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The phase field method (PFM) has emerged as a powerful tool for simulating multiphase flows. With its solid theoretical foundation, this method offers significant potential for further development and application. However, in many cases, interface dispersion can lead to inaccuracies in surface tension calculations, especially when dealing with large density ratio simulations. In this paper, we introduce an optimized PFM that includes profile-corrected, velocity-corrected, and flux-corrected techniques, along with a re-initialization step used in level set method. This method improves the performance of combined PFM corrections through neural networks and optimizes it via the re-initialization process. The present optimized PFM is first tested using the Rayleigh–Taylor instability, and then its performance is evaluated in the context of bubble rising, bubble merging, and falling droplet onto a liquid film. The results obtained show that the proposed method can effectively prevent interface dispersion in complex multiphase flows and capture the tiny interfacial structures. [ABSTRACT FROM AUTHOR]

The goal of this numerical study is to get insight into singular solutions of the two-dimensional (2D) Euler equations for nonsmooth initial data, in particular for vortex sheets. To this end, high resolution computations of vortex layers in two-dimensional incompressible Euler flows are performed using the characteristic mapping method (CMM). This semi-Lagrangian method evolves the flow map using the gradient-augmented level set method. The semigroup structure of the flow map allows its decomposition into submaps (each over a finite time interval), and thus, the precision can be controlled by choosing appropriate remapping times. Composing the flow map yields exponential resolution in linear time, a unique feature of CMM, and thus, fine-scale flow structures can be resolved in great detail. Here, the roll-up process of vortex layers is studied varying the thickness of the layer showing its impact on the growth of palinstrophy and possible blow up of absolute vorticity. The curvature of the vortex sheet shows a singular-like behavior. The self-similar structure of the vortex core is investigated in the vanishing thickness limit. Conclusions on the presence of posssible singularities of two-dimensional Euler equations for nonsmooth initial data are drawn by tracking them in the complex plane. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid numerical method for simulating the boiling heat transfer in particle-laden fluids. The coupled volume of fluid and level set method, immersed boundary method, and discrete element method are integrated for gas–liquid flow, fluid–solid interaction, and the collision between particles. The energy jump model is adopted to compute mass transfer during phase change. The height-function technique and improved continuum surface force (CSF) model are coupled to decrease the spurious currents. Multiple validation results are provided to test the effectiveness of all sub-models. The test cases include particle sedimentation, stationary droplets without gravity, bubble rise, droplet spreading on particle surfaces, and bubble growth. The test results are in good agreement with analytical results and previous studies. Notably, the average spurious velocity is reduced to less than 10−5 m/s, which is three orders of magnitude smaller than that obtained by traditional CSF model. Moreover, the hybrid method is employed to explore the boiling heat transfer of particle-laden fluids, thereby further validating its reliability. It was found that particles facilitate bubble detachment and enhance heat transfer. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic (EHD) printing enables large-area, ultra-high-resolution manufacturing across a broad range of ink viscosities, but inevitably encounters difficulties when printing on electrically insulating three-dimensional substrates due to unpredictable electric field and surface residual charges. To overcome these obstacles, a novel approach called plasma-induced electrohydrodynamic (PiE) printing has been proposed. PiE printing employs plasma to directly create a controllable local charge region directly on substrate surfaces, which triggers EHD ink ejection and mitigates the effect of residual charges. However, the underlying mechanisms of the jetting behavior with respect to printing parameters, such as the charge-induced electric field, remain unexplored. Here, we conduct a numerical investigation, based on the Taylor–Melcher leaky dielectric model and the level set method, on the jetting behavior of substrate surface charge-induced EHD printing. We first introduce the dynamics behavior throughout the entire printing process. Then, we carry out a comprehensive investigation on surface charge-induced EHD printing under four crucial parameters: the amount of preset surface charge, the radius of preset surface charge, the duration of preset surface charge, and liquid electrical conductivity. By analyzing the induced electric field, induced charge density, fluid velocity, jet diameters, and deposited droplet sizes obtained from the numerical results, we elucidate the influence of these parameters on the dynamic behavior, durations of jetting process, and printing quality. These findings offer valuable insights into surface charge-induced EHD jetting, advancing the understanding and optimization methods for this useful micro-/nano-manufacturing technology. [ABSTRACT FROM AUTHOR]

