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This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. A shape-independent test of the curvature estimation is introduced through the use of randomly oriented and shaped paraboloids as reference interfaces. The coupling of the curvature estimation, interface transport, and Navier–Stokes surface tension force is evaluated through the measurement of spurious velocities in simulations of stationary and translating droplets. These studies find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost when errors are introduced in the volume fraction field either artificially or through the interface advection and reconstruction steps. • Performance evaluation of curvature estimation methods from volume fractions. • Height-function and paraboloid-fitting methods evaluated with static and dynamic interfaces. • Relative performance of methods differs between static and dynamic tests. [Display omitted] [ABSTRACT FROM AUTHOR]

• Breakup dynamics of bubble formation in viscous liquids in a flow-focusing device are highlighted. • Bubble formation can be classified into a nonlinear stage and a linear final pinch-off stage. • In the nonlinear stage, the minimum neck radius of the gaseous thread and the remaining time can be scaled as a power-law. • In the linear pinch-off stage, both of the viscous force and surface tension control the evolution of the gas–liquid interface. • Liquid viscosity affects the breakup dynamics of gaseous thread via the viscous force and the enhancement of the confinement effect. The bubble formation in highly viscous liquids in a microfluidic flow-focusing device is highlighted. The influences of viscosity and flow rate of liquid phase on the bubble formation are studied. The glycerol-water solution (94–1000 mPa s) is used as the liquid phase, and nitrogen as the gas phase. Two different stages are observed in the gaseous breakup during bubble formation: at first, the relation between the neck radius of the gaseous thread and the remaining time can be expressed as a power law; while in the final stage, the gaseous thread thins linearly with time. Under constant gas flow rate, the exponent in the power law stage is influenced by the liquid viscosity, and the thinning rate of the linear pinch-off stage decreases with the increase of the liquid viscosity. The liquid flow rate has no obvious effect on the variation of the neck radius of the gaseous thread with time in both stages. The results show that the increase in liquid viscosity enhances the confinement effect on gas-liquid interface during bubble formation. [ABSTRACT FROM AUTHOR]

A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially when they are coupled to the momentum equation and applied in physically relevant regimes. In this article, we compare two techniques for simulating two-phase flows that possess attractive qualities, but belong to the two distinct classes of diffuse interface (DI) and volume of fluid (VOF) methods. Both of these methods allow for mass-conserving schemes that can naturally capture large interfacial topology changes omnipresent in realistic two phase flows. The DI solver used in this work is based on a conservative and bounded phase field method, developed recently. Similar to level set methods, this diffuse interface method takes advantage of the smoothness of the phase field in computing curvature and surface tension forces. Geometric VOF methods track the fractional tagged volume in a cell. The specific geometric VOF scheme used here is a discretely conservative and bounded implementation that uses geometric algorithms for unsplit advection and interface reconstruction, while employing height functions for normal and curvature calculation. We present a quantitative comparison of these methods on Cartesian meshes in terms of their accuracy, convergence rate, and computational cost using canonical two-dimensional (2D) two-phase test cases: an equilibrium static drop, an oscillating drop, damped surface wave and the Rayleigh–Taylor instability. We further compare these methods in their ability to resolve thin films by simulating the impact of a water drop on a deep water pool. Using results of these studies, we suggest qualitative guidelines for selection of schemes for two-phase flow calculations. [ABSTRACT FROM AUTHOR]

The liquid atomization process relies on the disturbance of the liquid surface by various forces. In the case of "flow-blurring" (FB) atomization, this is achieved by inducing flow instabilities near the liquid channel exit. In this study, we analyze the underlying dynamics of these coherent turbulent structures and their role in the primary atomization within the FB regime. For that purpose, Smoothed Particles Hydrodynamics (SPH) simulations have been conducted using alternative FB nozzle geometries at different operating conditions. An in-house developed visualization and data exploration platform (postAtom) was used to capture the time-resolved Lagrangian coherent structures (LCSs) via the finite-time Lyapunov exponent (FTLE) fields. Simulations were conducted at different gas/liquid momentum ratios at the nozzle exit by changing the mass flow rate of the gas phase and/or changing the position of the liquid injector. The effect of outer chamber design on the atomization performance is further assessed. The results indicate that the design of the mixing chamber can trigger an oscillatory behavior at the nozzle exit, which has a direct impact on the evolution of the micro-ligaments and the consecutive primary atomization. Comparisons between different operating points further reveal that FB atomization may not be achieved if the gas momentum is below a certain threshold value. • Flow structures developed during flow-blurring atomization are analyzed numerically. • Lagrangian coherent structures were extracted from two phase simulations. • Cases cover different gas to liquid ratios, h/d ratios and 4 different nozzle designs. • h/d ratio or GLR alone was not sufficient enough to categorize atomization process. • The transition between flow regimes is correlated with gas velocity at the interface. [ABSTRACT FROM AUTHOR]

