Viscous Droplets Research Articles

High-temperature deposition model for molten particle prediction based on droplet-surface interaction criteria

Particle deposition in gas turbine engines damages blade surfaces and diminishes engine performance. Deposition results from heat and momentum exchanges between fluid and particles, coupled with the interactions between particles and surfaces. The increasing turbine inlet temperatures cause particles to become molten, complicating their interaction with surfaces. Existing models fail to convincingly explain the deposition behaviors of molten particles. In the present study, considering particle fluidity and the nonlinear accumulation of deposits, the deposition criteria for viscous droplets and the maximum steady deposit layer model were incorporated to establish an unsteady high-temperature deposition model. The new model, validated against experiment results in the literatures, predicts molten particle deposition behavior with an average error of 3.89 % in capture efficiency at high-temperature conditions. It accurately predicts crown-like deposit morphology and nonlinear accumulation, matching experimental observations. Applied to nozzle guide vanes with film cooling, results show that deposits primarily occur on the leading edge and pressure side near the trailing edge. The particle capture efficiency initially rises before diminishing as particle size increases, whereas an inverse trend is noted with the escalation of the mass flow ratio. At a mass flow ratio of 0.15, the capture efficiency hits the minimum of about 13.2 %.

Leidenfrost Effect-Induced Chaotic Vortex Flow for Efficient Mixing of Highly Viscous Droplets.

Efficiently mixing highly viscous liquids in microfluidic systems is appealing for green chemistry such as chemical synthesis and catalysis, but it is a long-standing challenge owing to the unfavorable diffusion kinetics. In this work, a new strategy is explored for mixing viscous droplets by harnessing a peculiar Leidenfrost state, where the substrate temperature is above the boiling point of the liquid without apparent liquid evaporation. Compared to the control experiment where the droplet stays at a similar temperature but in the contact boiling regime, the mixing time can be reduced significantly. Moreover, it is demonstrated that the liquid mixing originates from the chaotic convection flow in the Leidenfrost droplet, characterized by the internal vortex motion evidenced by the microscale visualization. A correlation between mixing time and droplet volume is also proposed, showing a good agreement with experimental results. It is further shown that Leidenfrost droplets can be used to synthesize nanoparticles of the desired morphology, and it is anticipated that this simple and scalable fabrication approach will find applications in the biological, pharmaceutical, and chemical industries.

Photophoresis of a moderately large high-viscosity droplet in slip mode

Purpose of research. To obtain analytical expressions that allow calculating the strength and velocity of a moderately large, highly viscous droplet, taking into account the direct contribution of the evaporation coefficient, linear corrections by the Knudsen number and the reactive effect of a plane wave moving in the field of mono-chromatic radiationMethods. Methods of perturbation theory, gas kinetic methods, mathematical methods for solving linear partial differential equations with variable coefficients (the system of Stokes equations, Laplace and Poisson equations) were used.Results. In a quasi-stationary approximation, a theoretical description of the photophoretic motion of a moderately large evaporating highly viscous spherical droplet (there is no circulation of matter inside the droplet and interfacial surface tension forces) in a viscous binary gas mixture is carried out. A velocity-linearized system of Navi-Stokes equations and heat and mass transfer was solved. Expressions are obtained for the fields of mass velocity, pressure, temperature and the relative numerical concentration of the first component. The strength and speed of photophoresis of a highly viscous droplet was determined by integrating a stress tensor over the surface of the particle. Under boundary conditions on the surface of a highly viscous droplet, linear corrections in terms of the Knudsen number (isothermal, thermal and diffusion slips, temperature and concentration jumps, as well as sliding due to temperature inhomogeneity along the curved surface of the particle), the reactive effect and the contribution of the direct influence of the evaporation coefficient were taken into account. The contributions to the obtained formulas for the photophoresis of a moderately large highly viscous droplet are analyzed and the preliminary transitions to the results known in the literature (moderately large and large solid particles of spherical shape) are considered Conclusion. The obtained formulas based on the hydrodynamic method allow us to evaluate the effect of the direct contribution of the evaporation coefficient and linear corrections by the Knudsen number on the strength and speed of photophoresis of a moderately large evaporating highly viscous droplet in a binary gas mixture.

