Duez et al.

This paper presents a model, using a phase-field method, that is able to simulate the motion of a solid sphere impacting on a liquid surface, including the effects of capillary and hydrodynamic forces. The basic phenomena that were the subject of our research effort are the small scale mechanism such as the wetting property of the solid surface which control the large scale phenomena of the interaction. The coupled problem during the impact will be formulated by the inclusion of the surface energies of the solid surface in the formulation, which gives a reliable prediction of the motion of solid objects in/on/out of a liquid surface and the hydrodynamic behaviours at small scales when the inertia of fluid is less important than its surface tension. Numerical results at different surface wettabilities and impact conditions will be presented and compared with the experiments of Duez el al. [C. Duez, C. Ybert, C. Clanet, L. Bocquet, Nat. Phys. 3 (2007) 180-183] and Lee and Kim [D. Lee. H. Kim, Langmuir 24 (1) (2008) 142]. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

In this paper we simulate the evolution and free particle motion of an individual nucleus that grows into a dendritic crystal. The melt flow and the convective heat transfer around the crystal are simulated as they settle due to gravity. There is an intricate coupling between the settling and the evolution of the crystal. The relative flow induced by the settling enhances the growth at the downward facing parts, which in its turn affects the subsequent settling motion. Simulations have been done in two dimensions using a semi-sharp phase-field model. The flow was constrained to a rigid body motion by using Lagrange multipliers inside the solidified part. The model was formulated using two different meshes. One is a fixed background mesh, which covers the whole domain. The other is an adaptive mesh, where the node points are also translated and rotated with the movement of the solid particle. In the latter, the dendritic growth is simulated by the semi-sharp phase-field method.

The dynamical behavior of almost neutrally buoyant finite-size rigid fibers or rods in turbulent channel flow is studied by direct numerical simulations. The time evolution of the fiber orientation and translational and rotational motions in a statistically steady channel flow is obtained for three different fiber lengths. The turbulent flow is modeled by an entropy lattice Boltzmann method, and the interaction between fibers and carrier fluid is modeled through an external boundary force method. Direct contact and lubrication force models for fiber-fiber interactions and fiber-wall interaction are taken into account to allow for a full four-way interaction. The density ratio is chosen to mimic cellulose fibers in water. It is shown that the finite size leads to fiber-turbulence interactions that are significantly different from earlier reported results for point like particles (e.g., elongated ellipsoids smaller than the Kolmogorov scale). An effect that becomes increasingly accentuated with fiber length is an accumulation in high-speed regions near the wall, resulting in a mean fiber velocity that is higher than the mean fluid velocity. The simulation results indicate that the finite-size fibers tend to stay in the high-speed streaks due to collisions with the wall. In the central region of the channel, long fibers tend to align in the spanwise direction. Closer to the wall the long fibers instead tend to toward to a rotation in the shear plane, while very close to the wall they become predominantly aligned in the streamwise direction.

This paper presents a comprehensive three-dimensional, time-dependent model for simulating the adsorption kinetics and the redistribution of surfactants at the surface and in the bulk of a weld pool. A physicochemical approach that was included in this paper allows the surfactant concentration at the surface and in the bulk to depart from its thermodynamical equilibrium. The Langmuir equilibrium adsorption ratio was based on the k(seg) coefficient of Sahoo (1988, "Surface-Tension of Binary Metal-Surface-Active Solute Systems Under Conditions Relevant to Welding Metallurgy," Metall. Trans. B, 19B, pp. 483-491) and was finally used for calculating fluid flow and heat transfer in gas tungsten arc welding of a super duplex stainless steel, SAF 2507. In this study, the authors applied the multicomponent surfactant mass transfer model to investigate the effect of the influence of sulfur and oxygen redistribution in welding of a super duplex stainless steel.

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.

The motion of a three phase contact line, as in a droplet spreading over a dry surface, is ubiquitous in nature and common in technology, but is still not well understood. As has been recently shown, line friction may play an important role in rapid dynamic wetting. Recognizing this as a sometimes dominating factor, we identify the possible scenarios for dynamic wetting of a partially wetting fluid, given the fluid and substrate properties. In doing so, we also reconcile the seemingly different interpretations of dynamic wetting that have been put forward in the recent literature. Copyright (C) EPLA, 2015

We simulate numerically a novel method for dispensing, mixing and ejecting of picolitre liquid samples in a single step. The system consists of a free liquid film, suspended in a frame and positioned in front of a droplet dispenser. On impact, a picolitre droplet 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. Through this process the liquid in the droplet and that in the film is mixed in a controlled way. We model the flow using the Navier Stokes together with the Cahn-Hilliard equations. 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 passage through the thin liquid film matches the measured velocity from the experiment well.