Phenomena involving bubble flow play a significant role in numerous industrial, natural, and scientific systems. Thus, liquid–gas interfaces must be considered the influence of surface tension and buoyancy. This work analyzes a complete numerical study for bi-fluid flow problems in the deformation evolution of two bubbles coalescing in a viscous liquid. This study discusses diverse configurations of the coalescence bubbles process and their effect on the displacement of the center of mass, velocity, streamlines, and evolution of the morphologies' deformation. The resulting simulations revealed the process of the coalescence bubbles regarding three stages: approaching, drainage, and rupture of the interface. These steps reach different morphologies, defined as oblate ellipsoid, prolate ellipsoid, and ellipsoidal cap shapes between the trailing, leading, and merging bubbles. Likewise, an approximated bi-phase 2D methodology using the Navier–Stokes equations with Smoothed Particle Hydrodynamics (SPH) method and associated with the Continuous Surface Force (CSF) method was employed to approach the interaction between the bubbles, the surrounding liquid, and cavity walls. This approach with SPH and CSF for fused bubbles and their liquid interaction are validated employing numerical benchmarks in situations with high and moderate regimes of the Reynolds (Re) and Eötvös (Eo) numbers, and different sizes of diameter between coalescence bubbles. Correspondingly, examples of bubbles merging around a liquid owing to gravitational are rarely treated in the literature of mesh-free methods, especially to characterize different viscosity, density and surface tension regimes at the bubble–liquid interface, the effect of the method precision (distance between particles, Δ x), the size of the surrounding liquid cavity and the initial distance between lighter domains. According to the bubbles deformation, during the coalescence is observed significant influence of Δ x resolution and the cavity size, there are instances of instabilities, such as lateral tails, droplets inside the lighter domain, break-up, and satellite bubble formation. Finally, it is provided a robust numerical study of the coalescence process with a bi-phase SPH for different surfaces tension regimes (5 ≤ Eo ≤ 200), viscosity and density ratios (5 ≤ λ,Φ ≤ 100) and initial conditions in merging bubbles problems with moderates Reynolds numbers (5 ≤ Re ≤ 50). • The coalescence phenomena of co-axial bubbles via SPH and continuous surface force. • Investigation of liquid film drainage and interface rupture in bubbles merging. • Study of initial set-up and sidewall effects in the bubble coalescence process. • Bubbles merging stages for several surface tension regimes can be well simulated. [ABSTRACT FROM AUTHOR]

In Continuum Surface Force (CSF) model for implementing surface tension forces in multiphase flows, singular delta function is used to merge two continuous sets of flow equations. Discretizing the delta function has attracted a great deal of attention and has led to developing many different approaches. It has been shown numerically that two identical mathematical operators: Dirac delta function ( δ ) and the gradient of Heaviside function (∇H), lead to two different numerical solutions, and surprisingly the latter is the recommended method. Mathematically speaking, one would expect using the exact delta function prone to less numerical error. We explain the mathematical and mechanical reasons on why using the exact delta function leads to the reported numerical errors. [ABSTRACT FROM AUTHOR]