In this paper, we propose an anti-diffusion method to effectively prevent flotsams (non-physical tiny droplets and bubbles) and/or diffusion of the VOF (volume of fluid) function that occur in CLSVOF (coupled level set and volume of fluid), VOF (volume of fluid), and THINC (tangent of hyperbola for interface capturing) methods. In the proposed method, VOF functions that are not 1 or 0 and exist at a certain distance from the interface are identified as flotsams and/or diffusion ( C a d ), and these VOF functions ( C a d ) are moved to the transition region around the interface, where the VOF value is between 0 and 1, using a conservative advection method to prevent flotsams and/or diffusion. Additionally, the proposed method allows for some control over the position to which C a d is moved within the transition region. As a result of applying the proposed anti-diffusion method to various benchmark tests and droplet problems, it was found that the proposed method effectively suppresses flotsams and/or diffusion while ensuring conservation. In some cases, the anti-diffusion method even improves interface capture accuracy. Furthermore, investigating the impact of the position to which C a d is moved revealed that when handling C a d occurring on the gas side (liquid side), moving C a d as far as possible from the gas side (liquid side) increases the effectiveness of flotsams suppression. [ABSTRACT FROM AUTHOR]

Tight oil reservoirs require fracturing techniques to create complex fracture networks for efficient development. It is frequently accompanied by a dynamic matrix-fracture imbibition process, promoting enhanced recovery. At present, the mechanism of three dimensions (3D) matrix-fracture dynamic imbibition at the pore scale has not been fully elucidated. In this paper, the dynamic imbibition process of oil-water two phases in matrix-fracture was simulated based on the Navier–Stokes equations, and the level set method was used to capture the real-time interfacial changes between the two phases. It was found that during matrix-fracture dynamic imbibition process, oil-phase droplets in a single pore remain in the pore mainly due to the "stuck" effect. Cluster residual oil in the pore space is mainly retained due to the "flow around" effect. Continuous residual oil in the deeper regions of the matrix is due to insufficient capillary force. Water phase in the micro-confinement space of a tight reservoir intrudes into the pore space along the pore corners, forming the "fingering" phenomenon is beneficial for enhancing the efficiency of micro-dynamic imbibition. It differs from cognition obtained in the micro-view space during conventional water flooding. The enhancement of imbibition efficiency is often accompanied by the occurrence of fluctuations in the average pressure within the matrix. Therefore, a method involving impulse type of high-frequency and short-period for supplemental energy and imbibition is suggested to enhance recovery in tight sandstone reservoirs. This study reveals the detailed mechanisms of oil-water two-phase transport at different stages in the dynamic imbibition process and holds significant guiding implications for enhancing recovery in this type of reservoirs. [ABSTRACT FROM AUTHOR]

In this paper, we study numerically the motion of a pair of double-emulsion (DE) droplets in a two-dimensionally singly constricted capillary tube. The momentum and continuity equations are solved using the finite element method, and the interface is tracked via the level set method. The influence of interfacial tension, viscosity and density ratios, droplet size, pore throat size, and geometrical shape on the droplets' local extra pressure drop and instantaneous velocities are calculated. It is found that at higher interfacial tension, DE droplets are difficult to deform and lead to coalescence at the constriction throat. At low interfacial tension, droplets do not coalesce and can be easily deformed. Higher interfacial tension gives a larger pressure drop and reduces fluid flow mobility. More viscous oil drops pass through the constriction without coalescence and create larger pressure drops. Changing the inner drop size does not result in oil drop coalescence. However, the local pressure drop elevates as the inner water drop size decreases and vice versa. Small pores reduce the droplet and fluid flow mobility. Among the geometrical shape effects, the rectangular shape is more responsible for larger local pressure drop. [ABSTRACT FROM AUTHOR]

This study investigates the production of ferrofluid droplets in a T-junction geometry using the level set method and magnetic force manipulation in the three-dimensional. The analysis reveals key insights into droplet formation processes in four stages: entering, blocking, necking, and detachment. The results show that increasing the Capillary number leads to a significant decrease in volume for non-ferrofluid droplets. Application of a magnetic force enhances the balance of forces during droplet formation, directly impacting droplet volume. Moreover, increasing the magnetic Bond number substantially increases droplet volume, with a more pronounced effect at lower Capillary numbers. Modifying magnetic properties influences droplet volume, with doubling the magnetization results in a significant volume increase. Overall, magnetic forces emerge as a crucial control parameter for droplet volume in ferrofluid systems, offering potential applications in droplet-based technologies and microfluidic devices. [ABSTRACT FROM AUTHOR]