The objective of this work is to investigate numerically the different physical mechanisms of the transition to turbulence of a separated boundary-layer flow over an airfoil at low angle of attack. In this study, the spectral elements code Nek5000 is used to simulate the flow over a SD7003 wing section at an angle of attack of α=4(ring operator). Several laminar cases are first studied from Re=2000 to Re=10000, and a gradual increase of the Reynolds number is then performed in order to investigate one transitional case at Re=20000. Computations are compared with measurements where the instability mechanisms in the separated zone and near wake zone have been analyzed. The mechanism of transition is investigated, where the DMD (Dynamic Mode Decomposition) is used in order to extract the main physical modes of the flow and to highlight the interaction between the transition and the wake flow. The results suggest that the transition process appears to be physically independent of the wake flow, while the LSB shedding process is locked-in with the von Kármán instability and acts as a sub-harmonic.

An existing phase-fieldmodel of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.

Since the mechanical properties and the integrity of the weld metal depend on the solidification behaviour and the resulting microstructural characteristics, understanding weld pool solidification is of importance to engineers and scientists. Thermal and fluid flow conditions affect the weld pool geometry and solidification parameters. During solidification of the weld pool, a columnar grain structure develops in the weld metal. Prediction of the formation of the microstructure during welding may be an important and supporting factor for technology optimization. Nowadays, increasing computing power allows direct simulations of the dendritic and cell morphology of columnar grains in the molten zone for specific temperature conditions. In this study, the solidification microstructures of the weld pool at different locations along the fusion boundary are simulated during gas tungsten arc welding of Al-3wt% Cu alloy using the phase-field model for the directional solidification of dilute binary alloys. A macroscopic heat transfer and fluid flow model was developed to assess the solidification parameters, notably the temperature gradient and solidification growth rate. The effect of the welding speed is investigated. Computer simulations of the solidification conditions and the formation of a cellular morphology during the directional solidification in gas tungsten arc welding are described. Moreover, the simulation results are compared with existing theoretical models and experimental findings.

Dispersed multiphase flows occur in many biological, engineering and geophysical applications such asfluidized beds, soot particle dispersion and pyroclastic flows. Understanding the behavior of suspensionsis a very difficult task. Indeed particles may differ in size, shape, density and stiffness, theirconcentration varies from one case to another, and the carrier fluid may be quiescent or turbulent.When turbulent flows are considered, the problem is further complicated due to the interactionsbetween particles and eddies of different size, ranging from the smallest dissipative scales up to thelargest integral scales. Most of the investigations on the topic have dealt with heavy small particles (typicallysmaller than the dissipative scale) and in the dilute regime. Less is known regarding the behavior ofsuspensions of finite-size particles (particles that are larger than the smallest lengthscales of the fluid phase).

In the present work, we numerically study the behavior of suspensions of finite-size rigid spheres indifferent flows. In particular, we perform Direct Numerical Simulations using an ImmersedBoundary Method to account for the solid phase. Firstly is investigated the sedimentation of particles slightly larger than theTaylor microscale in sustained homogeneous isotropic turbulence and quiescent fluid. The results show thatthe mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. By estimatingthe mean drag acting on the particles, we find that non stationary effects explain the increased reductionin mean settling velocity in turbulent environments.

We also consider a turbulent channel flow seeded with finite-size spheres. We change the solid volumefraction and solid to fluid density ratio in an idealized scenario where gravity is neglected. The aim isto independently understand the effects of these parameters on both fluid and solid phases statistics.It is found that the statistics are substantially altered by changes in volume fraction, while the main effectof increasing the density ratio is a shear-induced migration toward the centerline. However, at very high density ratios (~100) the two phases decouple and the particles behave as a dense gas.

Finally we study the rheology of confined dense suspensions of spheres in simple shear flow. We focus onthe weakly inertial regime and show that the suspension effective viscosity varies non-monotonically with increasingconfinement. The minima of the effective viscosity occur when the channel width is approximately an integernumber of particle diameters. At these confinements, the particles self-organize into two-dimensional frozen layers thatslide onto each other.

We study the rheology of confined suspensions of  neutrally buoyant rigid monodisperse spheres in plane-Couetteflow using Direct Numerical Simulations.We find that if the width of the channel is a (small) integer multiple of the spherediameter, the spheres self-organize into two-dimensional layersthat slide on each other and the effective viscosity of the suspension  issignificantly reduced.  Each two-dimensional layer is found to be structurallyliquid-like but its dynamics is frozen in time.

We study the effect of varying the mass and volume fraction of a suspension of rigid spheres dispersedin a turbulent channel flow. We performed several Direct Numerical Simulations using an Immersed Boundary Method forfinite-size particles changing the solid to fluid density ratio R, the mass fraction and the volume fraction. We find that varying the density ratio R between 1 and 10 at constant volume fraction does not alter the flow statisticsas much as when varying the volume fraction at constant R and at constant mass fraction.