The phenomenon of capillary rise or imbibition is governed by the inertia, the capillary force, the gravitational force and viscous force of fluids. Besides, the geometry also plays an important role on the imbibition dynamics since the motion of contact line could be affected by the sharp transition of geometry, and the oscillation of meniscus could be observed due to the confinement of contact line. The imbibition is a multiphase flow problem, which involves the movement of contact line and differences of fluid density and viscosity. In this paper, an axisymmetric lattice Boltzmann (LB) model based on the phase-field theory is proposed for investigating the oscillation phenomenon in the imbibition process. We also introduce a dimensionless Weber number to further analyze the pinning and depinning of contact line at the edge of capillary tube, and consider the effects of tube length and contact angle. The process of liquid spreading onto the top surface of capillary tube is presented, and several distinct phenomena are observed: depinning up and depinning down, pinning up and depinning down, pinning up and pinning down, pinning below the top edge. These transitions among different phenomena are dependent on the Weber number, which indicates the relative importance of inertial force compared to the surface tension force. [Display omitted] • Propose an axisymmetric lattice Boltzmann model for pinning and depinning phenomena. • Present several distinct phenomena of pinning and depinning for the contact line. • Obtain the critical Weber number for pinning/depinning transition. [ABSTRACT FROM AUTHOR]

In this work a new two-phase solver is presented and described, with a particular interest in the solution of highly elastic flows of viscoelastic fluids. The proposed code is based on a combination of classical Volume-of-Fluid and Continuum Surface Force methods, along with a generic kernel-conformation tensor transformation to represent the rheological characteristics of the (multi)-fluid phases. Benchmark test problems are solved in order to assess the numerical accuracy of distinct levels of physical complexities, such as the interface representation, the influence of advection schemes, the influence of surface tension and the role of fluid rheology. In order to demonstrate the new features and capabilities of the solver in simulating of complex fluids in transient regime, we have performed a set of simulations for the problem of a rotating rod inserted into a container with a viscoelastic fluid, known as the Weissenberg or Rod-Climbingeffect. Firstly, our results are compared with numerical and experimental data from the literature for low angular velocities. Secondly, we have presented results obtained for high angular velocities (high elasticity) using the Oldroyd-B model which displayed very elevated climbing heights. Furthermore, above a critical value for the angular velocity, it was observed the onset of elastic instabilities driven by the combination of elastic stresses, interfacial curvature and secondary flows, that to the authors best knowledge, were not yet reported in the literature. [ABSTRACT FROM AUTHOR]

• Dynamic relation between the liquid/gas interface, pressure and velocity profile has been investigated. • Physics of capillary wave generation in liquid filament has been analyzed. • Satellite drop generation depends on the acceleration and distribution of the axial velocity at the cone-filament junction. • Satellite drop is less likely to be formed at high inlet velocity and low surface tension coefficient. Dynamics of primary and satellite drop formation has wide engineering applications. Drop formation from a vertical capillary tube in air goes through various stages that include necking, bifurcation, recoil, wave generation and secondary necking and bifurcation. In this study, the problem has been studied numerically where the free surface of the pendant drop is tracked by a coupled level set and volume-of-fluid method with the surface tension force determined by the continuum surface force model. The evolution of the complete droplet separation process has been simulated. The numerical results have been compared with published experimental data. The mechanism for the recoiling of the liquid filament after droplet detachment and the subsequent formation of a satellite droplet has been studied and dynamic correlation among liquid/gas interface topology, velocity and pressure field has been investigated. Bell shaped distribution of axial velocity profile and fast acceleration at the cone-filament junction has been found to lead to satellite drop generation. Parametric studies on the effects of inlet velocity, surface tension coefficient and viscosity have been performed. Satellite droplet is less likely to be formed at high inlet velocity and low surface tension coefficient. Viscosity, on the other hand, has been found to play an important role on the shape of liquid filament and satellite droplet. These findings can help better understanding of drop-on-demand liquid dispensing, inkjet printing, spray combustion and many more engineering applications. [ABSTRACT FROM AUTHOR]