Gravity plays a crucial role in influencing bubble behavior and heat transfer in flow boiling, and its impact can vary significantly in aerospace settings. Therefore, this study aims to numerically investigate flow boiling heat transfer in a rectangular mini-channel under hyper-gravity conditions, specifically at 12 times the normal gravity. To accomplish this, a coupled volume-of-fluid and level set method is employed, taking into account fluid-solid conjugated heat transfer as well as a nucleus site density model derived from experimental data. By reproducing the flow pattern and heat transfer characteristics under different heat flux and flow rate conditions, the study unveils the effects of hyper-gravity on flow boiling heat transfer. When the flow rate is lower under hyper-gravity conditions, a notable phenomenon occurs wherein numerous bubbles detach from the heating wall and coalesce into a vapor film at the top of the mini-channel due to increased buoyancy. In contrast, under normal gravity, bubbles merge and slide on the heating wall, leading to the formation of a dry patch below. Consequently, hyper-gravity results in a lower wall superheat, and the disparity in average wall superheat between normal and high gravities escalates as the added heat flux rises. Notably, in the hyper-gravity environment, the frequent detachment of bubbles in the middle and downstream sections of the mini-channel leads to an initial increase in wall superheating, followed by a plateau along the flow direction. As the flow rate increases, the inertial force intensifies. However, intriguingly, the discrepancy in flow boiling heat transfer between normal and high gravities does not exhibit a monotonic decrease with the increasing flow rate. This behavior can be attributed to the pressing of more bubbles onto the heating wall under normal gravity, resulting in the formation of dry patches at high velocities. [ABSTRACT FROM AUTHOR]

The interface tends to behave as a circular shape under the effect of surface tension in the two-dimensional two-phase fluid flow. In this study, based on the coupled volume-of-fluid and level set (VOSET) method, an accurate circle-based interface reconstruction (CIR) algorithm for structured meshes is proposed, which features a straightforward implementation procedure. A portion of the standard circle is employed to approximate the curve interface, without the need for complex classification, coordinate transformation, and equation transformation. The radius of this circle is computed simply by the curvature and signed distance at the mixed cell center, and the center of this circle is determined using a straightforward dichotomy method under the mass conservation constraints. Results indicate that the coupled VOSET and CIR (VOSET-CIR) method maintains superior computational accuracy in the signed distance, interface curvature, and dynamic interface reconstruction compared to the coupled VOSET and piecewise linear interface calculation (VOSET-PLIC) method, with accuracy improvements ranging from 34% to 1490% across different test cases. Furthermore, the VOSET-CIR method outperforms the efficient least squares volume-of-fluid interface reconstruction (ELVIRA) and PLIC algorithms in reconstructing random circles and surpasses the quadratic spline based interface reconstruction (QUASI) algorithm in reconstructing random squares. In terms of computational efficiency, except for the initial PLIC algorithm, the time costs of the VOSET-CIR method are substantially lower than those of the ELVIRA and QUASI algorithms, as well as the VOSET-PLIC method. [ABSTRACT FROM AUTHOR]

Directional transportation of droplets plays a crucial role in the fields of anti-fog, anti-icing, material transportation, and several other applications. Herein, the total directional transport of droplets on a surface with controllable wettability was numerically investigated by the level set method coupled with the volume of fluid method. The accuracy of the numerical simulation results was validated via high-speed photography experiments. The directional migration and morphological evolution mechanisms of droplets impacting on the superhydrophobic–hydrophobic interface were revealed. Moreover, the effects of the impacting position on the directional migration velocity, rebound height, and transport distance of droplets were systematically analyzed. Theoretical models were derived for predicting the transport distance and rebound height of droplets. The simulation results reveal that, for a droplet impacting on the superhydrophobic and hydrophobic interface, four stages exist, i.e., spreading, contraction, rebound, and directional migration, which differ from those for a droplet impacting on a normal surface. It is thus deduced that the adhesion length is a significant factor that affects the directional migration parameters. Moreover, there exists an optimal adhesion length for the impacting droplet, under which the transport distance can be maximized. The maximum transport distance of the droplet under the optimal adhesion length is 12 mm. Furthermore, the values predicted by using the theoretical models agree well with the actual ones, proving the feasibility of the prediction models. The results contribute to the fundamental theory of droplet directional migration and are valuable for related engineering applications. [ABSTRACT FROM AUTHOR]

The study is focused on the numerical simulation of the boundary slip of a water-in-oil (W/O) emulsion along an oleophilic surface in a 2D axisymmetric formulation of the Navier–Stokes equations for an incompressible laminar flow. Drops of emulsions with a volume fraction of the dispersed phase of 0.04–0.34 collide with a smooth glass wall at initial velocities of 1.2–3.6 m/s; the motion of the interface between the liquid and gas phases is resolved by the level set method. The influence of the wall wettability by oily liquids is demonstrated by varying the static contact angle up to 0.5° and by considering the dynamic one as a function of the empirically measured contact line velocity of the liquid drop according to Tanner's law. Numerical simulation of emulsion drop spreading dynamics reveals that the boundary slip of a heterogeneous liquid along a smooth oleophilic wall is different from that of a homogeneous. The temporal changes in the average viscous stress allowed the illustration of the interrelated effects of emulsion viscosity and the presence of disperse phase particles on the boundary slip of a heterogeneous liquid and its motion in the viscous boundary layer. The analytical expression evaluating the slip length for an arbitrary W/O emulsion was derived using the effective properties of the liquid. In testing the expression, the values of the maximum spreading factor of drops of an arbitrary W/O emulsion predicted by numerical simulation correspond to those determined from experiments at a moderate error of 7.4%. [ABSTRACT FROM AUTHOR]