Interestingly, the increase in overall drag found when varying the volume fraction is considerablyhigher than that obtained for increasing density ratios at same volume fraction. The main effect atdensity ratios R of the order of 10 is a strong shear-induced migration towards the centerline of the channel. When thedensity ratio R is further increased up to 100 the particle dynamics decouple from that of the fluid. The solid phase behaves as a dense gas andthe fluid and solid phase statistics drastically change. In this regime, the collisionrate is high and dominated by the normal relative velocity among particles.

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yetlittle is known about the behavior of finite-size particles inhomogeneous isotropic turbulence.

To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using anImmersed Boundary Method to accountfor the dispersed rigid spherical particles. The solid volume fractions considered are 0.5-1%,while the solid to fluid density ratio 1.02.The particle radius is chosen to be approximately 6 Komlogorov lengthscales.

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are phi = 0.5-1%, while the solid to fluid density ratio rho(p)/rho(f) = 1.02. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14% for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails arc associated with the intermittent fast sedimentation of particle pairs in drafting kissing tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling Velocity in a turbulent environment.

We study turbulent channel flows of monodisperse and polydisperse suspensions of finite-size spheres by means of Direct Numerical Simulations using an immersed boundary method to account for the dispersed phase. Suspensions with 3 different Gaussian distributions of particle radii are considered (i.e. 3 different standard deviations). The distributions are centered on the reference particle radius of the monodisperse suspension. In the most extreme case, the radius of the largest particles is 4 times that of the smaller particles. We consider two different solid volume fractions, 2% and 10%. We find that for all polydisperse cases, both fluid and particles statistics are not substantially altered with respect to those of the monodisperse case. Mean streamwise fluid and particle velocity profiles are almost perfectly overlapping. Slightly larger differences are found for particle velocity fluctuations. These increase close to the wall and decrease towards the centerline as the standard deviation of the distribution is increased. Hence, the behavior of the suspension is mostly governed by excluded volume effects regardless of particle size distribution (at least for the radii here studied). Due to turbulent mixing, particles are uniformly distributed across the channel. However, smaller particles can penetrate more into the viscous and buffer layer and velocity fluctuations are therein altered. Non trivial results are presented for particle-pair statistics.

We introduce and successfully demonstrate a novel method and system for subsequent dispensing, mixing and ejecting of picolitre liquid samples in a single step. The system consists of a free liquid film, suspended in a frame and positioned in front of a droplet dispenser. In this study we tested and modelled the flight of liquid droplets, ejected from an inkjet print head, through a suspended liquid film. Model and experiment are in accordance.

Abstract: The instability analysis of the liquid jet issuing into ambient air was conducted with an emphasis placed upon the evolution of surface waves of the jet. An experiment was designed to visualize the microscopic morphology on the surface of a liquid jet. A spectral method was proposed to measure wavelength from the obtained jet images. We also discuss key setup parameters that significantly affect the resolution of desired jet features and the accuracy of the spectral measurement. The results show that the liquid jet near the nozzle exit can be divided into a laminar section, a transition section, an instability section, and a turbulence section. Surface wave scales range from 0.06 to 0.11 times of the nozzle diameter with the atomization breakup regime. For the atomization breakup regime, the growth ratio of the surface waves of the instability section is 0.06 which is 1.5 times the value of the second wind-introduced breakup regime and 3 times the value of the first wind-introduced breakup regime. Graphical abstract: [Figure not available: see fulltext.]

The structures on the surface of high-speed capillary liquid jet were captured with the help of high-speed camera and microscope. Apower spectral density method is used to deal with the jet images. Based on captured jet image, the variation of surface structures near the exit of the nozzle is divided into three sections: laminar section, instability section and turbulence section. There is no clearly surface structures in the laminar section. The wave-like structures come out in the instability section with a sudden and are regularly increase with a small slope along the streamwise. The degree of order is rather weak in the turbulence section. The increase of the Reynolds numbers which based on the momentum thickness at the exit of the nozzle will accelerates the jet surface transition from the laminar section to turbulence section.

Under the three breakup regimes, the jet surface waves of different nozzles are captured and measured. The nozzles have different length to diameter ratios and contraction angles. The measured wavelengths are compared with the reported conclusions which were obtained by using spatial and temporal linear stability analysis. The results show that the jet wavelengths of different breakup regimes are covered by a single curve when the wavelengths are non-dimensionalized with boundary layer thickness. For the nozzle with equal length and diameter, the entire translation section starts at Re = 3 x 10(4) and ends at Re = 4.5 x 10(4). The wavelength non-dimensionalized with boundary layer thickness is independent of nozzle configuration. The ratio of initial wavelength to boundary layer thickness ranges from 2 to 4.