• The micro droplet impact on a structured superhydrophobic surface is simulated with VOF model. • Characteristics of both Cassie and Wenzel impact regimes are discussed. • The Laplace pressure of the droplet promotes the impalement transition in the Cassie impact regime. • The surface adhesion of the Wenzel impact regime decreases with the intrinsic contact angle. • The height of the micro pillar also significantly influences the impact result. In this work, the volume-of-fluid (VOF) model is applied to numerically study the micro droplet impact on the structured superhydrophobic surface with a large range of impact velocity. The droplet impact processes of both Cassie and Wenzel regimes are obtained and discussed. The influences of the intrinsic contact angle and pillar height on the impact are also studied in the simulation. The simulation results show that, due to the small diameter of the micro droplet, the effect of the Laplace pressure on the droplet impinging cannot be neglected, which could facilitate the impalement transition in the Cassie impact regime. The surface with a larger intrinsic contact angle can not only reduce the penetrate depth of the Cassie impact, but also significantly reduce the adhesion force of the surface in the Wenzel impact regime. When the intrinsic contact angle is large, the droplet can rebound even in the Wenzel impact regime. The height of the pillar also influences the bouncing ability of the droplet in the Wenzel regime. A shorter pillar is beneficial for droplet bouncing in the Wenzel impact regime while it is bad for maintaining the Cassie regime. These results can be used as a reference in understanding the mechanism of high-speed supercool droplet impact on anti-icing superhydrophobic surface and designing highly efficient anti-icing surfaces. [ABSTRACT FROM AUTHOR]

• A steady cone-jet occurs in a greater range of liquid flow rates for a hemispherical capillary. • Varicose and whipping regimes are easily obtained with a hemispherical nozzle. • The transition from varicose and whipping usually depends on interfacial forces on the jet. • A general parameter to determine varicose, transition, and whipping regimes is presented. A cone-jet regime in electrohydrodynamic atomization (EHDA) is widely applied into printing, electro-spinning, spray-coating, and biological mass spectrometry. Regulating different instabilities of jet is crucial for optimizing its operating parameters. In present work, an atypical, hemispherical capillary with inner diameter of 0.40 mm and cap size of 6.20 mm was employed as atomization nozzle, through which a steady cone-jet regime was confirmed versus suitable feeding liquid flow rate and electric potential. A permanent and highly charged jet emits from a Taylor cone apex and further disintegrates into fine highly charged drops in the form of varicose or whipping instabilities. The results indicate that a steady cone-jet is observed in the specific ranges of the feeding liquid flow rate, electric potential and conductivity. The typical breakup instabilities including varicose and whipping are clearly observed with an increase in liquid flow rate for a fixed electric potential for most of liquids, and the transition from varicose to whipping instability easily occurs. For a steady cone-jet, the jet breakup instabilities usually depends on the competition between interfacial forces on the electrified jet. The transition process involving a low-viscosity jet with a large flow rate is observed, and the general parameter G = Γ 2 δ μ 0.52 is calculated to account for surface charge, surface tension, and viscosity effects, where Γ is the electric force to surface tension ratio and δ μ is the inertia to viscous force ratio. Finally, the varicose, transition regime, and whipping are classified with first and second critical threshold values G = 40 and G = 102, respectively. Meanwhile, as the electrified jet transforms from varicose to whipping instabilities, the jet breakup length shows a trend of increasing first and then decreasing. [ABSTRACT FROM AUTHOR]

Highlights: [•] Convolution of surface force, density and viscosity is assessed. [•] Convolution of density and viscosity improves results. [•] Equal treatment of density and viscosity is critical for large density ratios. [•] Convolution of surface force reduces accuracy and does not effect numerical stability. [Copyright &y& Elsevier]

A new scheme is proposed for the approximation of the curvature field in the context of two-phase flows. Direct computation of the curvature from the volume fraction distribution produces so-called spurious currents, which are numerical non-physical velocities especially in the vicinity of the interface. The proposed method computes the curvature from the signed distance function. We have implemented the method inside Open FOAM® framework (an open source C++ toolbox for computational fluid dynamics simulations based on finite volume discretization). The surface tension force has been formulated into the sharp surface force (SSF). The implementation is applicable for general mesh topologies (two or three dimensional polyhedra). Different validation test cases have been performed; static air bubble in water, droplet undergoing linear shear, rising bubble into viscous fluid, and the impact of a viscous droplet on a thin cylindrical fiber. The proposed method shows an accurate calculation of the curvature and a significant reduction of spurious currents by several orders of magnitude. Such reduction of spurious currents allows accurate simulations of surface tension dominated flows such as micro-droplets, or liquid–liquid separation. • A new scheme for the computation of curvature field is proposed. • The magnitude of spurious currents is reduced by several orders. • Validations with published data for free surface and contact line dynamics is performed. [ABSTRACT FROM AUTHOR]