In this research, we have developed a computational method for droplet sorting using a non-uniform electric field. The method is based on a three-dimensional level-set method and the leaky-dielectric electrohydrodynamics (EHD) model. Level-set method is used for modeling the interface of the two-phase flow system. The electrostatic phenomenon is dealt with the leaky dielectric-leaky dielectric fluid system. At first, we validated our developed model for a classical flow case: a droplet subjected to a uniform electric field. The results obtained from the present computational method show good agreement with the existing results from the literature. After validation, we implemented the developed code in a practical application of droplet sorting using a non-uniform electric field (known as dielectrophoresis) in a rectangular microchannel with an orthogonal side channel. We mainly focus on the sorting of the droplet without and with the electric field effect as a function of different parameters of the problem. Depending on the intensity of the physical parameters, the droplet can flow into either the downstream main channel or it can sort into the orthogonal side branch. The sorting of a droplet is characterized by the critical branch ratio, qc above which the droplet enters the side branch. The results and conclusions from the present thesis facilitate the understanding of the fundamental principles and mechanisms of electrohydrodynamics (EHD)-based droplet sorting using dielectrophoresis in microfluidic channels. Therefore, present results can have potential usefulness toward the design and development of droplet-based microfluidic devices. [ABSTRACT FROM AUTHOR]

Heat transfer on a vapor bubble rising in superheated liquid is investigated by direct numerical simulation. The vapor–liquid system is described by the one-fluid formulation with the level set method capturing the interface. The proportional-integral-derivative controller is employed to keep the bubble's location fixed and evaluate interfacial forces. The heat transfer performance featured by the Nusselt number is evaluated based on the energy balance. Simulations are carried out for the bubble Reynolds number ranging from 20 to 500 and Morton number from 1.10 × 10−10 to 3.80 × 10−4. The aim of this paper is to shed some light on the effect of bubble deformation and oscillation on interfacial heat transfer. The results show that the front part of the bubble contributes to the majority of the interfacial heat transfer, while the rear part mainly affects the oscillation amplitude of the total heat transfer. The interface stretch during bubble oscillation is considered as a key mechanism in enhancing the instantaneous Nusselt number. The potential flow solution of the averaged Nusselt number is corrected by considering the influence of the aspect ratio. This research provides additional insights into the mechanism of interfacial heat transfer, and the results apply equally to interfacial mass transfer. [ABSTRACT FROM AUTHOR]

Under a low flow rate, gravity may become prominent for bubble behavior and heat transfer of flowing boiling because of the weakness of drag force from liquid, and its effect changes with the inclination angle of the mini-channel but without consensus. In this paper, based on a reasonable nucleus site density model and considering conjugate heat transfer, the coupled volume-of-fluid and level set method is adopted to study the subcooled flow boiling in an inclined three-dimensional rectangular mini-channel (0°–180°) with a characteristic size of 1.0 mm at a low flow rate of 88.8 kg m−2 s−1. The inclination angle is found to have a slight effect on the flow boiling, which is different from the conclusion drawn based on the traditional-macro channel. A bubbly flow appears when a heat flux of 300 kW/m2 is added. An unconventional impact force is proposed, which presses large bubbles to slip along the heating wall, with slight differences in the flow pattern under different inclination angles. When the inclination angle is close to 0°, the upstream small/medium bubbles leave the heating wall under gravitational effects, which is conducive to heat transfer. As the inclination angle approaches 90°, gravity pushes the large bubbles downstream to leave the channel, favoring the rewetting of the dry patches below. These two positive effects fail as the inclination angle approaches 180°, leading to slightly worse overall heat exchange efficiency. However, the maximum differences in the average and local wall superheating of the mini-channel are only 8.4% and 22.5%, respectively, across the range of inclination angles because the flow pattern remains similar under the effect of the impact force. In addition, the effect of inclination angle on flow boiling becomes weaker with the increase in heat flux because of happening of slug flow. [ABSTRACT FROM AUTHOR]