A Volume of Fluid (VOF) method is applied to study the deformation and breakup of a single liquid drop in shear flows superimposed on uniform flow. The effect of shearing on the breakup mechanism is investigated as a function of the shear rate. Sequential images are compared for the parameter range studied; density ratios of liquid to gas of 20, 40, and 80, viscosity ratios in the range 0.5-50, Reynolds numbers between 20, a constant Weber number of 20, and the non-dimensional shear rate of the flow G = 0-2.1875. It is found that while shear breakup remains similar for all values of shear rate considered, other breakup modes observed for uniform flows are remarkably modified with increasing shear rate. The time required for breakup is significantly decreased in strong shear flows. A simple model predicting the breakup time as a function of the shear rate and the breakup time observed in uniform flows is suggested.

Supercritical carbon dioxide (scCO(2)) is often used to replace harmful solvents and can dissolve a wide range of organic compounds. With a favorable critical point at 31 degrees C and 7.4 MPa, reaching above the critical point for scCO(2) is fairly accessible. Because of the compressible nature of scCO(2) and the large changes of viscosity and density with temperature and pressure, there is a need to determine the behavior of scCO(2) in microfluidic systems. Here, the influence of how parameters such as flow rate, temperature, pressure, and flow ratio affects the length of parallel flow of water and scCO(2) and the length of the created CO2 segments are investigated and modeled using multivariate data analysis for a 10 mm long double-y channel. The parallel length and segment size were observed in the laminar regime around and above the critical point of CO2. The flow ratio between the two fluids together with the flow rate influenced both the parallel length and the segment sizes, and a higher pressure resulted in shorter parallel lengths. Regarding the segment length of CO2, longer segments were a result of a higher Weber number for H2O together with a higher temperature in the channel.

Feedback control on was carried out on non-linear thermocapillary convections in a half-zone liquid bridge of a high Prandtl number fluid. In the liquid bridge, the convection changes from a two-dimensional steady flow to a three-dimensional oscillatory one at a critical temperature difference. Feedback control was realized by locally modifying the free surface temperature using local temperature measured at different positions. The present study aims to develop a new control scheme by taking spatio-temporal azimuthal distribution of temperature fluctuation into account. The new control scheme achieved significant attenuation of the temperature oscillation compared with the previous one in a high Marangoni number range.

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.

Sprays are used in a wide range of engineering applications, in the food and pharmaceutical industry in order to produce certain materials in the desired powder-form, or in internal combustion engines where liquid fuel is injected and atomized in order to obtain the required air/fuel mixture. The optimization of such processes requires the detailed understanding of the breakup of liquid structures.

In this work, we focus on the secondary breakup of medium size liquid drops that are the result of primary breakup at earlier stages of the breakup process, and that are subject to further breakup. The fragmentation of such drops is determined by the competing disruptive (pressure and viscous) and cohesive (surface tension) forces. In order to gain a deeper understanding on the dynamics of the deformation and breakup of such drops, numerical simulations on single drops in uniform and shear flows, and on dual drops in uniform flows are performed employing a Volume of Fluid method. The studied parameter range corresponds to an intermediate Weber number of 20, sufficiently high so that breakup occurs, but much lower than the limit for catastrophic breakup, and a range of Reynolds numbers covering the steady wake regime for liquid drops, Re = 20-200. In order to account for liquids in various applications, a set of different density and viscosity ratios are considered, ρ*=20-80, and μ*=0.5-50 respectively.

Single drop simulations show that depending on the Reynolds number and density and viscosity ratios, various breakup modes besides classical bag and shear breakup may be observed at a constant Weber number. The characteristics of the deformation process and the time required for breakup are considerably different for these modes; furthermore, both are significantly altered by velocity gradients in the flow. Dual drop simulations show that the relative position of the two drops, in addition to the Reynolds number and density and viscosity ratios, plays a crucial role in determining the interaction scenario. It is found that the behaviour of drops in tandem may be predicted based on data obtained for single drops: the breakup time and the length of the wake behind the drop. The region where collision is most likely to occur is identified as a two diameters wide and eight diameters long streak, however, weaker forms of interaction may occur up to twenty diameters behind the drop. Results presented in this thesis may be applied to formulate enhanced breakup models regarding the deformation, breakup, and interaction of liquid drops employed in spray simulations.

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. Specifically, initial separation distances of l = 1.5 − 5D drop diamters, and angles between β = 0◦ − 90◦ are considered. Simulations for a Weber number of W e = 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 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, similar or identical 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.