• The homogeneous mixture model is efficient because of reducing the number of governing equations for multi-phase simulation. • The analysis is performed by applying the preconditioning scheme, Noble-Abel Stiffened Gas (NASG). • The higher-order reconstruction schemes (MLP, THINC) are implemented. • Various compressible multi-phase flows at all Mach number are simulated and verified. • The numerical scheme is both accurate and stable for all speed ranges of multi-phase flows. The homogeneous mixture model with noble-abel stiffened-gas (NASG) equation of state is applied to solve the numerical simulation of compressible multi-phase flows. The gravity and surface tension forces are included, and a preconditioning scheme is used to improve the convergence of the low speed. In this study, oscillations of an elliptical drop were used to verify that the surface tension force and the sharp-interface-method works well without a numerical dissipation. These results were a success in that they were only about 1% differ from the analytic results. The dam-break problem to check unsteady and complex water surface tracking is comparable with the experimental data. The rising bubble with surface tension, viscous, and gravity effect is solved, and the bubble deformation and its evolution are comparable with the previous researchers. Air-Helium shock-bubble interaction and the underwater explosion problem for validation of a high-speed regime compared reasonably well with the experimental Schlieren results. The mixing and heat transfer between liquid and gas were analyzed during their interaction process. [ABSTRACT FROM AUTHOR]

• A novel technique called Rayleigh-Taylor instability induced atomization is proposed to destabilize the annular liquid sheet. • The experimental results from this study provide a satisfactory scaling relation with the theoretical model. • We believe that the proposed atomization technique can create a new avenue for the distinct classes of atomizers. A new atomization method to destabilize an annular liquid sheet ejected from a gas turbine engine injector, called the Rayleigh-Taylor instability induced atomization (RTA) is proposed. In contrast to the traditional coaxial atomizers, a liquid is allowed to flow through an annular passage in the axial direction and air is allowed to impinge on the liquid sheet in the radial direction. Due to this interaction, the liquid sheet exhibits a radial acceleration that induces the azimuthal instability and forms a ligament via azimuthal modes. Experimentally, we investigated the atomizer performance using a high-speed imaging technique by varying the Bond number. Here, Bond number (B o) is defined by the competition between the radial acceleration force and the surface tension force. We observed that the number of ligaments (N) formed from the liquid sheet is a strong function of B o and found that N ∼ B o . The experimental results agree well with the theoretical model and the proposed scaling is valid in the limit of Weber number ≤ 3.14. Here, Weber number represents the ratio of inertial force in axial direction to the surface tension force. RTA achieves a novel method of ligament formation and it can create a new avenue for the distinct classes of atomizers. [ABSTRACT FROM AUTHOR]

• Scaling of lift reversal of deformed bubbles is discussed. • Bubbles are in the surface tension and inertial force dominant regime. • A role of interfacial vorticity in lift scaling is discussed. • A lift coefficient correlation is proposed. Scaling of the lift reversal for a deformed bubble in the surface tension-inertial force dominant regime was discussed. Lift data of bubbles in water recently reported in literature were used. The negative lift component was well correlated in terms of the drag coefficient, which, in turn, implies that the vorticity produced at the bubble surface plays a key role in both drag and lift forces as is the case with the viscous force dominant regime. The scaling was confirmed to give good evaluations of the lift coefficients. [ABSTRACT FROM AUTHOR]

• A generalized conservative phase field-lattice Boltzmann model is proposed for N-phase flows. • The conservative phase field equations are reformulated using the gradient flow method. • family of continuous surface tension force formulations is given. • An analytical solution for spreading of liquid lenses with four phases is derived. In this paper a generalized conservative phase field-lattice Boltzmann model is proposed for immiscible incompressible flows with any number of components. In this phase field model, the each phase field variable satisfies a generalized eikonal equation and the volume fraction constraint. By introducing a quadratic functional, the dynamics of phase field variables can be treated as a gradient flow method. The phase field equations are reformulated based on the mass conservative law and the reduction-consistency conditions. Moreover, based on the generalized free energy functional, a family of generalized continuous surface tension force formulations is deduced by using the virtual work method. A lattice Boltzmann model (LBM) is developed to solve the generalized conservative phase field equations and the hydrodynamics equations. In the numerical simulation section, the motion of circular interfaces and Poiseuille flow with four phases are simulated first. The convergence rate and reduction-consistent of present model for the phase field equations are validated. The computational accuracy of present model for the hydrodynamics equations is also validated. Then serval two-dimensional (2D) examples with pairwise surface tension effect, including the droplets immersed in another fluid with four fluid phases, spreading of liquid lenses and spinodal decomposition with four fluid phases, are simulated. The obtained numerical results are in good agreement with the analytical solutions. Four continuous surface tension force formulations are also comparative studied. Finally, as a practical application, a three-dimensional (3D) bubble rising in a three-layer liquid is investigated. [ABSTRACT FROM AUTHOR]