The head-on-collision coalescence dynamics for droplets on surfaces with different wettabilities was numerically investigated by using the method of coupled level set and volume of fluid, and a high-speed video experiment was used to validate the simulation results. The simulated coalescence behavior of droplets is consistent with the experiment results. We compared droplets with different Weber numbers (3.67 ≤ We ≤ 50) coalescing on solid surfaces of different wettabilities and contact angles (80° ≤ α ≤ 160°). The result is a regional division diagram that relates Weber number and contact angle based on different coalescence phenomena. The factors causing droplet deposition, air entrapment, bounce, and partial bounce during collision coalescence are described based on an analysis of interactions involving inertial forces, surface tension, and wall adhesion forces. Furthermore, the effect of Weber number and contact angle on droplet coalescence behavior is elaborated by analyzing the relationship between coalescence time and wettability radius under different Weber numbers and contact angles. Finally, through an energy analysis, we explain the maximum spreading radius and oscillation of droplets with different Weber numbers on solid surfaces with different wettabilities and in the process of head-on-collision coalescence. [ABSTRACT FROM AUTHOR]

The present work investigates the deformation and acceleration of water droplets in continuous airflow. The numerical approach is based on the level set method for capturing the liquid–gas interface and the projection method for solving the three-dimensional incompressible Navier–Stokes equations. The effects of the incoming airflow velocity (10–100 m/s), initial droplet diameter (20–100 μ m), and supercooling on water droplet deformation are investigated. The results indicate that the droplet enters the breakup regime at a critical Weber number of 10, which agrees with the published literature. A dimensionless deformation factor L is defined to describe the droplet deformation. The results confirm that the extreme values of L increase with increasing Weber number during droplet movement. Two models are proposed to predict the minimum deformation factor and the corresponding dimensionless time. The effect of supercooling on water droplet deformation is analyzed, and it is found that the deformation factor of supercooled droplets is lower than that of room-temperature droplets, while supercooled water droplets exhibit greater acceleration. Furthermore, based on the numerical results, a model governed by the Weber number and the Ohnesorge number is proposed for predicting droplet acceleration. [ABSTRACT FROM AUTHOR]

This work focuses on three-dimensional simulation of the dynamics of droplets with contact-angle hysteresis. In order to consistently model the dynamics of the contact line, a combination of the linear molecular kinetic theory and the hydrodynamic theory is implemented in the present numerical method. Without presetting the contact line and/or the contact angle, such simulations are generally prone to irregularities at the contact line, which are mainly due to the imposition of the pinning and unpinning mechanisms associated with the hysteresis phenomenon. An effective treatment for this issue is proposed based on a simple procedure for calculating the nodal contact angle within the framework of enriched finite element/level set method. The resulting method also benefits from a manipulated momentum conservation equation that incorporates the effect of the liquid mass conservation correction, which is essentially important for simulations with a rather long (physical) run-time. In this paper, the proposed numerical model is validated against the previously published experimental data addressing the configuration of a water droplet on a tilted rough hydrophobic surface. In this test, the effect of the contact-line pinning as the underlying mechanism for droplet hysteresis phenomenon is also studied. The model is further employed to simulate a liquid droplet confined in a channel in the presence of air flow. [ABSTRACT FROM AUTHOR]

Submarine massive sediment movement, which may devastate submarine infrastructure and cause huge waves threatening the coastal areas, combined with the air–water interface is a significant issue of the multiphase flows in the areas of ocean engineering and geoscience. Currently, simulating rheology-based sediment flows is still a challenge because of the complex intergranular dynamics and its coupling with computational fluid dynamics. In particular, air–water–sediment multiphase models that can simulate such rheology-based flows while also taking into account the accurate capture of the air–water interface have not been developed yet. Coupling with the coupled level set method and volume of fluid method in the air–water two-phase flow, this study develops two new Eulerian–Eulerian multiphase models for simulating the rheology-based sediment flows. The difference between the two developed models is that how to model the drag force of the particle–fluid interactions. To demonstrate their capabilities, the two developed models are employed to simulate the gravitational collapse of submarine sediment column in air–water flow with loose-packing case and dense-packing case. The results of collapse process, induced air–water interface fluctuation, and contractancy/diltancy behavior are all agree well with those in previous experiments and simulations. In addition, comparing the results of two developed models, it can be concluded that different modeling methods of the drag force not only directly affect the water–sediment interactions, but also indirectly influence the air–water interface fluctuations and the intergranular stresses remarkably. [ABSTRACT FROM AUTHOR]