A two-dimensional numerical study on the coalescence of viscous double emulsion droplets in a constricted capillary tube

A two-dimensional numerical study on the coalescence of viscous double emulsion droplets in a constricted capillary tube

Comprehensive study on collision patterns of viscous droplets impacting on a heated particle

The collision process involving droplets and heated particles has gained significant attention due to its wide industrial relevance. This study utilizes a high-speed photography to investigate the collision dynamics between viscous droplets and heated particles. The research identifies six distinct collision patterns. In the bubble-breakup mode, the particle experiences the greatest temperature drop, resulting in the most substantial heat transfer. The particle temperature plays a crucial role in determining collision behavior when the Reynolds number exceeds 100 and the Weber number exceeds 55. The maximum spreading area demonstrates a linear relationship with the Weber number, while it reaches a peak and stabilizes with Reynolds numbers in the deposition regime. Contact angle fluctuations are caused by the instability of the contact line. The liquid film thickness exhibits linear and power growth phases, followed by a rapid decrease in the bubble-breakup regime. While the branch-breakup pattern sees smaller fragmented droplet sizes, the atomization-breakup pattern sees flow velocity rise with both Reynolds and Weber numbers. The predicted wavelength of the disturbance in the atomization regime, based on Rayleigh-Taylor instability theory, aligns well with the experimental measurements. The residence time correlates positively with the Weber number.

Dynamic Behavior of Viscous Droplets Impact on a Flexible Mesh Surface.

The dynamic behavior of a viscous droplet impacting a flexible mesh surface with a fixed end is studied by high-speed photography in this work. Our experimental results reveal that surface vibration occurs when the viscous droplet impacts the flexible mesh surface. Simultaneously, the droplet spreads on the upper surface and penetrates into the mesh surface, resulting in a decrease in the spreading diameter on the upper surface. On the lower surface, the droplet elongates and forms multiple ligaments. Notably, different dynamic behaviors are observed when the droplet impacts surfaces with varying Weber (We) numbers due to viscous dissipation and surface vibration. However, as the impact position deviates from the fixed end, the surface vibrational amplitude increases, leading to a decreased diffusion range of the droplet on the lower surface. In addition, the vibration amplitude significantly enhances with increase of the We number. The vibration induces stretching and eventual rupture of the cardinal ligament under specific conditions. The first breaking time of the cardinal ligament delays with the decrease of the We number. As the impact position moves away from the fixed end, this situation is enhanced. Especially, when the stretching direction of the ligament is inconsistent with the vibration direction of the surface, the vibration has a great influence on the stretching behavior of the cardinal ligament.

Decoupling effect stimulated independent dendrite growth of eutectic phases under microgravity and containerless states

Eutectic growth process is usually characterized by the simultaneous coupled growth of two different solids within one uniform liquid phase, while fluid dynamics normally predicts the equiaxed shrinkage for floating viscous droplets on freezing. Here a decoupling effect was induced by the microgravity and containerless states aboard space station, which led to the independent dendrite growth of two eutectic phases within extremely undercooled liquid Nb-Si refractory alloy. The confronting fluid flow pattern driven by polar heterogeneous nucleation was found to stimulate the elongated surface deformation of alloy droplet at a high dendrite growth velocity.

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

Dynamics of viscous droplet coalescence in the confined geometry of optical cells.

The dynamics of quasi-two-dimensional coalescence of isotropic droplets in nematic liquid crystal environment was studied. Investigations were made in confined geometry of a Hele-Shaw optical cell with different transverse droplet sizes. The existence of three distinct dynamic regimes was found for coalescence, namely, short-, middle-, and long-time regimes. The fast dynamics of bridge transformation was visualized. At short time the dynamics of droplet transformation is similar to the transformation of free (three-dimensional) droplets. At later stages, two regimes of the coalescence at different timescales are determined by Poiseuille flow. Experimental data are discussed on the basis of existing theories.