• Focused on the effect of contact angle and liquid velocity on the behavior of liqud film and the development of flooding waves using the VOF method. • An analytical force model is proposed to study the effect of contact angle on the onset of flooding including the shear force. • The histograms of the forces at various contact angles and liquid velocities are investigated for the mechanism of the onset of flooding. • The results of the numerical simulation provide ideas for the data divergence of different flooding correlations. The purpose of the present study is to investigate the characteristics of interfacial waves on flooding phenomena in an inclined pipe. The effects of liquid velocity and contact angle on the waves at the onset of flooding are studied with a two-dimensional computational fluid dynamic model. Flooding in a 30° inclined pipe is observed by using the Volume of Fluid (VOF) method. It is found when the contact angle is equal to 120°, the pipe wall cannot form a uniform liquid film and the gas velocity required on the onset of flooding decreases as the contact angle and liquid velocity increase. For a detailed understanding of the effects of contact angle and liquid velocity, an analytical forces model is proposed on the flooding waves, including gravity F gw , the pressure of the gas core F pc , pressure variations in the liquid film F pl , wall shear force F ws , interfacial shear force F ss and surface tension force F σ. Through the quantitative calculation of all forces, it is found that the amplitude and length of the flooding wave increase with liquid velocity. As the contact angle increases, the crests become sharper. Further, through analyzing the histogram distribution of the forces, the increase of the contact angle will change the mechanism of flooding from carrying droplets to rising waves. It provides a theoretical basis for the development of mechanistic models to predict the onset of flooding in the future. [ABSTRACT FROM AUTHOR]

• Gas momentum strongly influences the mechanism of bubble formation at micro-orifices. • Bubble formation at micro-orifices cannot be described by quasi-static force balance. • Ratio of bubble base expansion decreases by increasing the size of orifice. • The bubble in-rush phenomenon is inherent to micro-orifices. Fine gas dispersion into a liquid is requested in a number of industrial applications. One way to achieve fine gas dispersion is to downsize the openings from which gas bubbles are generated. Accordingly, we have investigated the dynamics of bubble formation from submerged orifices ranging from 0.04 to 0.8 mm at a comprehensive range of gas flow rates for a system of air and deionized water. In this range of orifice size, we observe a different mechanism of bubble formation compared with millimeter-range orifices. We discuss the observations on the basis of temporal change of the bubble shape, bubble base expansion, and detachment criteria. At submillimeter orifices, the mechanism of bubble formation is highly influenced by the capillary pressure and the gas kinetic energy. The latter results in congregation of small bubbles in the vicinity of the orifice, even at very small gas flow rates. Moreover, we studied the evolution of individual forces applied to the surface of bubbles during their formation. We have found that the formation of bubbles at submillimeter orifices cannot be described with a quasi-static force balance. Finally, we present a bubbling regime map using relevant dimensionless numbers. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• High resolution, quantitative liquid thickness measurements for engineering flows. • Fuel inertia/surface tension force balance defines fuel behaviour at prefilmer tip. • Upstream aerodynamic/hydrodynamic boundary conditions linked to primary atomisation. • Invariance in primary atomization statistics with gas pressure. This work describes an experimental study of the fuel flows on the prefilmer of an aerospace gas turbine airblast atomiser at elevated pressure. The work identifies the physics leading to contradictory findings within the literature. This concerns an important atomisation boundary condition, whether the thickness of the fuel film on the prefilming surface influences the downstream drop size distribution. Analysis of the experimental data shows that fuel film thickness becomes uncorrelated with the downstream drop size if surface tension forces dominate inertia at the prefilmer tip. Fuel film thickness however provides the initial length scale for primary atomization if fuel inertia exceeds surface tension forces. It is the high inertial conditions that are associated with gas turbine operation, but the low inertial conditions that are readily achievable at laboratory scale through momentum flux scaling. Additionally, a detailed statistical description of the fuel flow has been provided for the atomiser tested. This reveals the importance of upstream hydrodynamic and aerodynamic boundary conditions on the probability of a ligament forming. Surprisingly, operating pressure is shown to have limited effect on the probability of ligament formation, a significant advantage for future modelling of the primary atomization processes. [ABSTRACT FROM AUTHOR]