Microfluidic systems are an interesting topic for investigation due to their wide-spreading applications. Nowadays, polymeric solutions are used mainly for the generation of microparticles in biomedical engineering, food, and pharmaceutical industries. Droplet-based microfluidic devices have proposed an extensive interest in many applications such as chemical/biological/nanomaterial preparation to understand deeply the droplet size and formation in microchannels. However, numerous experimental and numerical studies have been done for oil–water combination, polymeric solutions behavior in the presence of oil has not been investigated widely. Therefore, it is important to understand the droplet formation mechanisms in a microfluidic device for both water and polymeric solutions to determine the flow regime mapping in order to control the characteristic of the produced droplets. Also, in many studies, the length of the droplets as a parameter to investigate the droplet size was studied. In this study, droplet generation in the T-shaped microfluidic junction with an enlarged horizontal outlet channel was studied to have opportunity to determine the diameter of spherical droplets. The water and the alginate 1% (w/v) solutions were used separately as a dispersed phase, and the mineral oil was used as the continuous phase in which the solution's flow rates were varied over a wide range. To perform numerical simulations of the droplet formation, a two-phase level set method was used which is a suitable method for the investigation and simulation of immiscible fluids. The flow regime mapping for the two different aqueous solutions was obtained. Furthermore, the influences of flow rates on droplet size, droplet generation frequency was quantified. In this study, flow regime, droplet size, and droplet frequency were studied. In general, flow rates of the oil and aqueous fluids readily control five main flow regimes including backflow, laminar flow, dripping flow, squeezing flow, jetting flow, and fluctuated flow. It was observed that generated droplets with alginate solution as dispersed phase were more in the region of the jetting flow regime while water droplets were more in the region of the dripping flow regime, this can be due to the difference in characteristics of polymeric solution and water. For both aqueous phases, larger droplets were obtained when flow rates of oil were decreased and aqueous phases were increased. Also, the frequency of droplet generation increases and decreases by increasing oil phase flow rate and increasing aqueous phase flow rate, respectively. In the same flow rates of aqueous phase and oil, the sizes of water droplets are larger than the alginate droplets and also water has a higher frequency of droplet generation compared to alginate. Finally, we characterized all the obtained data for flow regimes due to the capillary number (Ca) of the continuous phase. The findings of this study can help for better understanding of the detailed process of droplet generation of water and alginate solution as dispersed phase separately with mineral oil as the continuous phase in a T-junction geometry microfluidic and know the effect of characteristics of solutions as a dispersed flow in flow regimes. [ABSTRACT FROM AUTHOR]

The impact of microscale water droplets onto a solid superhydrophobic surface is numerically investigated. The multiphase problems are modeled by the three-dimensional incompressible Navier–Stokes equations and the liquid–gas interface is captured by the level set method. The numerical model is verified with our experimental impact results via the comparison of spreading factor ξ , which is defined as the ratio of the wetted surface area to droplet initial diameter. The simulation results suggest that when the droplet impacts with constant impact velocity and diameter, the maximum spreading parameter increases with the ambient temperature. As Weber and Reynolds numbers increase, the impact turns into doughnut-breakup regime; the droplet breaks up into a toroidal shape and a cavity is formed at the center. The results indicate that the diameter of the central cavity grows linearly related to the non-dimensional time. Finally, a new droplet impact spread/splash model that is governed by Weber and Reynolds numbers is proposed for superhydrophobic surface based on our numerical and experimental results. [ABSTRACT FROM AUTHOR]

In order to study the mechanism of ice formation after water droplets produced by splashing waves attach to ship superstructure in cold ocean regions, a numerical framework that considers the effect of supercooling degree on the meso-scale water droplet freezing is developed to explore the freezing mechanism of water droplets after impacting. This model can track the solid–liquid and air–liquid interface together using a coupled volume-of-fluid and level set multiphase method and Enthalpy-Porosity phase change method. The model introduces a mixed fraction to describe the problem of three-phase unification. The simulation results of the center freezing height and droplet spreading factor in this paper are consistent with the experimental results in related literature, which verifies the accuracy of the framework. The study includes a detailed description of the dynamic and thermodynamics mechanism of the water droplet. The influence factors of droplet impacting and freezing process are analyzed. The analysis results show that the surface wettability, supercooling degree, and impact velocity have a great influence on the freezing behavior of droplets. This model can deepen the understanding of icing mechanism on ship superstructure surface, provide an indication for engineers to develop an accurate prediction method of ice accretion on ship superstructure surface. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive coupled volume-of-fluid and level set (VOSET) method based on unstructured grids to simulate incompressible interfacial flows. In this study, a novel high quality refinement algorithm for unstructured grid cells based on level set and surface curvature is first developed to ensure a preset bandwidth of the adaptive region around the interface. Subsequently, the adaptive VOSET algorithm is integrated into a finite volume solver with a large-scale sparse matrix preconditioned bi-stable conjugate method. Finally, the accuracy and robustness of the current method are validated by four classical test cases: the dam break, single bubble rising, a Rayleigh–Taylor instability problem, and a liquid jet problem. It is found that the adaptive coupled VOSET algorithm makes the numerical results near the interface more accurate, especially the curvature and surface tension at corners. Moreover, the adaptive VOSET is more efficient since it reduces the number of grid cells significantly. The present results show that only 4.85%–24.5% of the number of adaptive grid cells and 5.31%–15.93% of the computational time are needed for VOSET compared to that of fixed unstructured grid cells, and thus, it has outstanding properties of both time and computational cost savings. [ABSTRACT FROM AUTHOR]