Experimental Investigation on Dynamic Characteristics of Highly Viscous Droplets and Liquid Bridges Under the Influence of Electric Fields

Experimental Investigation on Dynamic Characteristics of Highly Viscous Droplets and Liquid Bridges Under the Influence of Electric Fields

Impact of a spherical interface on a concentrical spherical droplet

<p>In this paper, an analytical and numerical technique are examined in order to analyse the Stokes flow determination problem due to a viscous sphere droplet moving at a concentric instantaneous position inside a spherical interface separating finite and semi-infinite immiscible fluid phases. Here, when only one of the three phases of the fluid (micropolar fluid) has a microstructure, attention is focused on this case. The motion is considered when Reynolds- and capillary-numbers are low, and the droplet surface and the fluid-fluid interface have insignificant deformation. A general solution is obtained in a spherical coordinate system based on a concentric position to analyse the slow axisymmetric movement of the micropolar fluid, considering microrotation and velocity components. Boundary conditions are initially fulfilled at the fluid-fluid interface and subsequently at the droplet surface. The normalised hydrodynamic drag force applying to a moving viscous droplet appears to be a function of the droplet-to-interface radius ratio, which increases monotonically and becomes unbounded when the droplet surface touches the fluid-fluid interface. The numerical outcomes of the normalised drag force acting on the viscous droplet are derived for different values of the parameters, and are presented in a tabular and graphical framework. A comparison was made between our numerical outcomes for the drag force and the pertinent data for the special cases found in the literature.</p>

How emulsified droplets induce the bursting of suspended films of liquid mixtures.

Emulsion droplets of silicone oil (PDMS) are widely used as antifoaming agents but, in the case of non-aqueous foams, the mechanisms responsible for the bursting of the films separating the bubbles remain unclear. We consider a ternary non-aqueous liquid mixture in which PDMS-rich microdroplets are formed by spontaneous emulsification. In order to quantitatively assess the effect of the emulsified microdroplets, we measure the lifetime of sub-micrometer-thick suspended films of these emulsions as well as the time variations of their thickness profiles. We observe that a droplet entering the film reduces its lifetime by inducing a local and fast thinning. In most cases, we ascribe it to the spreading of the drop at one of the film interfaces with air, which drags the underlying liquid and eventually causes the film to burst rapidly. We explain why, despite slower spreading, more viscous droplets cause films to burst more efficiently. More rarely, microdroplets may bridge the two interfaces of the film, resulting in an even more efficient bursting of the film, which we explain.

Role of droplet viscosity on the formation of residual droplets on grooved hydrophobic surfaces

Surfaces with groove structures, such as butterfly wings and rice leaves, are frequently observed in nature, and the anisotropic nature of grooved structures is known to control fluid transport. Although the receding contact-line dynamics of the droplets on the grooved hydrophobic surfaces affect the behavior of droplets in motion, their depinning mechanism has not been sufficiently addressed in the literature. In this study, the receding contact-line dynamics of viscous droplets moving on inclined grooved hydrophobic surfaces were investigated using high-speed imaging. The droplet viscosity and surface-inclination angle were systematically varied to observe changes in the receding motion of droplets. The receding contact lines of each droplet contracted along the top of the groove structure and then ruptured due to discontinuity in the structure, leaving small volumes of droplets on top of the structure. Various morphological changes in the droplet were observed when it retracted along the grooves, which depended on the surface-inclination angle and viscosity of the droplet. A Rayleigh-like instability induced additional breakup of the tail of the droplet, resulting in satellite droplets being deposited on top of the grooves. The lateral size of the residual droplets deposited on the grooves increased as both the droplet viscosity and surface-inclination angle increased. The sizes of the residual droplets on tested surfaces collapsed into a single curve through a simple scaling equation developed by dimensionless analysis.

Numerical investigation on heat transfer and vapour layer geometry of a droplet impacting on a spherical particle in Leidenfrost regime

Understanding the heat transfer mechanism and dynamic behaviors of droplet-particle collision in Leidenfrost regime is essential for the pyrohydrolysis process of pickling liquor, which is sprayed into a fluidized bed and then decomposes to oxides and acid vapour. In this study, the droplet deformation, heat transfer characteristics and vapour layer geometry of Leidenfrost droplet impacting spherical particle are investigated by constructing a microscale phase change model in VOF framework. The applicability of the computational model in capturing droplet dynamics and thermodynamics is verified by comparing it with experimental outcomes. The results indicate that the vapour layer geometry is relatively uniform in spreading but shows instability in recoiling. The vapour layer thickness increases rapidly in both spreading and early recoiling, while decreases in the late recoiling phase. Furthermore, the heat transfer and droplet evaporation depend on the vapour layer thickness strongly. Specifically, the thinner the vapour layer, the lower the heat transfer resistance. The increasing surface temperature, We and Re can effectively enhance heat transfer and raise droplet temperature. In addition, the maximum spreading factor and liquid–solid contact time play an important role in heat transfer and they both show a clear power-law dependency on We and Re for viscous droplets. The effect of droplet size on contact time is consistent with first-order vibration theory but the contact time is independent of surface temperature and impact velocity.