The effect of the surface viscoelasticity on the drainage of the film between two gently colliding fluid particles is studied. The interfaces bounding the thin film are treated as deformable ones, which follow the surface analogous of the Upper Convected Maxwell model. The presence of the elastic forces on the interface is found to delay the viscous response of the interface, i.e., the interface behaves as inviscid for a certain duration before recovering the Newtonian behavior. The duration of this delay scales with the magnitude of the surface Weissenberg number, whereas the surface viscous forces determine the time at which the deviation from the inviscid behavior begins. This delay also indicates a shift in the tangential mobility of the interface with time during the drainage, as the inviscid and the Newtonian interfaces' are the most mobile and the least mobile cases, respectively. Consequently, the coalescence time and behavior show a similar shift, yielding cases where the coalescence time estimated for the viscoelastic interface is significantly different than both the ones for the inviscid and the Newtonian interfaces. [ABSTRACT FROM AUTHOR]

• A new model for the calculation of the critical velocity of dislodgment of a droplet is derived. • This model consider the case of a permeating oil droplet in crossflow filtration. • The forces contributing to torque balance of the droplet for the critical configuration are identified. • Comprehensive verifications of the developed model have been conducted using CFD analysis. • Very good match has been obtained which builds confidence in the modeling approach. In this work, a new model is introduced to determine the crossflow velocity required to dislodge permeating oil droplets at the surface of a membrane. Oil droplets at the surface of a membrane face either of four fates; namely, pinning, permeation, rejection, or breakup. The conditions at which the first three fates are realized have been, to a large extent, satisfactorily explored. The conditions for the breakup, however, do not seem to be very well defined. Although there exist few attempts to define conditions for breakup by crossflow field, they seem insufficient and lack consistency with the physics. It is, therefore, the aim of this work to provide elaborate analysis based on a clear understanding of the physics involved and the forces contributing to the breakup. A mathematical formula is developed to estimate that critical crossflow velocity at which break up occurs. This formula is derived based on the balance of torques that are generated by the interplaying forces. These forces are essentially surface tension forces and drag force. When the droplet encounters a pore opening it forms an interface and if the pressure across the opening is larger than the entry pressure, the interface advances inside the pore. When the receding interface of the droplet reaches the pore opening, the droplet pauses and anchors itself by that portion of the droplet in the pore. The droplet then continues to deform in accordance with the interplay of the imposed drag force and the generated surface force. The droplet wraps around the pore opening and the central angle of encounter increases per the imposed drag force. When the central angle of encounter reaches π radians, this represents the critical configuration beyond which the droplet breaks down to two parts. As the droplet deforms while anchored in its place, the contact line around the pore opening uncover the surface and starts to contribute towards the torque about the pivoting point. The balance of torques generated by the drag force and the interfacial force at that portion of the contact line, which makes a central angle of π radians, is used to determine that critical velocity beyond which the droplet breaks up. Several verification exercises are conducted using computational fluid dynamics (CFD) analysis to build confidence in the derived formula of the critical crossflow velocity. Based on the comparisons, the newly derived formula compares very well with the data obtained using CFD analysis. [ABSTRACT FROM AUTHOR]