The breakup phenomenon of a ferrofluid droplet in a simple shear flow under a uniform magnetic field is numerically investigated in this paper. The numerical simulation, based on the finite element method, uses a level set method to capture the dynamic evolution of the droplet interface between the two phases. Focusing on small Reynolds numbers (i.e., Re ≤ 0.03), systematic numerical simulations are carried out to analyze the effects of magnetic field strength, direction, and viscosity ratio on the breakup phenomenon of the ferrofluid droplet. The results suggest that applying a magnetic field along α = 45° and 90° relative to the flow direction initiates breakup in a ferrofluid droplet at a low capillary number in the Stokes flow regime, where the droplet usually does not break up in a shear flow alone. At α = 0° and 135°, the magnetic field suppresses breakup. Also, there exists a critical magnetic bond number, Bocr, below which the droplet does not rupture, which is also dependent on the direction of the magnetic field. Additionally, the effect of the viscosity ratio on droplet breakup is examined at variable magnetic bond numbers. The results indicate a decrease in the critical magnetic bond number Bocr values for more viscous droplets. Furthermore, more satellite droplets are observed at α = 45° compared to α = 90°, not only at higher magnetic field strengths but also at larger viscosity ratios. [ABSTRACT FROM AUTHOR]

In the present work, we investigate the dynamics of a bubble, rising inside a vertical sinusoidal wavy channel. We carry out a detailed numerical investigation using a dual grid level set method coupled with a finite volume based discretization of the Navier–Stokes equation. A detailed parametric investigation is carried out to identify the fate of the bubble as a function of Reynolds number, Bond number, and the amplitude of the channel wall and represented as a regime map. At a lower Reynolds number (high viscous force), we find negligible wobbling (path instability) in the dynamics of the bubble rise accompanied only with a change in shape of the bubble. However, at a higher Reynolds number, we observe an increase in the wobbling of the bubble due to the lowered viscous effects. Conversely, at a lower Bond number, we predict a stable rise of the bubble due to higher surface tension force. However, with a gradual increase in the Bond number, we predict a periodic oscillation which further tends to instigate the instability in the dynamics. With a further increase in the Bond number, a significant reduction in instability is found unlike a higher Reynolds number with only change in the shape of the bubble. At lower values of Reynolds numbers, Bond numbers, and channel wall amplitudes, the instability is discernible; however, with an increase in the channel wall amplitude, the bubble retains integrity due to higher surface tension force. At a higher Bond number and channel wall amplitude, a multiple breakup in the form of secondary bubbles is observed. We propose a correlation which manifests the average bubble rise velocity and the fluctuating velocity (due to channel waviness) as a function of Reynolds number, Bond number, and channel wall amplitude. Finally, we conclude that the bubble dynamics pertinent to the offset channels with varying amplitudes does not remain the same as that of the symmetric channel. [ABSTRACT FROM AUTHOR]

Based on adaptive mesh refinement, the SIM (Sharp-Interface Method) is utilized to numerically study the interaction between a shock wave and a liquid column as well as the evolution of the flow field. The SIM consists of the LSM (Level Set Method) and the GFM (Ghost Fluid Method). The LSM tracks the gas-liquid interface, and the GFM generates the virtual domains near the interface based on the gas-liquid interface condition. The hybridized GFM has been developed by integrating the Riemann GFM and the modified GFM together, which ensures the accuracy of the interface Riemann problem in the small deformation region of the interface while ensuring that the large interface deformation can be processed correctly. By comparing with the experimental results and the numerical results in previous literature, the good agreement shows that the above algorithm can accurately simulate the interactions between shock waves and liquid columns along with achieving the evolutions of the sharp gas-liquid interfaces. Based on the algorithm above, the interactions between the shock waves and the inviscid, the Newtonian, and the shear-thinning liquid columns are simulated, respectively. The numerical results indicate that the viscous effect can cause the bending of the liquid column and large deformation in the high shearing region. However, the shear thinning effect alleviates the bending and the deformation of the liquid column in the high shear region. [ABSTRACT FROM AUTHOR]