Transit Time Theory for a Droplet Passing through a Slit in Pressure-Driven Low Reynolds Number Flows.

Soft objects squeezing through small apertures are crucial for many in vivo and in vitro processes. Red blood cell transit time through splenic inter-endothelial slits (IESs) plays a crucial role in blood filtration and disease progression, while droplet velocity through constrictions in microfluidic devices is important for effective manipulation and separation processes. As these transit phenomena are not well understood, we sought to establish analytical and numerical solutions of viscous droplet transit through a rectangular slit. This study extends from our former theory of a circular pore because a rectangular slit is more realistic in many physiological and engineering applications. Here, we derived the ordinary differential equations (ODEs) of a droplet passing through a slit by combining planar Poiseuille flow, the Young-Laplace equations, and modifying them to consider the lubrication layer between the droplet and the slit wall. Compared to the pore case, we used the Roscoe solution instead of the Sampson one to account for the flow entering and exiting a rectangular slit. When the surface tension and lubrication layer were negligible, we derived the closed-form solutions of transit time. When the surface tension and lubrication layer were finite, the ODEs were solved numerically to study the impact of various parameters on the transit time. With our solutions, we identified the impact of prescribed pressure drop, slit dimensions, and droplet parameters such as surface tension, viscosity, and volume on transit time. In addition, we also considered the effect of pressure drop and surface tension near critical values. For this study, critical surface tension for a given pressure drop describes the threshold droplet surface tension that prevents transit, and critical pressure for a given surface tension describes the threshold pressure drop that prevents transit. Our solutions demonstrate that there is a linear relationship between pressure and the reciprocal of the transit time (referred to as inverse transit time), as well as a linear relationship between viscosity and transit time. Additionally, when the droplet size increases with respect to the slit dimensions, there is a corresponding increase in transit time. Most notably, we emphasize the initial antagonistic effect of surface tension which resists droplet passage but at the same time decreases the lubrication layer, thus facilitating passage. Our results provide quantitative calculations for understanding cells passing through slit-like constrictions and designing droplet microfluidic experiments.

Xylan fast pyrolysis: An experimental and modelling study of particle changes and volatiles release

Biomass char particles produced by pyrolysis may have different morphologies, which has important implications on burning mode, conversion rate and boiler efficiency. These features are difficult to address due to the complexity of biomass structure and pyrolysis reaction models.The present work reports preliminary results on the morphological changes and volatile release that solid particles of Xylan experience upon fast heating in a Drop Tube Reactor (DTR) and in a Heated Strip Reactor (HSR) in a range of temperature between 1100 and 1573 K under inert atmosphere with heating rate in the order of 103 K/s. Two different Xylan samples were chosen as representative of Hemicellulose in angiosperm biomass: xylooligosaccharide extracted from Beechwood (hardwood biomass) and from Corn Cob (herbaceous biomass).During the heatup phase, Xylan particles do not retain the original shape and morphology, neither in DTR nor in HSR experiments. In the early pyrolysis stage, Xylan particles melt and form viscous droplets. As devolatilization proceeds these droplets in the DTR evolve into highly viscous sponge-like particles with spherical shape, which swell and eventually shrink, ultimately producing highly porous spherical char particles.The experimental results are compared with the predictions obtained by the Bio-CPD Xylan pyrolysis model. The model is fairly able to calculate the pyrolysis yields in the DTR, but predicts unexpectedly low extent of metaplast formation. To explain the remarkable melting phenomena and morphological changes observed in the experiments, tuning of some CPD parameters and inclusion of mass transfer and pressure build-up within the particles might be necessary in future work.

Numerical investigation of highly viscous droplet generation based on level set method

Piezo-driven needle valves are widely used in electronic packaging due to their fast response, high resolution and good dispensing consistency. However, the stable generation of high-viscosity droplets is one of the key issues to its packaging quality. To investigate the formation mechanism of the high-viscosity droplet. In this paper, a 2D finite element model of the drop-on-demand injection process of the high-viscosity droplet is established based on the level set method, the droplet formation and separation processes are numerically simulated, and the reliability of the simulation results is checked by comparing the outcomes with published data. Specifically, the detailed evolution of the high-viscosity droplet formation and separation process is gained by coupling the two-phase flow-level set method and the dynamic grid technique, and the pressure distribution in the injection chamber is further discussed and the effects of operating parameters on the droplet formation volume are examined. The results of the study show that the needle motion is the main factor of pressure fluctuations in the injection chamber. Moreover, we also found that among the parameters of needle stroke, nozzle diameter, supply pressure, fluid viscosity, and surface tension, the nozzle diameter has the most significant effect on droplet volume, while surface tension has the least effect on droplet formation.