• A theoretical model of liquid sheet considering effects of surface pro/hydrophobicity was established. • Method of controlling volume (CV) was applied to obtain the sheet characteristics. • The effect of surface pro/hydrophobicity is considered in energy conservation equation to determine the sheet velocity. • Theoretical model can well predict the liquid sheet shape at the azimuth angles between 0∘ and 150∘. The collision process between a Newtonian liquid jet and pro/hydrophobic surfaces was investigated in this paper. Based on the theory of impinging-jets, a theoretical model of liquid sheet was established which comprehensively considered the effects of pro/hydrophobicity on surface tension force and the energy loss during the entire impinging process. The sheet parameters such as the size, velocity and thickness distribution were obtained. In order to validate the theoretical model, a corresponding experimental set-up has been developed, using deionized water as experimental working medium and 3 different pro/hydrophobic surfaces as experimental parts. The comparisons showed the theoretical results are in good agreement with the experimental data. In addition, the influence of surface pro/hydrophobicity on the sheet characteristics was theoretically discussed, and the results showed the surface pro/hydrophobicity could significantly affect the size of liquid sheet on solid surface. [ABSTRACT FROM AUTHOR]

• Important role of surface tension force in bubble growth and pinch-off. • A moving contact line at the nozzle wall affects substantially the size of bubble and detachment time. • The surface tension force is important while buoyancy force is negligible. • A moving contact line yields bigger bubbles. The role of surface tension in the mechanism of bubble growth and detachment for a co-flowing air-water two-phase flow in a micro-tube is addressed. A numerical investigation for a horizontal axisymmetric flow with the assumption of zero gravity and an upward flow accounting for gravity contribution is carried out. The continuous liquid phase is flowing in a tube of 500 μm inner diameter and the gas phase is axially injected through a nozzle of 110 μm inner diameter and 210 μm outer diameter. A single-fluid model is used to determine the flow field, solving the continuity and momentum equations associated with the volume of fluid method for interface tracking. An open source software, OpenFOAM, is utilized for solving numerically this problem. The prediction results show that the surface tension plays a double role. First, it keeps the bubble attached to the injection nozzle during bubble growth and neck formation. Then, it destabilizes the interface by pinching off the neck in the immediate vicinity of the nozzle at about a distance of 0.5 the nozzle diameter rather than right at the nozzle exit. In-depth analysis of the mechanism of bubble formation induced by the effect of surface tension is carried out. It is highlighted that this latter acts as an attachment force at the injection nozzle during the bubble growth and it acts over the entire interface of the bubble yielding the formation of a neck. Later, the capillary effects reduce the diameter of the neck until it breaks and yields the detachment of the bubble. Further investigation at the nozzle wall allows depicting the motion of the contact line during the process of bubble growth and its significant effect on the bubble formation. [ABSTRACT FROM AUTHOR]

• One measure in the new formulation is that the mean interface curvature is calculated using the surface divergence of the unit normal instead of the divergence used in the previous formulations. This measure completely removes errors stemming from interior particles due to numerical discretization. • Another measure is that the size of the particle interaction domain is determined based on the physical characteristic length, rather than taken as a fixed multiple of the particle spacing, as in the previous formulations. This treatment is motivated by the knowledge of the nature of the fractional dimensionality of the interface/curve, for which the macroscopic characteristics of the measured value are dependent on the measure scale. • The new formulation is tested and verified using three numerical cases. It is shown that the new formulation is robust and accurate in calculating the surface tension, and meanwhile, it is able to adapt to different situations. In this paper, a new formulation based on the continuum surface force model (CSF) is developed for particle methods. In the new formulation, two measures are taken to amend the two drawbacks faced by previous formulations of the CSF model. One measure is that the interface curvature is calculated using the surface divergence of the unit normal instead of the divergence as done in previous formulations. This measure completely removes errors artificially stemming from interior particles that are caused by numerical discretization. Another measure taken is that the size of the particle interaction domain is determined based on the physical characteristic length, rather than taken as a fixed multiple of the particle spacing, as in previous formulations. This treatment is based on the knowledge of the nature of the fractional dimensionality of the surface/curve, for which the measured values of macroscopic characteristics are dependent on the measurement scale. Through the curvature calculation of a unit circle, the relation between the size of the particle interaction domain and the critical size of droplet/bubble breakup is established. The former, which is taken as approximately 0.38 times the latter, is accurate enough to obtain a reasonable interface curvature, even with severe irregularity. The new formulation is tested and verified using three numerical cases, including the oscillation and decay of a square drop under surface tension, the coalescence of two drops after a head-on collision, and the Rayleigh-Taylor instability. It is shown that the new formulation is robust and accurate in calculating the surface tension and is able to adapt to different situations. [ABSTRACT FROM AUTHOR]