We proposed the combined numerical and experimental study of the dynamics of droplets generation at shallow microfluidic T-junction, where the flow is strongly confined in the vertical direction. The numerical simulation is performed by employing quasi-2D Hele-Shaw approximation with an interface capturing procedure based on coupled Level-Set and Volume-of-Fluid methods. We investigate the effect of the capillary number, Ca, the channel geometry (cross section aspect ratio, χ), and the flow rate (disperse-to-continuous phases) ratio, Γ, on the dynamics of the droplet breakup. Depending on Ca, three distinct flow regimes are identified: squeezing, tearing and jetting. In the squeezing regime at low Ca, the size of the generated droplets depends on χ and Γ, while it is almost insensitive to Ca in agreement to previous studies. In the tearing regime at moderate Ca, the droplet size decreases as ∼Ca−1/3, while it is only a weak function of χ and Γ. Finally, in the jetting regime, the steady co-flow of both phases takes place at high enough Ca. The numerical predictions based on the Hele-Shaw flow approximation are in excellent agreement with our in-house experimental results, demonstrating that the proposed approach can be effectively used for computationally inexpensive and adequately accurate modeling of biphasic flows in shallow microfluidic devices. [ABSTRACT FROM AUTHOR]

In this paper, a modified level set method is proposed for simulation of multiphase flows with large density ratio and high Reynolds number. The present method simply introduces a source or sink term into the level set equation to compensate the mass loss or offset the mass increase. The source or sink term is derived analytically by applying the mass conservation principle with the level set equation and the continuity equation of flow field. Since only a source term is introduced, the application of the present method is as simple as the original level set method, but it can guarantee the overall mass conservation. To validate the present method, the vortex flow problem is first considered. The simulation results are compared with those from the original level set method, which demonstrates that the modified level set method has the capability of accurately capturing the interface and keeping the mass conservation. Then, the proposed method is further validated by simulating the Laplace law, the merging of two bubbles, a bubble rising with high density ratio, and Rayleigh-Taylor instability with high Reynolds number. Numerical results show that the mass is a well-conserved by the present method. [ABSTRACT FROM AUTHOR]

Using a conservative level set method we investigate the deformation behavior of isolated spherical fluid drops in a fluid channel subjected to simple shear flows, accounting the following three non-dimensional parameters: (1) degree of confinement (Wc = 2a/h, where a is the drop radius and h is the channel thickness); (2) viscosity ratio between the two fluids (λ = μd/μm, where μd is the drop viscosity and μm is the matrix viscosity); and (3) capillary number (Ca). For a givenWc, a drop steadily deforms to attain a stable geometry (Taylor number and inclination of its long axis to the shear direction) when Ca < 0.3. For Ca > 0.3, the deformation behavior turns to be unsteady, leading to oscillatory variations of both its shape and orientation with progressive shear. This kind of unsteady deformation also occurs in a condition of high viscosity ratios (λ > 2). Here we present a detailed parametric analysis of the drop geometry with increasing shear as a function of Wc, Ca, and λ. Under a threshold condition, deforming drops become unstable, resulting in their breakup into smaller droplets. We recognize three principal modes of breakup: Mode I (mid-point pinching), Mode II (edge breakup), and Mode III (homogeneous breakup). Each of these modes is shown to be most effective in the specific field defined by Ca and λ. Our study also demonstrates the role of channel confinement (Wc) in controlling the transition of Mode I to III. Finally, we discuss implications of the three modes in determining characteristic drop size distributions in multiphase flows. [ABSTRACT FROM AUTHOR]

Turbulent open-channel flow over a two-dimensional laboratory-scale dune is studied using large eddy simulation. Free-surface motion is simulated using a level set method. Two subgrid scale models, namely, dynamic Smagorinsky and dynamic two-parameter models, are employed to assess model effects on the free surface. It is found that the two models have very similar performance in predicting the free-surface turbulence. Two flow depths are simulated to investigate the effects of water depth on flow coherent structures and turbulence statistics. In the deep-water flow, experimental data are used to assess for the numerical predictions of the mean flow field and turbulence statistics. They are found to be in good agreement. In the shallow-water flow, there is strong interaction between the free-surface and large-scale vortical structures emanating from the bed, increasing turbulence intensity and free-surface disturbance. The simulations predict streaky structures in the wall layer after flow reattachment in the deep-water flow, but not in the shallow-water case, suggesting that interaction between the free surface and the flow structures is significantly affected by the flow depth. [ABSTRACT FROM AUTHOR]