Contact-time reduction of viscous droplets impacting a grooved superhydrophobic surface

Adding a macroscale groove structure to the superhydrophobic surface makes the water droplet to bounce in a petal shape and dramatically reduces the contact time of the water droplet. Most studies on petal bouncing have been conducted on water droplets without considering the effects of viscosity. In this study, the bouncing dynamics of glycerol/water droplets impacting a grooved hydrophobic surface were investigated by changing the viscosity and impact speed of the droplets. As the viscosity of the droplets increased, the Weber number range in which petal bouncing occurred decreased. Petal bouncing was observed in up to 50 wt. % glycerol/water droplets with a viscosity approximately six times that of water. In the low Weber number region (We < 25), as the viscosity of the droplet increased, a sufficient amount of capillary energy was not stored in the fluid penetrating the grooved structure, owing to the viscous dissipation of the fluid. In contrast, in the moderate-Weber-number region (25 < We < 40), the impact energy of the droplet became sufficiently large to overcome the viscous force of the fluid, enabling spreading and retraction along the bottom of the structure. This caused a discrepancy between the time at which the retraction of the fluid above the structure started and the time for the fluid to penetrate and empty the structure, resulting in a transition from petal bouncing to conventional rebound. The critical Weber number for petal bouncing was calculated using the energy-balance approach, and the results were similar to the experimentally observed values.

Jetting Dynamics of Viscous Droplets on Superhydrophobic Surfaces.

We investigated the dynamics of liquid jets engendered by the impact of droplets on a fractal superhydrophobic surface. Depending on the impact conditions, jets emanate from the free liquid surface with several different shapes and velocities, sometimes accompanied by droplet ejection. Experimental outcomes exhibit two different regimes: the singular jet and columnar jet. We found that droplet impacts at a lower impact velocity and low viscosity result in singular jets, attaining a maximum velocity nearly 20-fold higher than the impact velocity. The high-speed video frames reveal that the formation and subsequent collapse of the cylindrical air cavities within the droplet favor the formation of these high-speed singular jets. In contrast, the capillary wave focusing engenders columnar jets at a moderate to high impact velocity. With an increase in viscosity, singular jets are suppressed at lower impact velocities, whereas columnar jets are seen regularly. The columnar jets ascend and grow over time, feeding a bulbous mass, and subsequently the bulb separates itself from the parent jet due to capillary pinch-off phenomena. The quantitative analysis shows that columnar jets' top jet drop size varies nonmonotonically and is influenced by preceding jetting dynamics. At moderate viscosity, the drop size varies with jet velocity, following a power-law scaling. At very high viscosities, both singular and columnar jetting events are inhibited. The results are relevant to several recent technologies, including microdispensing, thermal management, and disease transmission.

Effects of a spherical slip cavity filled with micropolar fluid on a spherical viscous droplet

An analytical study for the quasisteady flow caused by a spherical viscous fluid droplet translating at a concentric position in a second immiscible micropolar fluid within a spherical cavity with a slip surface is presented. Attention is focused on the case when one of the two fluid phases has a microstructure nature (micropolar fluid). The droplet translates along a diameter connecting their centres under the conditions of low Reynolds numbers. To solve the Stokes equations for the velocity fields inside and outside the droplet, general solutions are obtained in terms of spherical coordinates based on the concentric position. For the case of the viscous droplet within a micropolar fluid, a boundary condition related to vorticity with microrotation is used. The wall correction factors acted on the viscous droplet for the different cases are represented through graphs for various values of relative viscosity, radii ratio of droplet and cavity, and the parameter that connects the vorticity with microrotation. The wall-corrected drag force is found to be a monotonically increasing function of the ratio of drop-to-cavity radii. The present work is important because of its applications in various natural, industrial, and biological processes, such as raindrop formation, the study of blood flow, liquid–liquid extraction, the prediction of atmospheric conditions, sedimentation phenomena, and the rheology of emulsions.